Notes from the Staff

Teaching Intonation

Leah Sheldon shares tips for teaching intonation, even when working with beginning students.
Chapters:
00:00 Introduction to Notes From the StaffIn this opening chapter, Leah Sheldon and Greg Ristow introduce the podcast and its focus on music theory, ear training, and music technology. They invite listeners to engage with the show by sending comments and episode suggestions.
01:06 Leah’s Background in Music EducationLeah shares her journey in music education, detailing her experience from teaching elementary general music to her current role in middle school instrumental music. She emphasizes the importance of teaching intonation at various educational levels.
02:01 Introducing IntonationThe discussion turns to the timing of introducing intonation when teaching beginners, with Leah explaining her approach to teaching it as early as possible. She highlights the need for students to produce a clear tone before focusing on intonation.
03:00 Tuner vs. EarLeah discusses the pros and cons of using tuners versus relying on the ear for intonation. She explains how both methods can be beneficial but emphasizes the importance of developing students’ listening skills.
04:57 The Importance of Ear TrainingLeah outlines her sequence for teaching students to tune themselves in an ensemble, starting with ear training. She discusses the gradual progression from simple pitch recognition to more advanced tuning techniques.
06:47 Exercises for Intonation PracticeLeah shares specific exercises to help students practice intonation, including the classic ‘F around the room’ exercise. She explains how this exercise helps students develop listening skills and blend their sounds.
10:00 The Role of Tone in TuningThe conversation shifts to the significance of tone quality in achieving good intonation. Leah explains how a clear tone is essential for blending sounds effectively within an ensemble.
12:25 Using Drones for TuningLeah introduces the concept of using drones in tuning exercises, emphasizing the importance of singing before playing. She explains how this technique helps students internalize pitch and improve their intonation.
16:56 Waterfall Tuning TechniqueLeah describes the waterfall tuning exercise, where students join in one by one to create a blended sound. This method encourages students to listen closely to their neighbors and adjust their pitches accordingly.
18:55 Chaos to Calm ExerciseLeah shares the ‘chaos to calm’ exercise, where students start by playing any note and then transition to a designated pitch. This fun exercise helps students practice tuning while also fostering ensemble cohesion.
22:02 Engaging the Whole GroupLeah introduces the ‘Who’s in Tune’ exercise, which engages the entire group in assessing intonation. This interactive activity encourages students to listen and respond to their peers’ tuning.
25:04 Understanding Tuning TendenciesLeah discusses the importance of recognizing individual tuning tendencies and how to address them. She suggests using tuning tendency charts to help students become aware of their specific intonation challenges.
30:41 Advanced Tuning TechniquesLeah shares advanced exercises for experienced players, including building chords during the ‘F around the room’ exercise. She emphasizes the importance of practicing intonation within a musical context.
Transcript
Theme SongThese are the notes from the staff where we talk about our point of view, and we share the things we're gonna do. And we hope you're learning something new, because the path to mastering theory begins with you.
Greg RistowWelcome to Notes From the Staff, a podcast from the creators of You uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
Leah SheldonHi. I'm Leah Sheldon, head of teacher engagement for uTheory.
Greg RistowAnd hi. I'm Greg Ristow, founder of uTheory and associate professor of conducting at the Oberlin Conservatory.
Leah SheldonThank you, listeners, for your comments and episode suggestions. We love to read them, so send them our way by email at notes atutheory. com. And remember to like us and subscribe wherever you get your podcasts.
Greg RistowToday, our topic is teaching intonation and leading us through this is our very own Leah Sheldon who is quite an expert herself in teaching intonation. Leah, for our listeners who may mostly know you, from uTheory, tell us about the other part of your life.
Leah SheldonSure. So I also teach middle school instrumental music. I started out over 10 years ago teaching elementary general music, kindergarten through 4th grade. I did that for 6 years before I moved into the world of instrumental music. And now my current position is 4th through 8th grade instrumental music, large and small group lessons and one ensemble.
Greg RistowAwesome. Can you teach intonation at such an early age and level?
Leah SheldonYou can always teach or fix intonation. There can there's always something that can be done, but, yeah, it looks different at different levels. That kinda leads me into the first thing I wanted to talk about, you know, do you teach intonation right from the very beginning or do you wait and introduce it a little bit later? And how do you decide that? There's a case to be made for both sides. In my experience, I try to introduce it as early as I can. With instrumental music, your students do have to be able to produce a clear tone before you can really start working on intonation.So there are some cases where maybe I wait a little bit longer to get into that. But as soon as the students are playing characteristic sounds, we start talking about it. We start addressing it right away.
Greg RistowThat's great. You know, I think this will be a this is such a good follow-up to our last episode where we talked about, tuning systems and these subtle differences between, say, equal temperament and just intonation and various other tuning systems, and I'm really excited to hear, how you, lead your students to be able to hear these things and and I may pop in and share some of my thoughts from the choral world as well.
Leah SheldonLeah. That sounds great. The other piece that comes up early on in intonation is, do you use a tuner or do you teach your students to rely on their ear? And I think there's great cases to be made either way here. When you start out using tuners right off the bat, your students have a visual. They can see if they are sharp, if they are flat. They can see how sharp or how flat and that in some ways helps them develop their Leah.But they may start to rely on the tuner and maybe not use their ear as much as they could be. Tuning by ear at first takes more time. The students need to practice it to develop that skill and get good at it. But in the long run, they'll have more independence and they will be more accurate at identifying whether they're sharp or flat and how to adjust their pitch.
Greg RistowSo way back when I was in band, which, you know, is in the 19 nineties, at the time we had one big tuner in the front of the room and that was kind of how that worked. It doesn't really look like that anymore. No.
Leah SheldonIt does not and I recommend if you are going to have your students use tuners, get a clip on tuner or like some sort of clip device that plugs into a tuner. I know Korg makes makes these or there's even like a a Peterson clip that can plug into a tuner and, Snark is another popular brand. But having the tuner clip right onto the instrument, will help the accuracy of what the tuner is hearing and showing the students.
Greg RistowAnd and then can they see even when they're playing at the same time how their own intonation is?
Leah SheldonYes. Exactly. That's how that works. And then there's probably a case for, you know, unplugging then at certain times and to be able to hear the intonation of others. But, yeah, that that gives you a lot more flexibility if you're going to use tuners.
Greg RistowMhmm. Oh, that's great.
Leah SheldonYeah. But before we even get to the the tuner piece of that, you have to start with ear training. So this is kind of my my sequence for how I I get to the point of students being able to tune themselves in an ensemble. You have to start with the ear training piece. And when you're teaching beginners, I'm talking 4th graders, sometimes that's just as simple as, is this higher, is it lower, and making it really obvious. Right? Playing on a piano, playing on an instrument, giving the students opportunities to to hear and answer out loud.This is higher, this is lower. Right? Just same or different. Then you have to teach the students how to adjust their voice or their instrument or what it is they need to be able to do. They're not gonna be able to tune until they can bring the pitch up or bring the pitch down. Once they can do that, I move on to this is where I start really letting them gain their independence. So putting on a drone and letting them tune themselves to a drone.Then from there, we we work on group tuning, and that's just like tuning with the people right around you, right next to you, tuning with your neighbors, then tuning with your section, and then finally tuning across the ensemble. So that's that's kind of my layout and that does not happen overnight. This is over the course of years.
Greg RistowNo. I can I can imagine? Right? Yeah. Yeah. I mean, just the the control of of embouchure or I I or whatever the mechanism is on the instrument to, to make fine adjustments to to pitch that takes some time to learn.
Leah SheldonAbsolutely. And I I'm not gonna go into the details of what that is for every instrument. There are lots of wonderful podcasts out there that do that just for the band directors who wanna hear that. But that that is essentially Leah students need to be able to adjust the pitch and know how they're doing it, not just, like, pushing more air and hoping on a whim that it's going the way they want it to go. So once they can really do that, then they could really start tuning on their own.
Greg RistowYeah. There's a similar series of exercises in the vocal world that, comes from Robert Shaw, where, who is an American choral conductor of the 20th century. And, he would have his whole choir sing a note that's really comfortable in everyone's range, say, like, an easy f natural, kinda middle of the voice. And over the course of 4 beats, have the entire ensemble gradually slide up a half step. The idea being that, you know, on halfway through on the 3rd beat of those 4th of those 4 beats, you would have reached a quarter tone above. And you really it's a fun it's a challenging exercise. But you start to hear the really fine innards of the half step.But more than that, you start to learn actually Leah do I have to do what am I doing physically that causes the pitch to go up or down when I sing. Singing is in some ways so, so natural that we don't necessarily think about the mechanics of it, but those kinds of exercises can help help, help us learn how to do that sort of thing.
Leah SheldonRight. And the the other thing is that the students need opportunities to do it. They need opportunities to practice. And so we, as the teachers, have to provide that. Intonation is not always something that they can do on their own at home when they're practicing.
Greg RistowThey can if they have a tuner or an in tune
Leah Sheldonpiano, but the They can if they have a tuner or an in tune piano but but to really get good at it, they need opportunities to do it and we have to provide that in the rehearsal. So I kinda have a little list of my regular go to exercises. If maybe I could take you through some of those that, get at ways to let the students practice hearing intonation.
Greg RistowThat sounds great.
Leah SheldonAlright. So for any band directors who are listening, you're gonna know this one. This is the classic f around the room. For someone who's not a band director, this is just an exercise where the students are passing a note around the ensemble. But the point is for it to sound like one continuous note. So you're gonna select a student to start and you want this to be a student who's going to play with clear tone, nice strong supported sound, really set a good model for the group. That student is gonna hold the note for 4 beats all the way to the downbeat of 1 of the next beat. Right? We're not cutting anything short.We don't want any gaps in the sound. The next student then picks up that note and carries it. So if, for example, we're playing concert f, that's a great starting place for this exercise. So first student plays concert f, holds it for 4 beats. The next student comes in, plays it, hold it for 4 beats, and so on. And the point is to match to fit into the sound of the person before you. And you can do this one at a time or you can do this by sections.But I generally start with low sounds. 1st, start with your tuba and work your way up. I find that that this when this it teaches the students to listen down. It also helps the the higher pitched instruments to fit into the sound, into the tone of a a lower pitched instrument versus the other way around.
Greg RistowOh, that's great. And that would also work for singers as well.I don't know. I've never thought to do that. How wonderful.
Leah SheldonAnd you you can do it like I said, you can do it with individuals. You can do it with sections. You can also do it with or without a tuner Ristow your 1st student off with a tuner and then everybody else by ear. So you can really make this work for wherever your ensemble is or whatever it is you wanna work on with them blending in the section or tuning without a tuner. This is that's a wonderful way to do it. It does take a little bit of time if you have a large ensemble, But every time a student plays, the rest of the students in that group get an opportunity to hear whether it is sharp, flat, or in tune.So it's great for everyone.
Greg RistowThat's great. You mentioned when you start this off, you mentioned, starting with a student who has a nice clear tone. Can you talk about the role of tone in tuning?
Leah SheldonYeah. So, a student who plays with an airy sound or a fuzzy sound, even if their pitch is right on, it is going to be really hard to blend that sound even just with 2 students. You're not gonna achieve that that classic one blended sound if one sound is airy and fuzzy or buzzy or standing out in some way.It's going to happen. We all have students that don't play with that clear tone especially with the beginners at first yet. So sometimes it's sort of a give or take. It's okay, we're we're gonna do this even though maybe these handful of kids aren't quite there yet but that also gives them an opportunity to hear, oh, that's what I should sound like or or oh, I don't sound that way, but if I, you know, firm my corners up, they're like like so and so always tells me to do and then, oh, I it works, you know. So, again, playing one at a time, it gives students opportunities to hear what they should or shouldn't do.
Greg RistowThat's great. And and the physics behind that, maybe it's just worth mentioning that, you know, when we when we talk about a a fuzzy sound or an airy sound, what we're saying is that there's more there's more noise, there's more out of tune overtones to the sound, rather than than, just primarily the the tuned overtones of the instrument, which is what makes it harder to tune to.
Leah SheldonExactly. Exactly. And if your students are ready for that, tell them that. Explain that to them. And and if they're beginners, maybe don't go there just yet, but
Greg RistowRight. Yeah. Excellent. F around the room.I love it. What's next?
Leah SheldonNext, this is just the drone. I don't even say anything. I just put the drone on and the students know what's going to happen.
Greg RistowDo you tell them what note it's on?
Leah SheldonOh, yes. Of course.But, generally, we're always tuning to the almost always tuning to the same pitch in our ensemble, and I would imagine that, you know, in any other ensemble, you you kinda build your routines and your students know. Right?
Greg RistowMhmm.
Leah SheldonSo you turn the drone on, tell them remind them which pitch they're playing. And then I have them sing it before they play anything. You need to sing or for those instrumentalists who are really resistant to using their vocal chords. Sing it or it first and then play. Again, this can be done individually if you have the time for that. It can be done one section at a time. It can be done with the whole group.It can be done with just your first chairs first and then the whole group. But, again, the point is giving the students opportunities to hear. If they're going one at a time or if you have a smaller group playing first, then the rest of those sitting in the ensemble can hear whether it's in tune or not and how they're adjusting it and bringing it into tune.
Greg RistowAnd what is what is the role of singing in that process? What does that do that if you skip singing, you miss?
Leah SheldonSinging centers the the pitch for the students. Honestly, it's just something that I do because it helps. When I don't do it, the students do not play as Intune at first. It helps them hear it. It helps them internalize it. And then when they play on their instrument, they can hear a lot faster if they are above or below the drone if they've just sung it and internalized it.
Greg RistowMhmm.
Leah SheldonRemind the students that when they're playing with the drone, that their sound should disappear when they are playing the same pitch. That's okay. A lot of times, beginners at first, you know, the first time we do this or the first time they're really truly playing in tune with someone, they say, I can't hear myself or my instrument stopped working. And we say, no, it's working fine. That's what you want. We're looking for that. You're fitting into the sound.
Greg RistowWe have the same thing that happens in singing a lot and, that when, you know, when you're singing with someone else, it's a very different experience from if you're singing by yourself. And there's a psychoacoustic effect that's called the Lombard effect. And this is this is, something that happens anytime you're in an environment where it's noisy or loud. We when it becomes harder for us to hear our own voice, we naturally speak louder and louder. So think about a restaurant, maybe you show up early for dinner, there aren't that many people there and gradually more people show up. You gradually speak more and more loudly. And it's a very natural thing that if we can't hear our own voice, we we work to compensate that.And so when you're doing this kind of exercise with drones, which is equally great for singing, it's sometimes worth reminding singers exactly as you said that it's okay to to to let your sound disappear into this, to sing at a really comfortable dynamic. And one trick I like sometimes to use is to say, if you can't hear your own voice, just bring a hand up to your ear and sort of cup it forward, and then you'll suddenly just hear your own voice a little bit more in that mix.
Leah SheldonOh, yeah. That's really great, to be able to use your ear. Of course, we can't do that with our hands as instrumentalists, but I never thought of that.
Greg RistowYou've got you've got your hands busy.
Leah SheldonYeah. Yeah. And a lot and along with that, another great exercise to do with the drone is to to play Remington's, if you have a more intermediate or advanced ensemble, because if you start on the notes, say, were concert f, right, and then you play up or down a half step probably, you know, and then return.
Greg RistowCan you can you just demonstrate Remington really quickly so
Leah Sheldonwe can Yeah. So we're let's let's say we're starting on concert f. Right? And we're starting on Oh, then we're down a half step then back up. So so working down.
Greg RistowSo you're basically going down a diatonic scale.
Leah SheldonExactly. Or or chromatically, however your group is gonna do it. But every time you return to that starting pitch, your sound should should disappear into the sound of the drone. Mhmm.
Greg RistowIt's sort
Leah Sheldonof like a magical thing that happens every time you move notes, you hear, you know, the sound you've it feels different and then it disappears again. It's a very once your ensemble does it well, it's a really, cool effect.
Greg RistowMhmm. Nice. Okay. So we've had we've got Efra in the room. We've got the drone. What's next?
Leah SheldonOkay. So I call this waterfall tuning.I don't know why. It just started that way at a previous district where I taught. The students knew what it meant, but so this is what it is. You just have one student start first and you just add on right down the line. So one student plays, generally, that student is looking at a tuner. Once that student is in tune, they glance over at the student next to them and then that student joins in but the first student keeps playing. Once their sound is in tune or blended then the next one.So all the way down the row. At first, I find I have to cue the students, like, when the next one should come in, when the first two are in tune or when the first three are in 3 and then cue the next one. Eventually, they'll be able to do that on their own. And, again, you can do this with individuals. You can do this with sections. You could do just first chairs first, then the, you know, then down the line for every Sheldon, however it works for your group.
Greg RistowGreat. Great. Okay. Waterfall tuning. Yeah. Awesome.
Leah SheldonOkay. So then I this next one, I just call it in and out. It's just if we're if we've got something that's out of tune, we we're playing a chord, it's out of tune. Right? We fix it, we tune it. I have them play it in tune. I tell them purposely, let's go out of tune.Let's all let's all go sharp or let's all go flat, right, on a cue. And then on my second cue, bring it back in tune. It gives them an opportunity to feel to, like, to learn to feel, oh, that's what was wrong with it.That's when it was wrong. This is how we fix it when we get here.
Greg RistowThat's great. What a wonderful what a wonderful experience too of of making it okay to do it wrong so that you so that you have that so that you know the difference in how they feel.
Leah SheldonAbsolutely. And and that kinda goes along with when you're teaching the students how to raise and lower pitch on their instrument. You have to let them do it wrong too. Okay. Let's all do let's, you know, bring it up too high, bring it down too low. That's part of it. They have to be able to know what wrong is to identify it and fix it.
Greg RistowThat's great. That's great.
Leah SheldonYeah. So that's just a simple quick one, right when you're in the middle of rehearsal, something's out of tune. Ristow, fix it, play it out of tune, bring it back in tune. Easy fix. Move on.
Greg RistowExcellent.
Leah SheldonGoing along with that one, chaos to calm. Mhmm. This is this is what I usually generally do, like, at the beginning of a rehearsal after we've warmed up after we've tuned. We get you know, everybody's in tune, warmed up, playing with nice warm tone. I tell them they may pick any note, any note that they can play comfortably on their instrument and play with nice sounds, so no blasting trumpets. And then that's what they're gonna play and hold on the first note, and I just cue them and we hold it for a good little while, at least 4 beats. Then on the second cue, we all go to a given pitch.Let's say concert b flat. We're all gonna go to a concert b flat. The first couple times you do this, that b flat is not going to be in tune and it's gonna take a little while to settle in. But the more you do it, the more quickly it will settle in. And then once once your students can go from this chaotic sound to Leah nice in tune concert b flat or concert f, then you can start working on balance. Right? Okay. Let's also balance this while we're here.And then you can start tuning to chords as well instead of just all going to a concert b flat, like, let's go to this chord and tell each group what pitch they're gonna play and what they're gonna land on. But, it's an opportunity for them to listen and make adjustments as quickly as possible. And they think it's fun. They think it is so fun to play have the whole ensemble playing whatever note they choose. And just to be clear, everybody's playing a different note.
Greg RistowRight. Right. I love I love the name too, chaos to calm.
Leah SheldonYeah. As soon as you say chaos
Greg RistowThat's great.
Leah SheldonThey know it's coming. Right?
Greg RistowYeah. Yep. I I've done this exercise a lot with choirs. Although typically, you know, we'll pick a note, we'll call it do. And I'll say, now pick any soul any other solfege and you you sing your own. And then on the second cue, we all come back to do. Typically, you know, a choir is gonna pick solfege within the major scale, so you wind up with sort of a pan diatonic thing, which is really beautiful.But also but that's great. I'm gonna try this without even saying that. Just say, okay, let's all sing Lou. And then on a cue, pick any other note so it can be pure chaos because I think that must be great that the crazy chromaticism of what is that? And for singers, especially to do that, to pick any other note and also hold on to the sound of the note we started on in the context of all that chaos is a great exercise.
Leah SheldonYes. I should have said that.Generally, the chaos to the to calm the calm notes, the concert b flat is gonna be what we use to tune to. So if you tune to concert f, make concert f your resolution note.
Greg RistowMhmm. Nice. Nice. Cool. What's next?
Leah SheldonOkay. So I just call this who's in tune, and this is a way to engage your whole group. Again, I have to think about the percussionists who are, you know, not necessarily tuning in the same way that the ensemble is, but they also need to develop that ear. They do have times where they need to be able to tune, such as tuning the timpani. So this is a great way to engage everybody in the group. You have one student or one section just play at a time, generally with a drone so that the group can hear whether the student is in tune or not. And then just simply have the rest of the group show whether they're in tune.If they're sharp, they're pointing up. If they're flat, they're pointing down. And if they're in tune, they're just holding their hand out straight and flat to show that there are no waves. They are in tune.Quick side story. When I first did this, I used to have them do thumbs up for sharp, thumbs down for flat, and we realized very quickly that was confusing because sometimes students interpreted the thumbs up as it's good. Move on. Oh, of course. So, of course, now I have them point up for Sheldon Town for Flat. But, yeah, the everybody in the group has to listen and answer.
Greg RistowThat's great. And I love, you know, you you as you mentioned, do this with the drone. Right? That that these things keep tying back to having something to listen to, and and that relates so much constantly. Right? When we're actually making music with other with other people, we're making compromises to adjust to each other's sound. And so, you know, so with with that constant listening element, whether it's a drone or the person who's just played right before you, you're really building those ear skills throughout.
Leah SheldonYeah. And I think that's something that's harder to do if you are just simply using tuners. Again, your ensemble is gonna sound great, and your students are getting that visual reinforcement. But then they're not gonna be as independent in making those adjustments by ear. Another thing is sometimes students will say, oh, well, I I just tuned to a tuner, and it said I was good there, but now I don't sound good in the group. And, you know, that's where we bring up the conversation of tuning can be relative, like you were just mentioning that we have to adjust to what's going on around us. You also lose that with the tuners sometimes.So, letting the students truly hear what's happening and may maybe for example, we're, playing something that's got a very prominent xylophone part, and maybe your xylophone is a little bit older and is just a bit flat. And you've gotta if if the xylophone is playing a part that matches the oboe and the flute, then the woodwinds have to tune to the xylophone in that case.
Greg RistowMhmm. Yep. Which is not an easy instrument to tune to.
Leah SheldonNo. Especially if it's been dropped out of flight of stairs and rebuilt a couple of times and held together by rubber bands. Yeah. Right.
Greg RistowYeah. I mean, to begin with, the overtones on a woodblock instrument are all over the spectrum and then yeah. It's like my nightmare. Change to a xylophone as a singer. Right?
Leah SheldonYeah. But it happens.
Greg RistowYeah. Yeah. For sure.
Leah SheldonThe last thing that I that I can offer, if if you don't have time to be doing these tuning exercises in your ensemble all the time, which I beg you, please make time. But, something that you can do then to make up for that or you can do in addition to our tuning tendency charts. I do these twice a year. We do them at some point in the fall, pretty near the beginning of the year, and then again in the spring because students grow and change as players and their tuning tendencies may change. So basically, I I give students a chart that has all the acceptable notes in the range based on the level that they play at, and I tell them take this home or go in a practice room and play every note. It like a long tone, not short. Right? Hold it out and see where that note is on your instrument.Does the tuner say that it's sharp, flat, or in tune? And mark that on the chart. It helps the students know before they even get to a note that what they Greg gonna need to do to help it be in tune immediately.
Greg RistowThat's great. That's great. I I've never thought of doing this with singers, but, I mean, certainly I know, you know, in my own voice, the parts of my range where I tend to push sharp or sit a little bit flat and I just have to be aware of that. But what what a what a great, way of helping musicians to understand their own individual tuning challenges.
Leah SheldonRight. And sometimes it's also understanding the mechanics of the instrument. There are some notes on some instruments that are almost always gonna have a similar tendency. For example, when on the flute, once you start playing above c above the staff, those notes are gonna be really Leah. You know? High e, e flat, e natural, high f, high g. Those are almost always going to be very sharp.And so just teaching the students that ahead of time knowing that they'll they're going to need to compensate for that. Same thing with the throat tones on the clarinet and, d on the saxophone and just knowing where those are ahead of time is really helpful.
Greg RistowYeah. And it it raises also the I think the the related the related topic that, you know, sometimes a poor intonation is coming more from a technical issue than necessarily from an ear issue. And sometimes we we have to this goes back to where we started. We have to help students to know throughout their range how to adjust and correct intonation.
Leah SheldonYes. And also as the teacher, keeping an eye out for that. I had a student just last week who is typically very in tune, plays in tune. She can adjust really well and almost always very accurately, and she was really out of tune. And then we put a tuner in front of her, and every note was different. It would start flat, sharp, flat all over the place. And she's never played like that before.But I knew right away, okay, something is wrong with this instrument. Sure enough, the cork in the head joint was loose, and it was just sliding around in her head joint. So that had had come loose and had thrown everything off. So we have to always be looking out for those kinds of things too. And I'm sure that it's the same in the choral world.
Greg RistowYeah. I've definitely had had the cork in my head joint come loose before. That's a great excuse. No. It's it is it is true that yeah. That we're always yes. We are always listening for whether there might be anything something wrong physiologically Leah but more commonly, just something wrong with how how a singer is approaching something technically.Whether it's with the breathing or whether there's, you know, tongue tension that's just messing things up Ristow strap muscle tension. And there are all sorts of so many so many tuning things are are related to the wrong kind of tension at the wrong time.
Leah SheldonYeah. So these are some very basic level things that you can do even with beginning students. Free more experienced players, I have a couple of quick things here I'd like to mention. If we could revisit the f around the room exercise again. Yeah. Once your students do that well with one pitch, then you can try f around the room in building chords. I usually start with a 5th.So your first student plays their concert f, holds it for 4 beats. The next student, just as before, pass it to the next student. Once the next student is playing concert f, that first student now drops to concert b flat.
Greg RistowMhmm.
Leah SheldonAnd the second student then, once they're done, passes the f on, then they drop to concert b flat. So you've now got a 5th going around the ensemble. And then once your students do that well, then adding the 3rd in there so you can you can build chords once your group is ready to start tuning at that level.
Greg RistowYeah. That's great. That's great.And, you know, it's related if we go back a couple of episodes to the interval ear training episode, a similar game that works really well with singers is to, you know, have one person just like that singing, say, a drone, and another person doing a Remington exercise around what that first person is singing, or taking turns, or both of them doing a Remington in the opposite direction from each other, but yeah, there there you're really getting to building not only intonation for a specific note, but intonation for all the different, possible intervallic combinations that could happen. Mhmm.
Leah SheldonYeah. And another great way to address, tuning chords is play chorales. Do them with your group as a warm up as much as possible. It's a much more musical way of of hearing them, but then also they they have moving notes, there are moving parts, there are lots of other things that you can address but but chorales are great for intonation and giving them opportunities to hear it and practice it.
Greg RistowYeah. And and and they have one of the things I love about chorales, right, is you get you get so many so many vertical moments that are major and minor triads that are really in different inversions, which are so good to practice tuning on. But you also get the wonderful dissonant passing tones and suspensions and sometimes appoggiaturas where you also can really learn to to practice and tune a note that's not part of the chord you're hearing.
Leah SheldonMhmm. Yeah. And this is great for advanced groups. But if you wanna do this with with a beginning group or more intermediate group, I'm just gonna do a quick plug here for John McAllister on his website. If you just Google John McAllister, I don't remember the exact, web address at this moment, but
Greg RistowWe can we can put it in the show notes also.
Leah SheldonOkay. That's a great idea.He has tons of free resources. He's he's an educator and composer, and he writes great warm up and, like, basic building block exercises for ensembles. They are free, and then he composes very exciting backing tracks to them. So students, like, have fun playing long tones, but then they also have a context to play it within too if they're at home practicing. But he has I believe there's a set of 4 and then a set of 8 chorales for ensembles that it some of those are appropriate for a beginning level group, and they're free and they're on his website.
Greg RistowOh, that's great.
Leah SheldonYeah. And then and then finally, specific to band students, teach your students alternate fingerings for notes that are really out of tune and, let them use that to their advantage. So, like, throat tones on the clarinet, putting your right hand fingers down on the flute, high e natural, taking the pinky off, make sure they're not using the thumb b flat, high f, adding your, ring finger, finger 6. Those little changes can make some of the biggest differences.
Greg RistowYeah. I I often wish as a singer that we had an alternate fingering we could, we could turn to or that little pinky slide on the trumpet. Right?
Leah SheldonRight. Yes. Oh, yes.This is a little bit off topic, but Leah, teachers, from the very beginning, teachers of trumpet students, Leah, teacher trumpets, to use their ring finger. The slide goes out on d right from the very beginning. Otherwise, it's always going to be very, very sharp.
Greg RistowLeah, these are just these are just great. Any others you wanna share with us?
Leah SheldonI I could go on for days. I won't do that to you, but I'm wondering if you have anything that you also wanna tie in, to your world of choral conducting.
Greg RistowYeah. You know, what what I find delightful is how similar these things are, and and it doesn't really surprise me. And I I think, like you, I would say that, I have I've known teachers who actually do teach intonation, and I've known teachers who don't teach intonation, and, generally, you can tell pretty quickly from listening to just a few seconds of of their ensembles playing, whether or not someone is actually teaching intonation. So, yeah. So totally Leah of these exercises that you've mentioned are are great within within the choral world also. We were just talking about chorales. I I love to use chorales, but I even more love to use, Renaissance music, when working on intonation with a choir because it's even more consonant and continuously consonant as a as a thing.And, one of the things you know, you you talked about tone and and listening to your neighbor in the rest of the section. There's a great book by, Pavel Chechnikoff, the the composer composer of probably his most famous piece is, The Salvation is Created. And, the book is called The Choir and How to Direct It. And in the first chapter, he talks about teaching he talks about a hierarchy of listening. He talks about, listening to yourself and then listening to your neighbors and the people around you, and then listening to your section, and then listening to the entire ensemble. And he also talks specifically about what to listen for. So to listen for the pitch.Am I singing the same pitch as my neighbors, as my section? Am I singing the same vowel? How is the balance of my voice within the people next to me, within my section, within the ensemble? And so you're gradually listening for all of these things from the level of just your own your own voice, your own instrument, working outwards to gradually taking in the entire ensemble Leah and and and raising your awareness of it. And and with the with the advice that when things start to go wrong, always start from the base of that pyramid, which is listening to your own voice, listening to the voices of those right around you, listening to your section, and working your way, to listening through to the whole ensemble, which I find is just, you know, oftentimes, especially Leah lot of times the singers I work with who have sometimes more solo vocal training than choral vocal training are really experienced at listening to their own voice, but may not be familiar. And and of course, when we practice, that's that's all we can do is listen to ourselves. Right? But they may not be familiar with with building up those stages and listening to, people around them.So it's I think it's good to have that sort of hierarchy of of listening needs.
Leah SheldonYeah. That's wonderful. And that's a great point about that we're so used to listening to ourselves. When I have an ensemble that gets to a point where they're really listening well to their section but they're not listening across the group, even if we've talked about what to listen for sometimes then I mix them up. I literally have them stand up and move around the room and they are allowed to sit anywhere as long as it is not next to the same instrument as their own. And that forces them now to have new neighbors to listen to. That forces them to hear other things they haven't heard before and after playing like that for a few moments or even a whole rehearsal, when they come back to their sections, they're able to listen so much better across the group because now they've heard it and they know what to listen for.
Greg RistowYeah. Totally. Totally. Well, this is just great. I I feel like I have learned so many things now today from the instrumental world that I can't wait to to try out with my choirs. This is, just wonderful stuff, you know.
Leah SheldonAnd if I could just end with one final plug here, when it comes to intonation, the worst thing that you can do is nothing. Don't do nothing. Do something. As the teacher, make time to address it in your group. Even if you have beginners. I I had a group yesterday of 4 beginners and right off the bat, they just did not have great sound together. It was very out of tune, and I just looked at 2 of them and I said pull your pull your head joint out half of an inch, pinky width, and we played it again.And that was it. We went on. They there was no why. There was no what what do I have to do this far.I was just just pull this out. They immediately, they heard it. They said, oh, that sounds better, and we moved on. It took 2 seconds. And then instead of letting them play in that out of tune sound and getting used to it, now they were playing in tune.So don't do nothing. And tell it to your students too. If they're playing and they hear something is not right but they don't know what to do, just do something. Bring your pitch up. If it got worse
Speaker 1Yes.
Leah SheldonGo the other way. Bring it down, but don't sit there and do nothing. Do not assume that it's someone else's responsibility to fix the sound.
Greg RistowYeah. Oh, I love it.I love it. It reminds me, actually, an an exercise one of my Dalcro's teachers did with us. We, had us stand in a circle and, gave us a note and said, you know, make a major chord off this. Now close your eyes. And then she would tap one of us on the Sheldon. And it was that person's job to go a little bit out of tune. And everyone else, when they heard someone go a little bit out of tune, was to readjust to tune the chord to that person.
Leah SheldonOh, I love that.
Greg RistowWhich was
Leah SheldonI'm stealing that. I'm using that this week. Yeah. That's great.
Greg RistowYeah. Thank you, Anne Farber. Yeah. So great. Awesome. Well, I think that's definitely plenty for this, and and what a what a joy. Leah, thank you so much for sharing these great ideas with us.
Leah SheldonThank you for giving me the opportunity.

Tuning Systems

In this episode we explore the difference between just intonation and equal temperament, and take a field trip to learn about an organ with 15 keys per octave (instead of the usual 12), that makes it possible to play purely tuned chords in almost all of the keys.
Links:
Tuning systems synthesizer: https://utheory.com/experiments/tuning-systems
Organ demo field trip video: https://youtu.be/A9Enpt8hREg
Chrome Music Lab: https://musiclab.chromeexperiments.com/
Intonation/Tuning System "Puzzle Pieces": https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/benedettis-puzzles/
 
Show Notes:
0:00:20.9 - Introduction
0:01:03.5 - Topic Introduction: Tuning SystemsGreg Ristow explains the complexity of tuning systems and opens the discussion on various aspects related to them.
0:01:58.4 - Just Intervals and Singing in ChoirsDiscussion on how choirs tend to move towards just intervals in their performances.
0:02:43.2 - Historical Context of Tuning SystemsWe delve into the historical variations of the A note’s frequency and introduces the concept of just intonation tuning.
0:03:22.2 - The Law of Superposition and Sound WavesExploration of how sound waves interact and affect what we hear, using sine waves as an example.
0:07:00.8 - Beating in Sound Waves and TuningDemonstration of how close frequencies can create a beating effect in sound, relevant to tuning and intonation.
0:11:25.7 - Constructing Scales with Tuning SystemsExamining how scales can be formed using different intervals, like perfect fifths, and the issues that arise in tuning systems like Pythagorean tuning.
0:21:16.4 - Assigning frequencies to notesA practical approach to assigning frequencies to piano notes, highlighting the challenges in tuning.
0:24:00.8 - The Pythagorean Tuning System and the Wolf FifthUnderstanding the Pythagorean tuning system, its implications, and the infamous 'wolf fifth.'
0:27:24.5 - Equal Temperament Tuning SystemDiscussion on equal temperament tuning, its compromises, and comparison with just intonation.
0:28:27.3 - Comparison of Major and Minor Thirds in Different Tuning SystemsExploring how major and minor thirds differ in various tuning systems, including just intonation and equal temperament.
0:31:04.3 - Just Intonation and Chord TuningDemonstration of how chords are tuned in just intonation, contrasting with equal temperament.
0:35:56.5 - Field Trip to Oberlin's Brombaugh OrganGreg Ristow and David Kazimir discuss the unique features of the Brombaugh Organ at Oberlin, demonstrating quarter-comma meantone tuning.
0:41:12.1 - Split Black Keys and Specialized Tuning on the Brombaugh OrganExploration of the organ's split black keys and how they impact tuning and playability.
0:47:08.4 - Musical Composition and Tuning SystemsDiscussion on how composers historically wrote music with specific tuning systems in mind, affecting the musical expression.
0:49:00.3 - Wrapping UpWe preview the next episode's topic, focusing on teaching intonation, and Leah Sheldon's experience in this area.
Transcript:
[music]
0:00:20.9 Greg Ristow: Welcome to Notes From the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:35.4 David Newman: Hi, I'm David Newman. I teach voice and music theory at James Madison University, and I write code and create content for uTheory.
0:00:42.4 Leah Sheldon: I'm Leah Sheldon. I'm head of teacher engagement for uTheory.
0:00:45.7 GR: And I'm Greg Ristow. I'm the founder of uTheory, and I direct the choirs at the Oberlin Conservatory of Music.
0:00:51.9 DN: Thank you listeners for your comments and episode suggestions. We love to read them. Send them our way by email at notes@uTheory.com. And remember to like us and subscribe wherever you get your podcasts.
0:01:03.5 GR: So, today our topic is tuning systems, and this one has taken us a while to put together, partly because we wanted to build some tools to show them off. It's a concept that I think a lot of us have heard little bits about, but maybe one that not all of us know mathematically and musically in a really deep way. So, I'm excited to talk about this one. Maybe to kick it off, what kinds of things come to mind when you think of tuning systems, Leah and David? 
0:01:32.2 DN: Oh, man. I let the harpsichordists decide what tuning system we're using. [laughter]
0:01:37.7 GR: That's right, 'cause you worked so much in the early music world, yeah.
0:01:40.7 DN: I trust that whatever I'm hearing is the one that we're supposed to be using. But I think definitely when we're singing in choirs, and I think this is probably true no matter what choir you're singing in, that you find yourself moving towards just intervals for reasons that may become apparent soon.
0:01:58.4 GR: Which of course, brings up this concept of just intervals. And that's something we'll have to unpack for sure. Yeah. How about you, Leah? 
0:02:05.5 LS: I know that there are different tuning systems, but what are the differences and when do you use which? 
0:02:11.4 GR: And so, maybe we should just talk about what we mean when we say tuning systems first off. Actually, we're deciding what frequencies to assign to our 12 notes on the piano. We can call A440, but we don't have to, right. We know that A has moved throughout history and locations. In northern Germany in the Baroque era it was probably somewhere pretty close to 415. A little bit earlier than that, down in Italy, it was probably somewhere closer to 465.
0:02:43.2 GR: So, what we think of as very much being a fixed thing today hasn't always been a fixed thing at all. And I think a lot of us, as David mentioned, right, have heard when singing in ensembles or playing in ensembles that we should strive for using more of a just intonation tuning. And that's a whole thing to unpack as well. So, shall we dive into some of this? I want to apologize in advance, listeners. This is going to be a little bit of a math-heavy episode, but hopefully in a fun, nerdy kind of way, so.
0:03:22.2 DN: But too, I think even us, definitely as singers, because we don't have a fingering system for our voices. A lot of what we do is, is literally by ear and not mathematical or necessarily carefully considered except for singing it until it sounds right. And I mean you have some plans to show us why that is. [laughter]
0:03:46.7 GR: Yeah, yeah. So to start off, I thought for all of this to make sense, there's one central principle of physics that we have to understand. And this is called the law of superposition. Have you guys heard of this? 
0:04:03.4 DN: I am not familiar with this.
0:04:05.3 LS: Me either.
0:04:06.2 GR: Okay.
0:04:06.7 DN: I feel like I should be.
0:04:08.1 GR: So the law of superposition has to do with what happens when you add two waveforms to each other. So, for instance, imagine that we were graphing a sine wave, right. And the sine wave starts from zero and goes up, then comes back down to zero, goes under, and then comes back up to zero, right. That's sort of the cyclical nature of a sine wave. Now, imagine if you took that same sine wave and shifted it over half of its cycle, which is to say that now the shifted version starts at zero but goes down and then comes up. So these two graphs are now mirrored.
0:04:47.9 DN: Right.
0:04:48.0 GR: What was up is now down and vice versa.
0:04:50.9 DN: Yes.
0:04:51.3 GR: Can you sort of picture that? 
0:04:52.5 DN: We're moving at exactly half a cycle? 
0:04:54.6 GR: Yeah. And so, picture a sine wave and its mirror image upside down.
0:05:02.8 DN: And this is how we used to remove lead vocals from recorded audio tracks.
0:05:08.7 GR: Good, David. Hold that thought. [laughter] Yes, yes, yes, yes, yes. Exactly, exactly right. So now if at any point in that graph we added the two graphs together, where we would have a positive number in the first graph, we'd have the same negative number in the second graph, and they'd add up to be zero.
0:05:25.5 DN: Yeah.
0:05:28.3 GR: Right. And so this is called the law of superposition, that to add waves together, you sum up the waves, and you get a composite wave. Now, how this works in sound is, sound is actually air pressure waves. It's air pressure traveling through the air, hitting our eardrum being translated into cycles. And if we were listening to a sine wave, and we mirrored it, and added exactly that same sine wave, as you said, David. This would cancel out the sine wave and subtract it from the sound. And this is, as you said, how we used to subtract lead vocals from recordings to make karaoke tracks. That's more usually done with machine learning these days.
0:06:19.6 DN: Right.
0:06:20.3 GR: It's also as David points to his earphones, go ahead.
0:06:22.9 DN: It's also how, how noise canceling earphones work.
0:06:26.9 GR: Exactly. By creating the negative image of the sound wave coming to your ear and adding that to... And then playing that negative image to cancel out what's coming to your ear. So yeah, so That's the law of superposition. It's how waves interact with each other. Imagine, for instance, I've got a little simple synthesizer I made up where I can play different frequencies. I'm gonna play just a 440 for us. Here it is. Easy enough. Right? 
0:07:00.8 DN: Mm-Hmm.
0:07:00.9 GR: Now imagine if we had a slightly out of tune version of that with it. Instead of 440 cycles per second, we had 441 cycles per second. Here's a 441, just listen to it by itself. And here's a 440. Almost imperceptibly different. Right? 
0:07:21.0 DN: Yeah.
0:07:21.8 GR: Now if we play them together, they're gonna sort of line up. They're gonna be, they're gonna start, they're gonna be going up from zero and coming down from zero together. But basically, each second or so, they are going to get more and more out of whack with each other until there will be a point where as the one is all the way at the top, the other is all the way at the bottom. And we'll hear a moment of silence and we'll hear that recurring as the waves line up with each other in opposite positions roughly once a second. You ready to hear this? 
0:07:58.0 DN: Mm-Hmm.
0:07:58.9 GR: Okay. So here is a 440 and here is our second slightly out of tune sine wave joining it at a 441. And you can hear how as the waves support each other. Right. As they're both going up or both going down, we hear noise and as they cancel each other, we hear silence and hear that wah wah wah sound, which we call beating.
0:08:29.4 DN: And so if they're off by, this sounds mathy, but it's really a not mathy. If it's off by one, will it be one cycle per second that we get beating? 
0:08:41.8 GR: That's exactly right.
0:08:42.6 DN: That is a, if we count the number of beats per second, we'll know how many cycles that is off.
0:08:48.3 GR: Correct yeah. And to prove that, here again is off by 1 Hz and now let's go to off by 2 Hz, which is gonna give us twice as many of those per second.
0:09:05.1 DN: Right.
0:09:07.5 GR: And similarly, you wanna do a couple more to hear them. Here's off by 3 Hz. [laughter] You see where this is going? Here's off by 4 Hz, right? 
0:09:24.0 DN: Wow.
0:09:25.4 GR: So, however many Hz those are off from each other, you'll hear that number of beats per second.
0:09:30.1 DN: And this isn't random, because Hz literally means cycles per second.
0:09:35.2 GR: That's exactly right. That's exactly right. Yeah.
0:09:36.9 DN: Yeah.
0:09:40.2 GR: Yeah. And so that's the law of superposition at work. That's how waves combine to reach our ears. They add up and subtract from each other. So yeah. Does that make sense.
0:09:52.1 DN: As far as tuning a note with itself? Yes. [laughter]
0:09:56.3 GR: With itself it sure does yeah yeah. Now it's worth pointing out that, we're listening to right now to pure sign waves, but most waves have, most sounds are more complex than that. They have overtones to them. And you won't hear these, these beats as obviously. Just to... Just so that we, hear what that's like, I'm going to turn the, harmonicity of this up a little bit. I'm gonna add a couple of overtones to the sound just so we hear it. Here's now a much fuller overtony sound.
0:10:30.0 GR: Alright? It's a richer sound, more buzziness to it. And then here is one Hz off with it. We still hear the beat, but because there're more overtones in the sound, it's not fully canceling it out. There's other stuff happening.
0:10:51.8 DN: Right.
0:10:54.7 GR: Yeah. And that's just when I've added some rich overtones to the sound, which I will take away for most of these demos because...
[laughter]
0:11:01.5 GR: It's much easier to hear when we're dealing with the pure sine wave.
0:11:05.5 DN: Cool.
0:11:08.4 GR: Okay. Making sense so far? 
0:11:09.2 DN: Sure is.
0:11:10.1 GR: Great. Okay. So We discovered when we offset by one Hz when we had 440 and 441, we got those awful beats. Let's do a little math experiment. Let, could we come up with a couple of numbers that would generally sound good with each other? 
0:11:25.7 DN: 880 [laughter]
0:11:28.0 GR: 880? So We're gonna double it. And effectively what that means is right, with our one sine wave, the other one's gonna be going twice as fast. Will there ever be a moment when they're exactly in opposite states? 
0:11:43.4 DN: Nope.
0:11:45.3 GR: No, there won't. And so we won't hear any beating between 440 and 880. Here's 440, and here's 880. And they're in perfect tune with each other. And by the way, what interval was that? Here's 440, here's 880.
0:12:06.8 LS: An octave.
0:12:07.6 DN: It's an octave.
0:12:09.8 GR: Yeah. It's an octave. Right? [laughter] Yeah yeah Good.
0:12:13.6 DN: We're all waiting for the kids to respond. [laughter]
0:12:18.5 GR: [laughter] Exactly. Always good to leave time in the classroom for, everyone to answer. Good. 880 works with it as well. Really about anything that's, a nice, multiplication or divisor of it will work pretty well also, like 550 sounds great with 440. Here's 440, here's 550.
0:12:41.3 GR: And the interval is.
0:12:45.1 LS: Major 3rd.
0:12:46.9 GR: Major 3rd. Yeah. And a really beautiful one at that, right? 
0:12:52.4 GR: Yeah. So, and we can do that with 660 as well. Let's see, what do we get when we do 440 and 660? 
[laughter]
0:13:01.1 GR: We get... Yeah. David holds up his hand...
0:13:06.2 LS: Perfect fit.
0:13:06.8 GR: With five fingers...
[vocalization]
0:13:08.5 GR: Because we get a perfect fit. Yeah, yeah, exactly. Exactly. And so it turns out that these natural multipliers make, the really basic intervals that we're familiar with. And that's largely why when we talk about consonance and dissonance, that's largely where that comes from, is the presence or absence of beats in a sound. So, yeah. Now this brings us to overtones and [laughter] that's kind of exciting and always weird and magical. But effectively think of a string, and if you pluck it in the middle it, and let it vibrate like a guitar string, for instance, right? The middle of that string is gonna go back and forth and back and forth, some number of times per second. That's determined by how long the string is and how tense it is.
0:14:04.5 GR: Easy enough. Right? But that's not gonna be the only vibration on that string. It turns out that there's also a vibration that happens from sort of a still point in the middle of the string where either half vibrates twice as fast as the length of the full string. And both of those vibrations are going on within the same string, the full length and the half length, which is twice as fast. And in fact, any ratio that you can divide the string evenly by, that's true. If you divide the string in three you get two still points in the middle and the 3rds around those are vibrating at three times the speed of the full length of the string. And that then that's actually the interval of an octave and a 5th at that point.
0:15:04.4 DN: Yeah.
0:15:05.2 GR: And if we go another one, right? We have the string divided in four. We've got two octaves from the original, the string divided in five. We have two octaves and a major 3rd from the original. So shall we build those up? Shall we imagine that we have a low guitar string at one 10. The low guitar string that happens to sound like a sine wave. It also vibrates in the middle at two 20. And then if we divide it into 3rds, and then if we divide it into fourths, and then finally if we divide it into 5ths, we could keep going. We could divide it into six and so on and so forth. But you hear we're basically building up a giant, major triad, which are the first notes on the overtone series.
0:16:08.5 DN: Yeah. And you were reducing the volume of the upper harmonics as we went. Right? 
0:16:12.8 GR: I wasn't actually, those were all, those are all set equally on this synthesizer.
0:16:18.1 DN: Interesting. They started sounding loud and then they seemed to dip afterwards. But of course on a guitar string each, every time you divide the string in half, yes it's... Or into the more sections you divide the string into, also the less amplitude you're gonna get from each of those...
0:16:39.9 GR: That's right.
0:16:40.6 DN: Harmonics. So that they will be less and less loud. But still contributing to the tamber of the sound that we hear.
0:16:48.1 GR: Yeah. Absolutely. And so we stopped, I stopped here, I went all the way up to two octaves in a perfect 5th. If I had gone one more, we get the first note that is not on a major triad. And let me just, actually hold on a second. So here is up to the octave in the 5th, and then I'm gonna go one more, right. And lemme play just that note. So that is the, right, so here's our root, and here's that note.
0:17:34.1 GR: Yeah. So that's, we finally get a minor seventh up there on top of all of that. So, and that's the overtone series. And when we talk about, when we talk about hearing overtones in a sound, that's what we're talking about is hearing the combination of those different ones. And of course, that's significant for brass players on brass instruments. The pitch is determined by the length of the instrument, and then how many times that's divided. Right? How many of those standing nodes you create within it, in the same way that the guitar string is vibrating at multiple waves at the same time, on a brass instrument you buzz your lips and you can create a tone at the frequency, the length of the instrument, or twice the length, or three times or four times, et cetera. And that is the overtone series on there. Now there is a slight difference because some brass instruments are conical. And with those instruments, you actually lose the very lowest overtone because instead of having, low pressure, high pressure, low pressure, a full wave cycle, you only have low pressure, high pressure for the length of it. So yeah.
0:18:48.4 DN: So I've gone to, musiclab.chromeexperiments.com, or you can just Google Chrome Music Lab and it'll take you to this. And this has a whole bunch of different sort of ways of exploring music. And one of them has an explanation, not an explanation, just a experiment. Place a playground for harmonics. And if you go to the playground for harmonics, it shows you some things that look like they could be waving strings. And it shows you that. And if you click on the one string, you get the sound of one string. And if you do that and it's octave, you can hear them as you touch them, and you can sweep through them and get something that sounds a little more like a complex tone. There is also a, spectrogram.
0:19:56.4 GR: A spectrogram shows in, on a graph by the intensity of the different frequencies within a sound. The different overtones within a sound, generally red, representing more intense and blue, or black representing less intense.
0:20:17.3 DN: And so it gives you a number of different presets as well as a microphone, which if you allow it access to your microphone will show you the spectrum of the sounds that you're making.
0:20:29.1 LS: And there are also strings and sound waves and arpeggios and lots of lovely experiments.
0:20:36.2 DN: Yeah. There are lots of games to play, there.
0:20:39.3 GR: Yeah. Excellent. So we'll put that in the show notes. But you can just google, Chrome Music Lab experiments and that will come up for sure. Great. Okay. So with all that, I think we're in a pretty good place to actually turn and talk about, well, how do we get to a scale with all of this? So let's say we wanted to create all of the notes on the piano. Can we think of an interval that's on the overtone series where if we followed it through over and over, we'd eventually get all 12 notes on the piano? 
0:21:16.4 DN: I mean, obviously you could just do half steps, right? 
0:21:20.2 GR: You could absolutely do half steps.
[chuckle]
0:21:22.4 GR: You have to do half steps. Now, finding, it's gonna be a long time on the overtone series before we find a half step.
[laughter]
0:21:31.7 GR: So it's, that's a good thought. But maybe we can find one a little lower down little earlier on in the Harmonic series.
0:21:37.9 DN: And I think the first one that makes, the first one that's gonna make a difference is that 5th, that's the first one that we hear as a different note. Or if you're gonna use fancy speak, the a different pitch class.
0:21:51.5 GR: Yeah, absolutely. And we know also that if we go around by perfect 5ths, we're gonna get all 12, because circle of 5ths is exactly that, right? It's a collection of all the 5ths.
0:22:04.5 DN: And also because the harmonics get generally softer as you go up, in the series on any instruments, on most instruments. Generally the 5th is gonna be the one that's gonna come out the strongest. Likely to come out the strongest.
0:22:21.5 GR: Yeah.
0:22:21.6 DN: Right? 
0:22:21.7 GR: Yeah. Yes, that's right. Yeah. Okay. So now our goal is to assign to the notes on the piano frequencies based on going around the 5ths. And so our 5th, when we found on the harmonic series, when we had, we multiplied by, we divided our string in three, right. And that, and it vibrated three times as fast as the original. That's actually an octave in the 5th. So we're gonna divide that frequency in half, to make it just a 5th. So we're multiplying by three dividing in half, and that gives us our 5th each time. So yeah. So let's sort of work our way through this. Here's A, and I'm actually gonna take us up a 5th and down an octave. So down a 4th to E and down a 4th to B, up a 5th to F sharp, down a 4th to C sharp, up a 5th to G sharp, down a 5th, down a 4th to D sharp which let's call E-flat just to make our life easy. Up a 5th to B flat, down a 4th to F, down a 4th to C, up a 5th to G, down a 4th to D. And finally up a 5th back to A. And now we've gone through our whole series and we have all 12 notes of the piano. But here's the bad news. This is the A that we ended on, and this is the A that we started on. Hear that difference? 
0:24:00.8 DN: [laughter]
0:24:01.8 GR: Here's the A we ended on, and here's the A we started on, and if we play them together, we get that right. [laughter] And so this way of tuning is called the Pythagorean Tuning System. We tune by 5ths throughout, and it leaves a problem in there somewhere, right? Because, when we get back to A, it's no longer A, and the end result is that the 5th from, that the second to last 5th is pretty rough with itself. It's not well in tune with itself.
0:24:55.8 GR: You're sort of going wah-wah-wah-wah-wah in there.
0:25:00.7 DN: Right.
0:25:01.8 GR: And just to compare that, the 5th that we should have had instead would've been, and here is what's called the wolf 5th, hear that difference that out of tune ness of it? 
0:25:23.4 DN: It also through the headphones. I don't know if it's gonna come through in the recording, but it through the headphones, it also gets a whole nother set of tones that sound along with it.
0:25:36.1 GR: Yeah. From the, yeah. The distortion.
0:25:38.6 DN: Yeah.
0:25:40.8 GR: The sound could by the distortion. Yeah. And that's called the wolf 5th, because it sounds a bit like a wolf howling. And actually it sounds even more like a wolf howling if we turn up the overtones of the sound itself. So remember I had no overtones in each of those. Those are pure sine waves. But so now here is our good 5th with some overtones in it.
0:26:06.1 GR: And here's our wolf 5th.
[laughter]
0:26:13.8 GR: Yeah, right? Good 5th.
0:26:20.4 GR: Wolf 5th.
0:26:23.7 GR: Isn't that awful? 
[laughter]
0:26:28.5 GR: And because when we go by perfect 5ths all the way around, we come out significantly higher than where we started. In this case, we start from a 440. We wind up coming out exactly six Hz higher. We have to make a compromise. And this is true of every tuning system that we have to... That there's always a compromise to make some intervals sound better and some intervals sound worse. And so the compromise that we make in equal temperament is we say, let's divide the problems of that wolf 5th, equally around all of the intervals. And that does that... That works out pretty well. Unfortunately, it means that in equal temperament, there's no interval anywhere in equal temperament that is a pure overtone interval.
0:27:24.5 DN: Yeah. And that it's funny because I have a colleague who has done a lot of work on Bach's tuning system and the imagination, I think that is in the public sphere is that they didn't know about equal temperament at that time, but they did know about equal temperament and they didn't want it because they so valued the sound of pure chords.
0:27:55.1 GR: Yes. Yeah. That's absolutely right. And so just we compare these a little bit, right? So here's in equal temperament here is actually, let's start with if we did a just major 3rd, here's a just major 3rd. So that's the overtone major 3rd, and here's what we actually get on the piano.
0:28:27.3 DN: With sine waves. It sounds shockingly bad.
[laughter]
0:28:29.7 GR: It's exactly, it does, it does. It very much does with sine waves because they're so pure, it becomes so obvious when there's basically no overtones to balance that out. The more overtone rich something is, the harder it is to hear these detailed tuning things. And that, I mean, for instance, like on organ, depending on which pipe it is, some of them sound very... Have really simple overtone structures. And so you can really hear these things a lot. Yeah. So, and that's what we call equal temperament, where we compress every 5th a tiny bit so that it comes out with all of them being equal. And there are lots of... So the three intonations as we've talked about, I guess we've only talked about two really.
0:29:22.9 GR: We've talked about, Pythagorean, where we go around by perfect 5ths. And we have one terrible, perfect 5th wolf 5th. And we have equal temperament where we have 12, not quite perfect 5ths. But there are lots of other tuning systems that try and adjust for this. Quarter-comma meantone is a Pythagorean system where we compress, we spread out the wolf 5th across four different 5ths. And that sort balances some of the 3rds, so they sound pretty decent. And then, when we talk about just intonation itself, right? If we don't have an instrument that plays with fixed pitches, we can actually adjust in real time to tune different chords in a just way. So, and I've created, and we'll share this link, I've created a little synthesizer where you can build a chord. So for instance, here is, I don't know, B flat major in just intonation and it automatically adjusts and makes it just. For comparison, here's that same cord in equal temperament. You hear how wobbly it is compared to here's just, yeah. And actually if we... Let's hear that same cord in a Pythagorean temperament. And you'll hear the 5th is really beautiful in the Pythagorean temperament. The 3rd is quite high.
0:31:04.3 GR: Let me take the 3rd out of this. So it's a true perfect 5th. And now here's that Pythagorean 3rd in there.
[laughter]
0:31:16.2 GR: As we all cringe, right? 
0:31:18.1 DN: This is the reason why society is so tense today.
0:31:21.5 GR: Yeah. [laughter]
0:31:22.1 GR: And so, okay, here's...
[laughter]
0:31:24.3 DN: It's all the fault of our tuning system.
0:31:27.7 GR: It's all the fault of these tuning systems. So just intonation has that same 5th, exactly the same as Pythagorean, but listen to its 3rd, right? And that's significantly lower than our equal temperament, major 3rd. Now I want to share another one with you, which always feels crazy to me. So here's that 5th again, and let's have a minor 3rd and that's a just tuned minor triad. Compare that with our equal temperament minor triad. And I'm gonna take the 5th out so we can hear it more. Obviously. Here's our equal temperament minor 3rd, and here's our just intonation minor 3rd.
0:32:19.9 GR: Which 3rd is bigger? Here's equal temperament. And here's just intonation.
0:32:28.7 LS: Just intonation? 
0:32:32.0 DN: Yeah.
0:32:32.8 GR: The just intonation, that's right, yeah. So it turns out our minor 3rd in just intonation is about 14 cents higher. There are 100 cents in every half step. So it's about like, what's that? Like a seventh of a step higher than, a seventh of a half step higher than on the equal temperament version. And similarly our major 3rd is 14 cents lower...
0:33:02.6 DN: Lower, yeah.
0:33:04.0 GR: In just intonation compared to equal temperament. Yeah. Isn't that cool and wacky and wild? 
[laughter]
0:33:11.6 DN: So the thing is, and if you're tuning by ear, you're just going to nudge it to the thing that sounds good.
0:33:20.8 GR: Yeah, yeah.
0:33:22.3 DN: If you're listening carefully, you're going to nudge it to the thing that sounds good. Which is also one reason sometimes why choirs go out of tune, is 'cause pieces have been written so that the adjustments that they keep making keep going in one direction.
[laughter]
0:33:36.6 GR: Yeah, exactly, exactly. That's true. There are these wonderful puzzle pieces from the Renaissance era that cause you to modulate up bit by bit. And I'll share a link. Ross Duffin, who's a retired Musicology Professor from Case Western University, has a wonderful article on that. He also has a wonderful book called How Equal Temperament Ruined Harmony and Why You Should Care, which is a delightful read. All of this is great and feels maybe a little bit abstract, so I thought it'd be fun to take a field trip. And so I got together with Oberlin's Curator of Pipe Organs. Oberlin has one of the largest pipe organ collections in the world, David Kazimir to take us to the Brombaugh Organ in Fairchild Chapel, which actually has, instead of five black keys per octave, it has eight black keys per octave, because three of those black notes are split with a sharp version and a flat version, which lets it be in a quarter-comma meantone that works around different places. Quarter-comma meantone, remember, is where we split up the wolf 5th into four of the 5ths in the Pythagorean tuning. So shall we go visit with David? 
0:35:07.5 DN: Let's go visit! 
[music]
0:35:56.5 GR: That was great. What was that? 
0:35:58.1 David Kazimir: That was the opening verse of the Magnificat on the 9th tone by German composer Samuel Scheidt.
0:36:05.6 GR: So, that's excellent.
0:36:06.4 GR: I'm here with David Kazimir, who is the curator of pipe organs at Oberlin. It's amazing that Oberlin has a curator of pipe organs. How many pipe organs do we have and what do you do? 
0:36:17.4 DK: There are 34 pipe organs on the campus. My job is like a family practice physician. I have a little bit of instruments who are newborns and some that are a little bit older, and no one's in palliative care, so I'm doing my job. But a lot of it is just tuning, regulation, general maintenance, and working with the facilities to keep everything and everyone moving and playing smoothly.
0:36:43.2 GR: This organ, that you're at, is a pretty special instrument. Now, most of our audience is listening, but we'll also post a video of this online. Can you tell us a little bit about this organ, and why it's so special? 
0:36:55.8 DK: This instrument was built in 1983 by John Brombaugh, one of the 20th century's great American organ builders. It utilizes the tuning system called quarter-comma meantone tuning, and is unique amongst organs in that it has split sharps to accommodate those unique interval tuning systems that we find in quarter-comma meantone. Well, on a normal piano keyboard, there are 12 notes in an octave. Not here. There are 15. I'm going to start at C and go up, so middle C, C sharp, D, D sharp, E flat, E, F, F sharp, G, A flat, G sharp, A, A sharp, B flat, B, and C an octave higher.
0:38:12.9 GR: Wow, that's crazy. So if I heard right, that means that what we think of as being the enharmonically equivalent notes in equal temperament, like D sharp and E flat, always the flat version was higher than the sharp version.
0:38:27.0 DK: Correct. And as they are oriented on this keyboard, the more commonly used of those enharmonic notes, E flat, G sharp, and B flat, they are at the front of the key. And behind it, and a little bit higher, is the less commonly used one. So you have D sharp behind E flat, you have A flat behind G sharp, and you have A sharp behind B flat.
0:38:56.9 GR: So I wonder, maybe, could you just play some chords with the right and wrong black notes, so we can hear the difference? 
0:39:03.8 DK: Sure. E major is E, G sharp, and B. This is the right version with the G sharp.
0:39:15.9 GR: And that, as we listen to that, that G sharp is significantly lower, that E to G sharp interval is significantly smaller compared to our modern piano.
0:39:24.3 DK: Correct. The 3rds on this organ, and in quarter-comma meantone tuning are left pure. So they don't beat as much. If you listen to that, there's no oscillation. The thing that gets interesting in quarter-comma meantone to make those 3rds pure, you end up with 5ths that are narrower.
0:39:51.3 GR: Yeah. So we hear a little bit of the beats in that 5th. Can you hold that 5th out a bit longer? That's that wah-wah-wah-wah-wah... [vocalization] effect we hear in it. Yeah. Yes
0:40:01.9 DK: You don't hear that in equal temperament, which is twelfth-comma meantone. Pure 3rd. Now I'm going to play it with the wrong note. Hold on to something.
0:40:19.2 GR: Oh, that's painful. So that was E, A flat, and B.
0:40:23.0 DK: Yes.
0:40:23.9 GR: Wow. Could you just play the E and A flat together? And now the E and G sharp. That's so much better. [chuckle] That is amazing. But then that lets you get, I imagine, other places that would use A flat. Can you play an A flat major on this organ? 
0:40:46.7 DK: You can play an A flat major, so.
0:40:48.0 GR: And it's really, it's quite nice, actually.
0:40:55.3 DK: Yes, it's very sweet. Now I can use the wrong key, in that case, D sharp.
0:41:06.5 GR: Which is a little bit diminished. What if we use both G sharp and D sharp there? So what if...
0:41:12.1 DK: G sharp and D sharp.
0:41:16.3 GR: Wild.
0:41:18.1 DK: It gets really crazy.
0:41:21.8 GR: So normally in like a quarter-comma meantone, the farther you get away from the normal keys, the weirder it sounds.
0:41:32.6 DK: Right.
0:41:33.4 GR: Is that still true with this organ? Or because of the split keys, are you able to keep things sounding normal-ish? 
0:41:41.3 DK: Well, with the split keys, you have more options to keep intervals that use a pure 3rd running. So with the option of F to F sharp to A sharp, that can be pure and comfortable because the difference between F sharp and B flat.
0:42:04.3 GR: Yeah.
0:42:05.9 DK: The wolf tone that we have in this...
0:42:08.1 GR: So the wolf tone is usually where you put all the leftover 5th change from adjusting the 5ths to be smaller. You still have one 5th that has to be way out.
0:42:21.4 DK: Right.
0:42:21.8 GR: And normally that's between, G sharp and E flat.
0:42:27.4 DK: Yes. So if we listen to that G sharp and E flat.
0:42:33.0 GR: Yeah. And it's called the wolf because it kind of howls.
0:42:35.5 DK: It howls. There's no way of getting around that. The theory practice of this time is through the use of these pure 3rds. It strengthens in some keys the function of the dominant going into the tonic. 'Cause you have pure 3rds in the dominant and you also have it really pure in the tonic when you resolve.
0:42:58.0 GR: Could you maybe just play some tonic dominant tonics for us and tell us what keys you're playing in there? 
0:43:01.9 DK: Alright, so tonic, dominant tonic, this is C major. The weight of G major in that case really has, strength, but it also sets you up for... You really enjoy your resolution when you have those crunching, dissonances, like. The arrival at the cadence just goes... And that tension you hear in the music of this time period as well.
0:43:43.1 GR: David, could I give it a try? 
0:43:44.5 DK: Of course you can.
0:43:45.0 GR: I'm just really curious to like, to explore this and... Okay. You may have to remind me which ones are the sharps and which ones are the flat. So I'm gonna try playing something in E major.
0:43:54.1 DK: Okay.
0:43:54.5 GR: And I think you said the part of the G sharp...
0:43:57.3 DK: Front? 
0:43:57.7 GR: A flat closest to me is the G sharp.
0:44:00.5 DK: Correct.
0:44:00.9 GR: Okay. So in other words, I can have a beautiful E major triad...
0:44:04.3 DK: Triad.
0:44:05.2 GR: Like this and then the front of the E flat D sharp, the wait don't [0:44:12.4] ____ the front of it is the E-flat, right? 
0:44:14.4 DK: Correct.
0:44:14.8 GR: And the back is the D sharp.
0:44:16.1 DK: Correct.
0:44:16.7 GR: So if I'm playing in E major and I wanna play 151. In my one chord, I have to use the front part...
0:44:22.8 DK: Right.
0:44:24.3 GR: Of the G sharp, A flat.
0:44:26.4 DK: Yes.
0:44:26.7 GR: But in my five chord, I have to use the back part...
0:44:29.6 DK: Correct.
0:44:30.3 GR: Of my... And if I get that wrong, it's going to be really spectacular. Like there.
0:44:41.5 DK: Yeah.
0:44:43.0 GR: And there's a much smaller target area.
0:44:46.1 DK: Yes.
0:44:47.0 GR: For these, is this an E down here on the bottom? 
0:44:50.1 DK: Yes. Oh no. Short octave.
0:44:53.4 GR: Thank you.
0:44:53.9 DK: Yes.
0:44:54.5 GR: Got it.
0:44:54.8 DK: We should probably point out the short octave to them.
0:44:56.8 GR: Yeah. So... Oh, that's great. You know the question that we get all the time when we're teaching beginning students, is why do we need a D sharp and an E flat? And this really answers that.
0:45:11.1 DK: Yes.
0:45:11.6 GR: Because we can hear, right? Like, so if I play C minor using C, E flat, by G. But if I play C, D sharp, G that's just, it's just, that's just out.
0:45:27.2 DK: And the body reacts accordingly.
0:45:30.0 GR: Yeah. And that difference between the D sharp and the E flat, I mean that's like what? Quarter? Less than a quarter total.
0:45:40.0 DK: It's less than a quarter.
0:45:41.1 GR: Yeah.
0:45:42.0 DK: It really gets into micro tonal adjustments.
0:45:45.3 GR: Yeah.
0:45:46.6 DK: And we use this specialized tuning machine to make sure that we're getting right to the core of where that pitch needs to be. 'Cause there is a huge difference.
0:45:54.4 GR: David, this is amazing. Do you wanna play something for us to take us out? 
0:46:00.4 DK: Okay.
[music]
0:46:57.2 GR: It's just really cool to hear the organ playing in pretty constant just intonation because of, yeah, because of those different black notes, so.
0:47:08.4 DN: And the funny thing is though that people were writing with these intonations in mind and therefore there are pieces that are deliberately flexing on the out-of-tuneness of a thing that then resolves into more pleasant tuning.
0:47:27.9 GR: That's right, that's right. Yeah, and think of like the farther you modulate away from a normal key, a key that's central to the tuning, the more and more out-of-tune it becomes. And if you think of like even classical sonata form, right, where in the exposition we go up to the 5th, which would be a little more out-of-tune, but in the development we go to some really remote places, which would be very out-of-tune. And equal temperament as we think of it today really didn't fully come about until the 20th century, right? The tunings were decidedly more flexible and preferenced more normal keys prior to that. Anyway, having said that, kind of cool to hear it on a real live organ, right? 
0:48:15.5 DN: Yeah.
0:48:16.2 GR: And if you wanna try this experience out for yourself, you can try out our Tuning System Synthesizer, where if you plug in a MIDI keyboard and set it to automatic just intonation and play any chord, or click the notes on your screen, it will tune that chord in just intonation for you. And some of them I find really shocking. Like for me especially, first inversion triads are just weird beasts. So here is a first inversion F major triad, which sounds really beautiful, compare it to equal temperament.
0:49:00.3 DN: Whoa! 
0:49:01.6 GR: Right? Shocking, isn't it? Yeah. And if we spread that out a little bit more on the keyboard, so I'm gonna give us a really beautifully spaced now, first inversion major triad. Here we go. That's just intonation, here's equal temperament. Right? Isn't it something that these things we don't think of as out of tune in equal temperament, when we compare them to just intonation, we can really hear, especially with a simple tone like this, how many beats there are in it, which is kind of cool and amazing. Now this has been a really almost esoteric episode for us, we haven't really talked at all about what do we do with any of this, but fear not, because our next episode is actually gonna be on teaching intonation. And Leah, I'm so excited that you're gonna help with that, because that's something you do quite constantly in your day-to-day life, yeah? 
0:50:10.9 LS: I live and breathe it, yes.
0:50:16.5 DN: Wow. Excellent. Excellent.
0:50:17.8 GR: Well, thank you all for joining, and a special thanks again to David Kazimir for showing off the Brombaugh organ at Oberlin's Fairchild Chapel, and we'll see you all next time.
[music]
0:50:34.6 LS: Notes From the Staff is produced by uTheory.com.
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Interval Ear Training

In this episode, Greg Ristow and David Newman talk about the value and role of intervallic ear training, why it's time to move beyond Here comes the bride, and ways of teaching intervallic hearing that build fundamental skills for sight singing and dictation.
Links:
Karpinski, Gary. "A Cognitive Basis for Choosing a Solmization System," Music Theory Online, Vol. 27, No. 2. June 2021. https://mtosmt.org/issues/mto.21.27.2/mto.21.27.2.karpinski.html
 
Transcript
[music]
0:00:21.2 Gregory Ristow: Welcome to Notes from the Staff, a podcast from the Creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:35.5 David Newman: Hi, I'm David Newman, and I teach voice and music theory at James Madison University. And I write code and create content for uTheory.
0:00:43.4 GR: Hi, I'm Greg Ristow. I conduct the choirs at the Oberlin Conservatory of Music, and I'm the founder of uTheory.
0:00:49.9 DN: Thank you listeners for your comments and episode suggestions. We love to read them, send them our way by email at notes@uTheory.com, and remember to like us and subscribe wherever you get your podcasts.
0:01:01.7 GR: So today we'll be talking about interval ear training. And interval ear training is central to many teachers' and textbooks' approaches to sight singing and dictation. But the title of this episode is maybe a little bit misleading because research in music cognition suggests that for most common aural skills, ear training tasks we process notes by their relationship to a tonic or by their position in a scale rather than by actually hearing adjacent note to note intervallic relationships. So in our conversation today, we'll look at this research on how we hear and the role that intervals play in that hearing. We'll talk about why classic techniques we're teaching intervals can actually undermine students' reading skills. And we'll look at ways of teaching intervals that instead compliment and strengthen students' aural skills. It's a lot to get through in the course of an hour. [chuckle]
0:02:03.2 DN: It is.
0:02:04.5 GR: But David and I have agreed to play particular roles on this. So I'm going to, I'm gonna be sort of the the playback, keep us on track role and David's gonna be the the color commentary, [chuckle] role.
0:02:14.0 DN: Playing to our strengths.
0:02:15.4 GR: Playing to our strengths for sure, for sure. It is hard to talk about or even to think about how we hear, so much of how we hear music is really innate, that we don't, especially for someone with a well-developed ear, "how do I know how I know what I'm hearing?" is a hard question to answer.
0:02:40.1 DN: Yeah.
0:02:40.8 GR: And fortunately we have scientists and researchers who've been looking at exactly this question for a little, I don't know little over 40 years now. And what they have pretty consistently found is that when someone who is experienced in a particular musical culture, and so let's say broadly Western music, music that exists within the notes on a Western piano.
0:03:17.7 DN: An equal tempered scale.
0:03:19.2 GR: Yeah. A tempered major-y minor-y or rotation of its scale as opposed to for instance, some of the Turkish collections that have more notes in the scale than we have and notes that don't exist on our piano. So when someone is encultured in a musical system, when first they start hearing notes, the primary thing that their brain does is seek to determine a central pitch, what we would call a tonic and that's known in music cognition as the primacy hypothesis. The idea being that David, if I throw a few notes at you, before you're going to do anything with those notes, your mind is going to say, "what could potentially be tonic given these notes?" And we're gonna hold onto them.
0:04:20.8 DN: We contextualize it.
0:04:22.5 GR: Exactly. We seek to find the context in which that's occurring and will tend to hold onto our belief of that central note as long as we reasonably can even through the first few notes that contradict it.
0:04:39.1 DN: Yeah. I even think this is central to so much of why we enjoy music. And so if you enjoy music, you probably do this.
0:04:47.8 GR: Yeah, absolutely, absolutely. Yeah, yeah. And it should be said we're saying this and let's just imagine that if I'm someone with really strong absolute pitch. And even in those cases although yes, someone with absolute pitch will know immediately, yes I'm hearing these particular letter names. They are also still working to contextualize them within some sort of tonal framework. If that's something that you're interested in reading about, one of my favorite articles on this is by Gary Karpinski and it's his, it just came out a couple of years ago in Music Theory Online. We'll put the link in the show notes, but this is freely accessible online and it's "A Cognitive Basis for Choosing a Solmization System." And in the first, I don't know, 15 or so paragraphs of it Karpinski goes through and just summarizes all of the research that has occurred over the past 40 years to this.
0:05:53.0 GR: And the big conclusion that he lists there is, and I'm gonna quote here, "These studies and observations lead to the conclusion that while attending to the pitches of tonal music, the first and most fundamental process listeners carry out is tonic inference. And from that, we can conclude that the single most immediately knowable tonal characteristic is the tonic." Now, what does all this have to do with intervallic ear training? What it really comes down to is this question of how do we actually hear music? And we really hear music based on how the notes relate to a sense of tonic. And we don't actually hear music based on the pitch relationship of immediately adjacent notes or even of vertical notes sounding together.
0:06:45.6 DN: And in fact, I know even for myself that if I'm singing a tonal melody I probably could very easily tell you what generic intervals I'm singing at any given time, but I would have to stop and think about what specific intervals. And when I say generic intervals, I just mean, I could tell you that I'm singing a 5th. I could tell you that I'm singing a 6th, but 6th especially, I would've to stop and think for a second to tell you what quality of 6th that was that I was singing, because I'm just going between notes in the scale.
0:07:24.5 GR: That's right.
0:07:24.9 DN: That's the simple thing. And to add intervals to that would be an additional step for me.
0:07:31.3 GR: A really great example of this is to even, to ask someone who believes they're sight singing by intervals, to take a song they know and to sing that song on the specific intervals of the song. Sing the Star Spangled Banner on specific intervals. And you get. First note, obviously, Unison. 'Cause you have nothing before. So unison, minor 3rd, major 3rd, major 3rd, minor 3rd, perfect 4th.
0:08:02.7 DN: Major 3rd, major 2nd, major 2nd. Oh gosh. Yeah, that would be a minor 6th. [chuckle] Oh, whole step, half step.
0:08:21.4 GR: Yeah. It is not how we hear. On the other hand, as you said, I think totally, yeah, very often we're we're of, oh yeah, I'm singing a 3rd, I'm singing another 3rd. Those two thirds were different, right? But, to us...
0:08:40.2 DN: They were thirds in the key.
0:08:42.3 GR: They were thirds in the key. Yeah. And as we've talked about on a number of previous episodes, our musical notation system reflects this. Our staff system with its use of key signatures is designed to show us very quickly, generic intervals, interval distance within a key and not specific interval distance or chord quality. It's really... It makes primary, this idea of our seven note key collections.
0:09:11.8 DN: Yeah. It was designed for tonal music.
0:09:15.6 GR: Because that's what it reflects.
0:09:16.6 DN: That's what music was. [laughter]
0:09:18.8 GR: Yeah. And largely still is.
0:09:21.5 DN: Yeah.
0:09:22.5 GR: And what we're getting to here is two approaches to learning and thinking about intervals. Intervals in the context of a key, which throughout this episode we'll refer to as contextual interval hearing and intervals as pure relationships between any two notes or what we'll call acontextual interval training. And if we look at the classic way intervals are taught, which I've started to call the naive approach to teaching intervals. It blends these two, it blends contextual and acontextual interval hearing without being explicit about which is which, which can lead to some real problems.
0:10:08.2 DN: Yeah.
0:10:09.9 GR: So what I mean by the classic or naive approach is the approach of saying, okay, a perfect 4th is "Here Comes The Bride." And of course, "Here Comes the Bride" comes along with context. Because it's 5, 1, 1, 1. And there are six perfect 4ths within our diatonic collection, and they don't all feel like 5, 1 and they can feel very different than that.
0:10:33.5 DN: I have a song about that. [laughter]
0:10:34.9 GR: Yeah. [laughter]
0:10:35.4 DN: We should... Yeah. That should go in the show notes too. There's an interval song as specifically about 4ths actually.
0:10:44.7 GR: That's...
0:10:45.0 DN: Some say that ascending 4th sound like, "Here Comes the Bride," but change the context and that perfect 4th may not sound the same and your song won't help as planned [laughter]
0:10:56.9 GR: Shall we just take a moment and pause and listen to it? 
0:11:00.0 DN: Oh sure.
[music]
[laughter]
0:12:18.0 GR: Yeah. And that's exactly it. That they... That these 4ths are very different. And so let's now carry that out to its dangers with dictation. So if I'm trying to do dictation and I come across a leap and I'm like, "Okay, does that sound like here comes the bride?" If it was from five to one it sure does, but if it was one of those other 4ths, it does not. And frankly, the more sensitive musical listener you are, the less another 4th will sound like the 4th of five to one. And so if we are using this approach it will disadvantage our most sensitive listeners. Okay. And so now let's flip and let's say what if we're using this for sight singing. And this is... I call this the how do you measure a mile problem? So, David, we can see each other on video, our listeners can't. But, if you wanted to measure the size of the room that you're in there, what tool would you want? 
0:13:25.4 DN: I would want a really long tape measure.
0:13:28.4 GR: Yeah, absolutely.
0:13:31.1 GR: I'm sorry, David, you only have a ruler. What's going to go... A foot long ruler, what could go wrong? 
0:13:37.2 DN: Well, it sounds like when I try and measure a room by pacing it or by measuring my foot lengths, assuming that they're about a foot, but since my feet are probably not exactly a foot, even if I had an exact ruler, I'm gonna make a little mistake every time.
0:13:57.2 GR: Mm-hmm.
0:13:58.4 DN: And if I'm lucky, the mistakes will kind of cancel each other out by the time I get to the end. But if I'm not lucky, I'm gonna end up with an incorrect number.
0:14:11.0 GR: Yep. And you will have... And if you're lucky you'll buy more carpet than you need. And if you're unlucky, you'll wind up with a couple feet of un-carpeted room. Right? Yeah. So there's this element, if we're sight singing by interval, that if I ever-so-slightly misjudge an interval, the inaccuracies can add up. But it's more than that because in fact, as we know, and especially as you know, singing early music, there are many different ways that are correct of tuning intervals.
0:14:47.7 DN: Yeah. Every single one.
0:14:49.8 GR: Every single one, absolutely.
0:14:51.4 DN: But although in early music, yeah, I know every single one. Yep.
0:14:55.7 GR: Yeah.
0:14:56.1 DN: And some more than others. Some notes are more equal than others. Like Animal Farm. Some intervals are... Yeah.
0:15:04.2 GR: And we're gonna do an episode on tuning systems coming up soon. But to give a really strong example of that, if we tune a major 3rd like it appears on the overtone series.
0:15:19.6 DN: Right.
0:15:21.4 GR: First off, we should say, the distance between a half step on a piano or any half step on a piano can be called 100 cents. And the difference between a major third as it appears on the overtone series, and the major third as it appears on the piano is 14 cents.
0:15:40.0 DN: Mm-hmm.
0:15:42.0 GR: So if, for instance, you ask someone to arpeggiate an augmented triad until they come back to the starting point with overtone major 3rds. Right? So each of those, each of those intervals is a major third.
0:15:58.4 DN: Right.
0:16:00.3 GR: You're going to add 14 cents of difference from the piano each time, which comes up to 1, 2, 3... 42 cents difference, in other words, all just pretty darn close to a quarter tone away by the time you get to the top.
0:16:16.5 DN: Right. And it's gonna be 42 cents flat. Right? 
0:16:18.9 GR: That's right. Yep.
0:16:20.1 DN: Yeah.
0:16:20.7 GR: So yeah. So we have that issue, right? With sight singing by intervals it... And then we have the issue that's more related to what we were talking about before, which is to say that, if I come across a 4th when I'm sight singing, if that's five to one, "Here Comes the Bride" is a really useful tool. But if it's not five to one, and I summon to mind, "Here Comes the Bride," I have brought with it the context of whatever note I'm starting from being five, even though it's not actually five in the key I'm in, and whatever note I'm going to being one, even though it's not actually one in the key I'm in and I've caused myself, I've had to briefly erase my tonal context to sing that perfect 4th, which is problematic.
0:17:00.6 DN: That's the most important thing about this whole conversation. If there was a clip to take out, that's the one to share and say, "Here's the main point."
0:17:12.5 GR: For me... Absolutely. Right? And this... I was joking last episode. I was like, this is the hill I will die on. Is that we cannot primarily do dictation of sight singing by intervals. It works too strongly against tonal context, which is where so much of the meaning of our music comes from.
0:17:31.5 DN: So tell me if I'm distracting from the stream of thought here. But the issue then, the problem is that when we're teaching early skills in music theory, even in aural skills, we'd still need to refer to intervals. So we kind of need the people to know what intervals are. And I guess the trick then is, how do we introduce intervals without creating these problems? 
0:18:05.3 GR: Yeah. Yeah. Absolutely. For sure. And a related, but different thing is, I think that it seems, it is such a simple idea that if I know all of my intervals, I should be able to sight sing anything or do any dictation.
0:18:21.4 DN: Right. That's a lovely thing in imagination.
0:18:25.1 GR: In... But that ends up failing in practice. That's right. That's right.
0:18:29.1 DN: Yeah.
0:18:29.2 GR: Yeah. Yeah.
0:18:32.6 DN: So instead we teach frameworks.
0:18:35.5 GR: Right.
0:18:35.6 DN: For tonal music, we teach for frameworks.
0:18:38.5 GR: Yeah. And you might be rightly at this point saying, should we even bother to teach intervals in an ear training context? 
0:18:48.6 DN: And I think we have to, but the question is how do we do it? 
0:18:53.2 GR: Yeah. No, I will tell you, in all of my undergraduate ear training, we had zero intervallic training.
0:19:01.1 DN: Uh-huh.
0:19:02.9 GR: That's not true. In the last semester when we got to atonal stuff.
0:19:07.6 DN: But did you do that? 
0:19:07.8 GR: There was some intervallic training.
0:19:09.9 DN: But did you have it in written theory at least? 
0:19:12.5 GR: Oh, for sure. For sure. Yeah.
0:19:14.7 DN: Yeah. And then I think, again, like it's not so hard in that exercise that we did earlier to name the generic intervals.
0:19:25.3 GR: Right.
0:19:25.3 DN: And I think that's something that's pretty straightforward. And of course, if I know the generic intervals and I see a third going up and I see that the second note is raised from what it was going to be in the key, then I know, "Oh, that's gonna be different."
0:19:42.5 GR: Yeah.
0:19:42.5 GR: Yeah, yeah.
0:19:44.3 DN: It's probably gonna be a major third.
0:19:47.3 GR: Right, but you know for me, even when I sing a song I know on specific interval names, if I'm being honest, I'm not really hearing the specific intervals, I am hearing...
0:20:00.4 DN: No.
0:20:01.1 GR: The generic intervals, intervals within a key and using my knowledge of music theory to label those specific intervals.
0:20:07.0 DN: Yeah, yeah, that's a thing that I don't even think about.
0:20:10.3 GR: Yeah, yeah, so let's... So again coming back to this idea of the classical or naive approach to interval training, the learn a name of a tune for each interval approach.
0:20:20.8 DN: Oh, I just try and get people not to do that.
0:20:25.0 GR: I do too, I do too, because I think it conflates contextual intervallic hearing, intervals within a key with acontextual intervallic hearing, pure relationships between two notes. But I do think there's value, and as you were just saying, in learning intervals within the context of the framework of a key or scale. And also, I think there is value in learning intervals out of that context as pure sonorities of relationships between notes, especially if we're concerned about tuning in context. For instance our... If we're playing in an orchestra, if we're, basically anything other than a pianist.
0:21:12.2 DN: Right, barbershop.
0:21:14.6 GR: Then we have to make decisions about how we tune our intervals. So I thought it would be just, it would be great to be really practical and go through a bunch of exercises of contextual intervallic practice and of acontextual intervallic practice. Sound good? 
0:21:36.5 DN: Sure. Yeah.
0:21:37.8 GR: Okay, great. So these exercises, although we're gonna demonstrate these pretty much throughout in major keys, in practice, I also like to do these in harmonic minor as well, because that'll introduce fun intervals like the augmented second and diminished seventh that don't exist in the major scale. And although we'll generally demonstrate these using scale degrees, movable solfège works the same way, pick your system of choice. And although this is a little bit evil, when I do these exercises with my students, I like to switch between a functional system like scale degrees or movable solfège, and a fixed system like letter names or fixed Do, because I want my students at all times to be thinking...
0:22:32.2 DN: To suffer...
0:22:33.9 GR: To suffer, yes, yes.
[laughter]
0:22:35.8 GR: Although I want them at all times to be thinking about both the, sort of, the abstraction that function gives us, and the specificity that note names or playing it on an instrument give us.
0:22:55.8 DN: And I have just started atonal music, aural skills with my class in the last week, and I told them if their brains are hurting, it just means they're growing neurons, that their brain should hurt a little bit, it's probably good.
0:23:10.8 GR: Yeah. Yeah.
0:23:12.4 DN: Growing neural pathways, they already have neurons.
0:23:15.6 GR: Yeah. Yes. Yeah. So let's just dive in and let's... Shall we do some exercises together, David? 
0:23:23.3 DN: I am always game for exercises.
0:23:25.5 GR: Okay, great, I'm gonna give you a pattern, and would you just take it and continue it as you know it, yeah? 
0:23:30.6 DN: Okay.
0:23:31.3 GR: Great. [Singing] 1 to 2 is a Major 2nd, 2 to 3 is a Major 2nd
0:23:42.6 DN: [Singing] 3 to 4 is a half step. Or I should say... minor 2nd. 4 to 5 is a Major 2nd. 5 to 6 is getting high... Major 2nd. 
[vocalization]
0:23:55.5 GR: Why did I pick this key is...
0:23:57.5 DN: [Singing, drops octave] 6 to 7 is a Major 2nd, 7 to 1 is a minor 2nd.
0:24:02.3 GR: Great, excellent. We're in the key of D, would you do the same game on letter names, please? 
0:24:06.2 DN: Okay. Is that D? 
0:24:08.8 GR: Yes.
0:24:09.4 DN: Okay. D... Oh gosh.
0:24:14.3 DN: It's morning.
0:24:14.4 GR: It is morning.
0:24:15.1 DN: D to E is a Major 2nd, E to F# is a Major 2nd, F# to G is a minor 2nd.
0:24:25.1 GR: Et cetera, yeah, yeah. Good. And of course, and for me, by doing that first with numbers or solfège, right? Do-to-RE, is a major second, RE-to-MI is a major second, the words are always the same no matter what major key you're in if you're using a movable system, but they change when you're using letter names or fixed Do. And to me, there's huge value in thinking about that. I also love to do this game with instrumentalists and have them play on their instrument D, E and then sing major second, E, F sharp and then sing major second.
0:25:05.9 DN: Great.
0:25:06.2 GR: So the analytical part they sing and the note naming part they play.
0:25:10.3 DN: Well, I noticed two things about doing that is, having just gone through it with just saying the interval names, which of course, I know very well. When I did it again with letter names, I've noticed two things happen is one, I already knew what that pattern was 'cause I had just done it. And in thinking about what the next note was, I already knew what that pattern was and therefore I had another contextual clue, just in recognizing my own brain process, I had another contextual clue about what that next note would be. And secondly, because I play the piano, I also didn't have to think about what I just, I know what that next interval is going to feel like. And I think I was envisioning a piano keyboard, and I know that we have the keyboard advantage...
0:26:15.6 GR: Sure.
0:26:16.2 DN: In music theory, but also a keyboard bias sometimes but I just was recognizing that both of those skills were...
0:26:26.1 GR: Coming into play.
0:26:27.0 DN: Contributing to my ability to do the exercise.
0:26:30.1 GR: Yeah.
0:26:30.3 DN: Just in terms of thinking of how, how we think and that's likely to be the skills that are also being developed in the students that are working with it.
0:26:38.1 GR: That's right. And the other thing is in giving it the specific letter names, whether we realize it or not, we are practicing interval building in a written theory context, aurally.
0:26:51.3 DN: Right.
0:26:51.9 GR: And we're also practicing interval recognition in a written theory context aurally.
0:26:57.2 DN: Yeah.
0:26:58.4 GR: That we are... Not only are we acknowledging that we have all these different seconds in a scale, we're looking at them in various different scales and naming them within the context of those keys.
0:27:11.7 DN: Can I also just explicitly add what this is doing is that you were talking about measuring a room. And so we're sitting here, we're naming a bunch of intervals in a row, and each of them is a small interval, but we're always, and it's not like measuring with a ruler, it's like taking the tape measure and extending it another foot.
0:27:32.8 GR: Yeah. Yeah. And sort of looking at each number on the tape measure as you go through the room.
0:27:38.2 DN: But we're still measuring from the same starting point.
0:27:41.8 GR: Absolutely. Yeah.
0:27:43.3 DN: Yeah.
0:27:44.2 GR: Yeah. Yeah. And you know, and with this, and with all these exercises, if you find you have a student or a class that loses tonic, that tonic shifts after a while or that has intonation problems, these are all great exercises to just, to have a drone going. Right.
0:28:01.5 DN: Right.
0:28:02.9 GR: And to just have, have a, like in this case it was D Major, have a D drone going in the background to play it against that and to just, and which can also make really beautifully explicit the feeling of each note against tonic. Of course, we just did this with seconds and we could do this with any other interval. We could do it with thirds 1 to 3 is a major third. 2 to 4 is a minor third, 3 to 5 is a... And so on and so forth.
0:28:33.6 DN: And as we said in the last episode those... That builds patterns that they need to know for other things. They? We.
0:28:43.0 GR: Absolutely.
0:28:44.1 DN: We all need to know those patterns for other things.
0:28:47.9 GR: Right. Especially the thirds. Right. Which get us towards triads, which are such a fundamental building block...
0:28:53.8 DN: Right.
0:28:54.2 GR: ...of our harmonic system. So those are... I think of those as being I call them Intervallic walks. We're gonna walk in interval up or down the scale. Right. You know, the sequencing of that seems pretty darned straightforward. Start with the second, go to the third, et cetera, gradually extend by the time you get to the seventh, things are really fun and there are only certain keys that work well. Right. Like, you gotta start on a pretty low key, it works pretty well with like a key of G A-flat, A, beyond that things get a bit ridiculous.
0:29:27.9 DN: Right.
0:29:28.7 GR: But it's still pretty darn fun. A complement to that is taking a note of the scale and finding all the intervals from that note of the scale. So let's be in this key since it's morning.
0:29:40.3 DN: Yeah.
0:29:41.7 GR: And David, here's the start of this pattern. Do to Re is a Major 2nd. Do to Mi is a Major 3rd. Would you continue?
0:29:51.3 DN: Do to Fa is a Perfect 4th. Do to Sol is a P5. Do to La is a M6. Do to Ti is a M7. Do to Do is a P8.
0:30:07.0 GR: Great. And then shoot the upside down version starting... "Do to Ti..."
0:30:08.3 DN: Do to Ti is a m2, Do to La is a m3, Do to Sol is a P4.
0:30:18.8 GR: Great. And so on and so forth. Yeah, absolutely. Absolutely. We're in the key of B flat. Would you do the version coming down on letter names? 
0:30:23.2 DN: Oh, okay. Bb to A is a m2. Bb to G is a m3. Bb to... 
0:30:33.7 DN: Wait, what I'm I doing? 
0:30:35.7 GR: Yep. You're right. You're right.
0:30:38.0 DN: Bb to F is a P4. Bb to Eb is a P5. Bb to D is a m6. Bb to C is a m7. Bb to Bb is a P8.
0:30:57.0 GR: Yeah, yeah, yeah. It engages your brain in a very different way, doesn't it? 
0:31:00.7 DN: It does.
0:31:02.0 GR: And I love that. That's why I will pretty much always do this both ways.
0:31:08.6 DN: And again, that pattern is really obvious. But then having established that pattern there's, you have another tool to do the... Note naming pattern that you've just done if you do it in that order.
0:31:25.9 GR: Right. And you know, the other thing about this, going to note names like that is a preparatory exercise for sight singing. Where we are looking at notes on the staff that have names. And yes, we could do it just by spotting the intervallic distance. This is some sort of 4th, right. But or saying, oh, yeah, I recognize I'm going to, I've spotted which line Sol is on, or which space in this case so is on if we're thinking in treble clef... But here, by doing specific names, we're reinforcing the note names of the staff we're hopefully causing all of these things to come together to be thought about in all those different ways at once. And did you stop thinking about your solfege as you were singing letter names?
0:32:22.3 DN: I wasn't explicitly thinking about solfege.
0:32:25.3 GR: Were you aware of your solfege? 
0:32:28.0 DN: If you had asked me at any moment where I was then I would... Yes, I would know.
0:32:32.0 GR: Yeah. This to me, is, I think the big truth about this right? Is that exercises like this, we have to know where we are in the scale to do them.
0:32:40.0 DN: Oh, right. Yeah.
0:32:40.5 GR: Even if we're not explicitly naming out loud where we are in this game.
0:32:46.0 DN: Yeah. Yeah, that's good. And then that solves the dilemma that we were talking about earlier, of how do I teach intervals without confusing people about... Yeah. Without introducing a problem into the situation.
0:33:06.0 GR: Yeah, yeah. Now, that exercise, it's a little less obvious of how you continue from there. Like what's the next step with that exercise? I love to do, to continue this one in two different ways. To take Do and we still do intervals to Do or to tonic. But let's start the pattern. Let's work in the octave of five to five instead of in the octave of one to one.
0:33:35.8 DN: All right. That's a very Dalcroze thing.
0:33:38.0 GR: It is a very Dalcroze thing. So let's imagine that we were in this key. [Piano] So there's a one. We're gonna work in the octave of one to five. So we're gonna go 1 to 5 is a perfect 4th, 1 to 6 is a minor third, would you continue? 
0:33:54.5 DN: Oh. 1 to 7 is a minor second. 1 to 1 is a unison. Ooh, that rhymes. That should be a song. 1 to 2 is a major second. 1 to 3 is a major third. Then the rest feels like just what we were doing the...
0:34:13.8 GR: The same. Exactly. Exactly. Yeah, yeah, yeah, exactly. And so, and as you're discovering the farther up we move 1, the harder that becomes, right? So that if we say, now, let's say, this is 1.
0:34:27.8 DN: 1.
0:34:31.8 GR: And okay. And we're going to work in the octave of 3 to 3. So starting from 1 down to 3. Go ahead, David.
0:34:38.2 DN: 1 to 3 is a minor sixth. 1 to 4 is a perfect fifth. 1 to 5 is a perfect 4th. 1 to 6...
0:34:48.1 GR: Etcetera, etcetera. Now, do that in the key of A flat. Can you do that in letter names? 
0:34:52.3 DN: Oh gosh. A to C is a minor sixth. Oh sorry, A flat to C, A flat to D is a...
0:35:02.9 GR: D? What kind of D? 
0:35:03.4 DN: D flat. Thank you. A flat to... Yeah. Woof. You know, gotta visualize my keyboard.
[laughter]
0:35:08.8 GR: Yeah. Yeah, yeah. And it's, you know, and this is also a good one because, it works pretty well to do this game, as you introduce the various keys, right? So like you can... Like, you know, once you get two sharps and two flats, this game is really easy to do from like B flat as a low one just going up, or D, right? And yeah. Okay. So there's this version of it, and then the related version of it is, instead of moving 1 up or down, take any note of the scale as the note we're bouncing to and from. So for instance, let's come to this key. [Piano]
[laughter]
0:35:52.9 GR: And now we're going to go to 5 always. Like this. 1 to 5 is a perfect fifth, 2 to 5 is a perfect 4th, would you continue? 
0:36:03.8 DN: 3 to 5 is a minor third. 4 to 5 is a major second. 5 to 5 is a unison, which doesn't rhyme. 5 to 6 is a major second. 5 to 7 is a major third. 5 to 1 is a perfect 4th.
0:36:25.4 GR: Yeah, exactly. Exactly.
0:36:26.2 DN: Did I do that right? 
0:36:27.1 GR: You did that. Yes. You absolutely did. Yeah. Yeah. And then the reverse is just 1 to 5 is a perfect 4th. 7 to 5 is a major third. 6 to 5 is a major second, etcetera, right? And similarly, we can switch to note names here. I'm in C major, so that...
0:36:41.4 DN: I should practice these.
0:36:43.3 GR: Pretty easy. Yeah, yeah, yeah. Right. And there're...
0:36:46.1 DN: I could use some refresher course.
[laughter]
0:36:50.6 GR: And so right of course you have all the various varieties of those and yeah, and I quite love those. And if you wanna get really crazy, you can combine the two of them. And were we working in the compass of 1 to 1, right? The range of 1 to 1. But we could work instead in the compass of like say, 5 to 5, going to 2 every time.
0:37:13.1 DN: Right.
0:37:13.4 GR: Right. So in other words, let's say we're in this key, [piano] 1 and we're gonna do, 5 to 2 is a perfect fifth. 6 to 2 is a...
0:37:25.7 DN: Oh my gosh. I don't even think of that. All right. Wait. 5 to 2, 5 to 2 is a perfect fifth. This requires so many levels of thinking.
0:37:40.4 GR: Yes, it does. Yes, it does.
[laughter]
0:37:42.1 DN: So 6 to 2 is a perfect 4th. 7 to 2 is a minor third. 1 to 2 is a major second, 2 to 2 is a unison. 2 to 3 is a major second, 2 to 4 is a minor third, 2 to 5 is a perfect 4th.
0:38:06.7 GR: And sing 1.
0:38:08.3 DN: 1.
0:38:09.3 GR: Yes. Yes. Always sing 1 at the end of that exercise to give a sense of closing it off. Yeah.
0:38:18.2 DN: And, yeah, yeah. And then just to make sure that you've kept your tonic in mind, that would be a good diagnostic...
0:38:25.3 GR: Yes. Yes.
0:38:25.8 DN: Tool to see if you've lost track of your tonic.
0:38:29.2 GR: Yeah. Yeah. And if we were in F sharp major, right? So...
0:38:38.6 DN: Oh God! 
0:38:39.2 GR:  But you see, right. And you just see how you can layer this up and up and up and effectively.
0:38:45.6 DN: Yeah.
0:38:46.8 GR: I think about these as just being exercises to prepare us for whatever might come at us in the context of a key.
0:38:55.2 DN: It's great. And listen, this is absolutely tangential, except that I'm totally obsessed with Duolingo. And I'm also going to Poland soon. And so I've been doing Polish and Polish is hard. And, unfortunately I started learning Polish on Duolingo a couple years ago, and then I kind of stopped doing it for a while and now I started again. And now it thinks I know more than I know.
0:39:18.6 GR: Than you actually know. Yeah.
0:39:20.6 DN: And throws really hard things at me. But I was just thinking this feels like that, you sit and you do something and you go, well, I don't remember. And you... But the process of doing it, the process of suffering through it a little bit, is the process that makes us better. It's just great. I'm... That's probably just stating the obvious but, when I think of something like this that where when it feels challenging, is the part where a part of us tends to want to go, ooh that's scary. I'm gonna avoid it. Those are the times when we should dive in and try it, and by doing it, we're gonna get better and it will get easier.
0:40:07.0 GR: Yeah. Just lean in a little bit to that. Yeah totally. There is, the mind is very good at self-protection, right? It wants to, it will happily divert from things that make us recognize our limitations. And it does take a little bit of self managing, to lean into those. Or a teacher. Right? I mean, I think this is the real value of a teacher who picks something for us to do, rather than letting us just keep playing the music that we already play. Well, because it's so fun to do.
0:40:46.3 DN: Right.
0:40:50.0 GR: Okay. So, these can be extended. The other thing of course, you can go from these to then doing this with triads, right? Like, let's say we're in this key and doing, [piano] "one, three, five, major I, two, four, six minor ii, three, five, seven, minor iii,' and so on and so forth.
0:41:12.2 DN: Yeah.
0:41:15.7 GR: Which of course is preparing students to, both... Is helping remind students of the qualities of each triad within the scale. But also of their spellings in scale degrees or, solfege. Do Mi Sol, Major I; Re Fa La, minor ii; Mi Sol Si, minor iii. Fa La Re...
0:41:39.2 GR: Right? And especially if you're a theory teacher who is, who loves scale degrees, but whose aural skills classes are taught in solfege, this is a great way to help your solfege fluent students with their roman numeral spelling and identifications.
0:41:55.4 DN: So it just occurred to me that I can make another version of my court spelling song, which I wrote to teach court spelling, but I could, change it from.
Do Mi Sol, Fa La Do, So Ti Re Ti Sol, Do Do Do.
0:42:15.6 DN: You could then do major I, major IV, major V,' and then 1,1,1.
0:42:20.3 GR: Yeah, totally yeah.
0:42:25.0 DN: Interesting.
0:42:25.9 GR: And so, that gets pretty easy, pretty quickly. Though. Same rule applies, right? [piano chord] 'B, D sharp, F sharp, major I; C sharp, E sharp, G sharp, minor ii; D sharp, F sharp, A sharp Right? 'Cause we're, because I put us in B major.
0:42:44.6 DN: But I can hear that you're already, but you're already recruiting other things that you know.
0:42:49.4 GR: Right? 
0:42:50.4 DN: To do that.
0:42:51.2 GR: Yeah. And then, having done that, I love to then do that in inversion. So let's move first inversion triads up the scale, right? I called these triadic walks, in the same way that we had interval walks, right? So, one, three, six, minor vi; two, four, seven, diminished vii; three, five, one major I, four, six, two, minor ii. And then B D sharp, G sharp, minor vi, C sharp, E, A sharp diminish vii, D sharp F sharp, B major I, E, G sharp, C sharp, minor ii, right? Or second version, one, four, six, major IV, two, five, seven major V, et cetera, right? 
0:43:58.2 DN: Yeah.
0:44:00.6 GR: And then, spelling them as well. And then of course, dealing with the seventh chords, and the seventh chords in inversions are just delightful, right? Especially like your 4/2 position chords.
0:44:12.4 DN: Right? 
0:44:13.1 GR: Right. Yeah. So anyway.
0:44:16.7 DN: There's certainly unlimited potential for making your students suffer in a good learning fashion.
0:44:25.5 GR: Yeah. And I always like to say to my students, well, you've always gotta walk places. You've always gotta drive places. Or, you're making dinner or you're doing dishes, or you're vacuuming or whatever, folding laundry. Here's something you can just do like, just pick one of these and go and gradually build up your fluency.
0:44:49.6 DN: Now there's another pattern. I don't know if it fits with these, but it's an alternative. I did... John Peterson showed me a pattern where you, look at all the half steps and you sing the half steps first. So you sing, you take toe and you sing Mi to Fa is a half step and Ti to Do is a half step. And then you do, Do to Re is a major second Re to Me is a major second. You do Fa to So is a major second. So to La is a major. You do all the half steps, you do all the minor seconds, then the major seconds, then the minor thirds.
0:45:26.2 GR: Yeah.
0:45:26.8 DN: Then the major thirds. But you're doing them out of order.
0:45:30.7 GR: This is beautiful within this. I love that. I love that. Oh. That is great.
0:45:38.6 DN: But then you really have to think about, it's particularly useful just right at the beginning that you're cementing where those half steps are.
0:45:47.4 GR: Yeah. Well, but then also to, with each of the intervals. I'm gonna add this to my... David, thank you for that. I'm gonna add this to my list. And it is worth just being really explicit here about the fact that these are exercises, these are not especially musical things and I trained as a pianist and so to me these are like the Hanon exercises in piano [plays piano]  they're just these different little finger wiggling patterns, that effectively force us to get familiar with all the possible ways of wiggling our fingers. And this is that for ear training.
0:46:43.9 DN: And on top of that, sorry, that just connected to a thing that I was just talking to. I have a former student who's a wonderful, middle school choir director and college choir director in Virginia, Tim Drummond. And we were talking about intervals 'cause I told him we were doing this podcast and we were talking about intervals and solfege and we were talking about the fact that you really, the goal, if you compare it to reading, just doing one interval at a time is reading one phoneme at a time or one letter at a time. And, ideally we want to broaden to seeing words. And those Hanon exercises allows you to see this finger wiggling pattern as a word. And similarly we want to develop some of that with singing, maybe that's out of the context of intervals.
0:47:40.2 GR: Okay. So David, one other fun thing I like to do with this, is what I call coded melodies. And so, I've written here, do you see on our shared Google doc, do you see my outline for a coded melody? 
0:47:53.5 DN: I do. Yeah.
0:47:53.6 GR: So a coded melody, you're given the starting solfege or scale degree. And then you're given a series of generic intervals from that and part of the challenge is like you'll see plus one and your instinct is to go up a second, but plus one means just a unison. So just beware.
0:48:12.6 DN: Okay.
0:48:13.8 GR: Right. Which is our weird system. So I'll just read off this one to our listeners.
0:48:19.9 DN: This could get confusing then.
0:48:21.8 GR: It does, but so are intervals. Right? So, here's the coded melody for you. Do plus one plus two minus three plus two plus two plus two plus one plus two minus two minus two minus two plus two minus two minus two plus two. And so now...
0:48:40.3 DN: Okay, well as soon as I got to the third interval, I recognized it.
0:48:42.8 GR: Of course. Of course. But would you sing it for us on those interval? And actually would you turn it into specific interval names and let's put it in this key.
0:48:52.9 DN: So Do unison, major second, minor third, minor second, major second, major second. Or no, sorry. Major second, unison, minor second, minor second. Major second, major second. I have to put my finger on them. So I keep track of myself. Major second, major second, minor second, minor second.
0:49:26.0 GR: Yes. And part of the challenge of that is David's looking at like plus two, minus two minus two, minus two plus two. And each of those twos are different. There are different kinds of twos. And so you really have to keep track as you're doing that of, and there was that moment where you sang major second unison, Maj--minor second. Right? 
[laughter]
0:49:53.8 GR: As you went from three to four, from me to fa there.
0:49:57.4 DN: And what happened in my brain? I didn't think, ooh, this sounds like a minor second. I thought, I'm going from mi to fa, I have to sing a minor second.
[laughter]
0:50:07.1 GR: Yeah. But it does then start to draw on both of those things of, "Oh right, that's mi to fa. That does sound a minor second."
0:50:14.3 DN: Which, and the moment we start to sing more complicated music, we need to have sort of both of those strategies at hand because the music that we sing is going to modulate. [laughter]
0:50:26.6 GR: Yeah. And here, I want to come back to why do I torture my poor students and have them sing these things both on letter names and on scale degrees. It's because by going through this kind of series, when a student is doing something like, [piano chord] D to F sharp is a major third, E to G is a minor third, they're also thinking two to four is a minor third. But there's also this awareness that that could be three to five is a minor third, at which point we could have modulated down a whole step, granted it's a weird modulation. But there becomes this explicitness of, "Oh yeah, I recognize that. I've seen D two F sharp as one to three. I've seen it as four to six. I've seen it as five to seven. I've seen it as six to one in F sharp minor. I've seen it as all these different things." And what that opens up then as we talk about more complex music, is this potential to take any combination of two notes and to recontextualize them in a different collection, a different scale, a different key which opens up then that world of modulation and the world of mixing between major and minor and all of that wonderful stuff.
0:51:51.7 DN: Yeah. And re-contextualization is the source of all goodness in music.
0:51:56.8 GR: It is. That is heaven for me. Honestly.
0:52:00.1 DN: Hyperbolic, but... [laughter]
0:52:01.6 GR: I don't know. Hyperbolic, yeah. But like... it's when you stand still and the world changes around you, that is an experience that we don't get mostly in life, but we can have in music, and it's magical.
0:52:19.1 DN: And Taylor Swift exploits it all the time. [laughter] Although she's just exploiting... Here's what this little melodic fragment sounds like in this harmony. And now I'm gonna change the harmony and now I'm gonna repeat this melodic fragment one more time with a completely different harmony. And we obviously love that, she sells a lot of albums.
0:52:43.1 GR: Yeah. No, I love that and let's be honest, that trick is, we find that in Beethoven as well like, it's... That's great.
0:52:53.4 DN: Yeah.
0:52:56.1 GR: So, okay, all of these have been contextual intervallic training exercises of intervallic training within keys. We can also do acontextual intervallic training. And I think there's real value to this, especially for learning intonation. And so I thought maybe just to share a couple of quick exercises for this, brass players are especially familiar with this game. There's a series of exercises called the Remington exercises. And the way the Remington exercises work is you start on a note and you work chromatically down going between that note and a half step below back to the note, whole step below. Why am I describing this when I could just be singing it, David? But as far as the Remington exercises usually on instruments you go, doo-doo-doo, which is a minor second, doo-doo-doo major second, minor third, major third, etcetera. And I love to do... So I learned these from brass players, by the way, Emory Remington was a professor of trombone at the Eastman School of Music for ages and ages and ages, and has a room named after him, the Remington room on the ninth floor of Eastman's Annex, which is totally random, which was at one point the basketball court. And prior to that was the dance studio when Martha Graham, when Eastman had a dance program, and when Martha Graham was on the dance faculty of Eastman.
0:54:33.3 DN: I met her.
0:54:35.1 GR: You met Martha Graham? 
0:54:36.2 DN: I did.
0:54:36.8 GR: Oh my gosh.
0:54:37.5 DN: In Spoleto in 1989, in Charleston.
0:54:41.4 GR: Yeah. Near the end of her life.
0:54:43.3 DN: Spoleto Festival in 1989, I think.
0:54:47.3 GR: Amazing. Amazing. Anyway, so these Remington exercises, I do these all the time with my choirs. And the way I do them is we start from a mid-range note, usually F or F sharp, let's take F sharp. And I have them sing half steps working their way out. So we go. Half step, half step, whole step, whole step, minor third, minor third, major third, major third etcetera, up to the seventh. And as they go get good at that, I have them do it in canon. So in other words, canon at one note. So I'm gonna do that with a piano and myself. Minor, let me put my... Here. Minor second, minor second, major second, major second. Or go in opposite direction. So some go up, while some go down, etcetera, etcetera. And, always as I'm doing this, when I'm doing with a choir, I conduct it. And anything that's ever so slightly out of tune, I just freeze on that until we find the exact tuning of it and then we come back. Yeah.
0:56:24.7 DN: Of course, the danger is so within, what is the exact tuning? [laughter]
0:56:29.2 GR: That's right. That's right. And I'm so glad you asked this. And so when I'm doing this exercise, I will take the just intervals for each, so the minor third higher than the piano, the major third lower than the piano, etcetera. And yeah, we're gonna do an episode on tuning systems and so we can dive into that more there, but, Yeah. For me, that is really about helping a choir to hear... and this is why brass players do it so much because they are really trained to hear those overtone intervals.
0:57:09.3 DN: And they have to.
0:57:10.8 GR: And they have to, because of how their instruments work, the fundamental is so present that we hear any lack of tuning much more strongly. And because of the shape of the bell, the dampening of every other partial, we hear intonation so much more clearly with those. So yeah, anyway, Remington exercises, and you can see how those can play out in a variety of ways. So I learned this from a student of a student of Nadia Boulanger which as I said before is like everyone in the world is a student of a student of Nadia Boulanger. So, she had this exercise I am told, where she would play an interval at the piano and you had to name it, using the distance in half steps of that interval. So a minor second would be called a one, a major second, a two, because they're two half steps in and a minor third a three, a major third a four, a perfect 4th a five, an augmented 4th a six, and so on and so forth. And she started with just half and whole steps. So one versus two. And the way this works is I'm going to play and you are to listen, not for the separate notes, this is very important in this exercise. Do not concern yourself, but intentionally try to pay no attention to hearing the two notes, the two distinct notes you hear. Instead, would you listen to how they rub with each other? 
0:58:46.4 DN: Right.
0:58:47.4 GR: Would you listen to the sound of their relationship rather than to the sound of each note? 
0:58:53.0 DN: So should I be explicitly listening for the beating between them? 
0:58:58.5 GR: Effectively, yes. Imagine you were kind of a tuner and you're listening to... Yeah. So shall we try this? 
0:59:04.5 DN: Sure.
0:59:05.2 GR: Just ones and twos. So just the half and whole steps. Here we go.
0:59:07.8 DN: Should I answer? 
0:59:12.9 GR: Yes. You should say it loud. Either one or two, yes.
0:59:14.9 DN: Right. One. Oh yeah, two. One. Oh, sorry, Two. One. Two. Two. Two. Two. One.
0:59:45.8 GR: And so on and so forth.
0:59:46.7 DN: Suddenly that becomes more... That's interesting. That is not an exercise I've done before, especially on the last two, the beating became very apparent.
1:00:01.9 GR: Yeah. Yeah. And the more you do this, to me, each interval has its own color. And in this kind of exercise, you really can't... You can't be thinking about key so much. 'Cause the key is constantly changing around you.
1:00:20.5 DN: Right.
1:00:21.9 GR: And you actually start to focus in on what the interval itself sounds like.
1:00:29.0 DN: It is, it's a focusing exercise. That's great.
1:00:34.0 GR: Yeah. I love this exercise. I adore it. And so she would do ones, twos, then she'd do threes, fours. So major minor thirds. Then she'd do one, two, three, four.
1:00:44.8 DN: Right.
1:00:45.4 GR: Then she would do fives and sevens. So perfect 4th versus perfect fifth.
1:00:53.6 DN: Right. Ooh, that's... Those are astoundingly tricky.
1:00:58.7 GR: Those are astoundingly tricky. Absolutely so. Absolutely so. And to be clear, I believe those are astoundingly tricky for one primary reason, if I play a perfect 4th, this note in it has the overtone, an octave higher. So you're hearing this perfect 4th and this perfect fifth. They're both present, but the perfect 4th is under. If I play now a perfect fifth, this note has this octave in it. So you're hearing a perfect fifth and a perfect 4th. So it's impossible to play on an overtone rich instrument. It's impossible to play a perfect 4th and not hear a perfect fifth. It's impossible to play a perfect fifth and not hear a perfect 4th.
1:01:44.8 DN: Right.
1:01:45.4 GR: So you really have to focus down to the fundamentals of each note. Okay. So then... Yeah. So five and seven, perfect 4th, perfect fifth, then after that, six, eight, and nine altogether, the tritone, the minor six and the major six and then 10 and 11 together. So at which point... And then finally... Yeah, you've got everything. Right? And then having done that, you go back, and you do the whole cycle again with three notes and you're to name the bottom interval. For instance, if I play [piano cluster], that's two, two, but if I play; that's two, one, or if I play, that's one, two. And you gradually build it up that way so that you're...
1:02:45.7 DN: And you're still hearing the beating of those twos separate? 
1:02:48.1 GR: That's right. You listen for the beating. Yeah.
1:02:51.7 DN: Alright.
1:02:55.5 GR: And this training as painful as it is, that training has made me more effective than I care to admit at hearing wrong notes and out of tune notes, in choirs and orchestras. I owe a huge amount of the work I do on the podium to that kind of training of saying, oh, I should have been hearing four, three, four. Right? Or four, three, three. And I'm hearing it, right? Or I'm expecting to hear two, three, two, and instead, I'm hearing something different. And especially in non tonal contexts, this is... Yeah, in my mind I hear a chord and those Boulanger numbers popped out at me. There is a two in that chord. There is a five in that chord. There is a seven in that chord.
1:04:05.6 GR: And yeah. Anyway, it's a different way of hearing and thinking about intervals, but the combination of that with tonal contextual stuff, I find very powerful.
1:04:17.7 DN: Well, I think, as long as a strategy is useful, then having multiple strategies is just gonna make you a better musician. [laughter]
1:04:28.5 GR: For sure. For sure.
1:04:31.9 DN: Yeah.
1:04:32.8 GR: Well, we got through everything in about an hour. I feel like this was a lot. My mind actually feels a little bit tired of... I need to stop thinking about intervals for a while now. I don't know about yours. [laughter]
1:04:43.0 DN: Mine is... Yeah, mine is also running at a million miles a minute, but I'm also thinking like, [chuckle] I think I know what I'm doing in class tomorrow morning.
[laughter]
1:04:55.2 GR: Right. So, yeah. We'll soon be talking about tuning systems, and temperament, and as we found, you can't really talk about intervals without talking about that. So I think that'll be a lot of fun. But... Yeah. David, it's been fun to do some interval stuff with you.
1:05:16.4 DN: I feel once again, enlightened.
[laughter]
1:05:19.6 GR: Excellent. And yeah, I am going to take that exercise from John Peterson, and I am going to go and do it through the full interval cycle, 'cause that, what a delight that is.
1:05:33.3 DN: Yeah.
1:05:34.1 GR: Yeah. Excellent. Awesome. Well, see you next time.
1:05:37.1 DN: All Right. See you soon.
1:05:42.4 Leah Sheldon: Notes from this staff is produced by utheory.com.
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1:05:49.2 LS: With video lessons, individualized practice, and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm, and ear training.
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Teaching Intervals

David Newman and Greg Ristow chat about four ways to teach intervals in music theory, as well as how to overcome some of the challenges of teaching intervals.
 
Transcript
[music]
0:00:20.8 Greg Ristow: Welcome to Notes from the Staff, a podcast from the Creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:33.4 David Newman: Hi, I'm David Newman, and I teach voice and music theory at James Madison University and I create content and code for uTheory.
0:00:42.0 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and Associate Professor of conducting at the Oberlin Conservatory.
0:00:47.8 DN: Thank you listeners for your comments and episode suggestions. We love to read them, send them our way by email at notes@utheory.com and remember to like us and subscribe wherever you get your podcasts.
0:01:00.1 GR: Today we'll be talking about teaching intervals, teaching reading and writing intervals more so than teaching the oral side of intervals, which we'll save for another episode and this David, I find to be one of the most challenging things to teach in fundamentals of theory.
0:01:17.0 DN: There's certainly a lot of approaches to use and picking one is hard.
0:01:22.5 GR: Yeah.
0:01:23.1 DN: And doing them all is also hard.
[chuckle]
0:01:24.8 GR: Yeah, for sure. For sure. And there's just a lot involved too, right? I mean, it's like you've got the generic interval size. You've got the specific size or quality, you've got the inversions, you have the compound intervals, consonance and dissonance. It just adds up and it's one of those concepts that it seems like, I often forget to budget enough time for because there's almost always a next step.
0:01:56.0 DN: And it's one of those foundational concepts that if you are struggling with it, you're gonna struggle with everything else.
0:02:02.7 GR: Yeah, for sure. For sure. And I find it's also one that can be hard to motivate students to learn, because if you're not careful, it feels really like a terrible set of math problems.
0:02:13.2 DN: Yeah. Also, it's really easy to do if you have plenty of time but it's, you need to know it better than that. You need to know it so well that it doesn't take you time.
0:02:26.2 GR: Yeah and I think for a lot of us who are teaching it there's also that challenge that both Leigh VanHandel and Melissa Hoag talked about of we already know it so well, it's really hard to conceive of what it's like not to know it.
0:02:40.2 DN: Yeah. And there's all these extra concepts involved, the letter names and...
0:02:46.2 GR: So I guess one of the things that I think about a lot is this challenge of how do we keep the teaching of intervals musical, right? 
[laughter]
0:02:55.6 GR: I think I'm gonna be really honest here and say, I think the first 15 times I taught intervals it was the dullest thing. I remember saying to classes, I'm sorry, this is gonna seem really boring, but it's really critical. As like a motivator, and I guess it's an okay motivator but there may be better ways the more I've taught it recently I've focused a lot on ways to keep it musical and make it musically relevant.
0:03:25.3 DN: Yeah. Yeah. And of course we've also had... We've talked to people this just recently about other ways of making it fun, but making it fun is not necessarily the same thing as making it musical. And making it musical is certainly more compelling.
0:03:40.4 GR: Yeah. Yeah. And if you can do both, all the better, right? Yeah.
0:03:44.5 DN: Right.
0:03:45.2 GR: Yeah. So I guess I don't know. I'd be curious your take on this. For me, I spend a lot more time teaching when I teach intervals now than I used to talking about consonance and dissonance really early on and talking about intervals as a way to get into how notes work together or work against each other.
0:04:06.3 DN: Ooh. I think that's fabulous. Yeah. And I think we we're... We said, we're just gonna talk about the written theory of things today, but the intervals that are most fundamental to our physical world are those early low notes in the Harmonic series. So the octave and the fifth and the fourth. Well arguably not well. Yeah. But the fourth.
[laughter]
0:04:36.4 GR: Yeah, certainly before the third on the Overton series.
0:04:38.9 DN: Right. And those intervals are those Pythagorean, those things that are closest to the Pythagorean ideal.
0:04:49.6 GR: I feel like we should unpack some of these things, right? Like, so...
0:04:53.1 DN: Yeah. Yeah, yeah, yeah, yeah, yeah. Yeah.
0:04:54.0 GR: So when we say the Pythagorean ideal, we're talking about the, that these intervals come from ratios of frequencies or ratios of length of strings.
0:05:02.3 DN: And so when you have the, especially those notes that are close, those simplest ratios, so one to two.
0:05:08.9 GR: Which is the octave.
0:05:09.7 DN: And two to three.
0:05:11.2 GR: Which is the fifth.
0:05:12.3 DN: And three to four.
0:05:13.8 GR: Which is the fourth.
0:05:14.8 DN: Those are the ones that we're going to perceive most readily when they're perfectly in tune. And those are sounds that the, that we gravitate to. And if we can build everything else from that. And of course, when you tune a harps accord, you tune it by fifths because that's the interval that you can hear.
[chuckle]
0:05:39.7 GR: I mean, to be fair, you have to adjust some of those fifths along the way.
0:05:44.3 DN: Yes you have to adjust.
0:05:45.4 GR: Exactly.
0:05:45.7 DN: Whether you put all of that mess in one of the fifths or spread it out among four or more. Yeah. Yeah. We should do an episode on tuning systems. That would definitely be worth doing. We should add that to our list. In any case you were saying, although we said we're gonna talk about this from a written concept, we can't fully separate it out from the oral concept. And I'm getting this right in that those early intervals, which are effectively the perfect intervals on the Harmonic series have a particular sound and when we connect to that, it starts to make a lot more sense.
0:06:25.8 DN: And to some level, not in all cases. But to some level, when we're talking about consonance and dissonance, we're talking about resolution back to one of those simpler ratios.
0:06:40.1 GR: Yeah. It's interesting, right? Because of course, the third is... And especially when we talk about if we're resolving, say to a major chord versus a minor chord, and of course that minor chord, we don't get on the overtone series.
0:06:57.0 DN: Right...
0:06:57.3 GR: And it's still...
0:07:00.0 DN: Not very low down. [laughter]
0:07:00.8 GR: Yeah, 'cause it's not early on, yeah. Not as a collection of the first in notes on the series. Yeah.
0:07:07.1 DN: Although I'm discovering through some other methods that Riemann was on to something when he was making up SAP harmonics.
0:07:19.0 GR: The undertones? 
0:07:21.1 DN: The undertones. [laughter]
0:07:21.7 GR: Yeah. And that, we should also save for another episode.
[laughter]
0:07:28.1 DN: This feels like a teaser for a whole other season.
0:07:30.9 GR: Right. Doesn't it? Yeah, it's always good to have ideas for our coming episodes. Maybe we just dive into the ways that we teach this because, I know for myself, when I was first starting to teach fundamentals of theory, I taught this like I had learned it, and like I'd always taught it, and I remember observing another teacher teaching intervals completely differently, and thinking, oh, that's totally wrong, the right way to do it is this, right? And I think...
[laughter]
0:08:03.9 GR: Like everything else, the more I've done it, I'm like, oh, there are, maybe right elements to all the different ways that we can teach this, so...
0:08:12.5 DN: Right, and there are some philosophical things to consider, 'cause you need to know about intervals early...
0:08:21.4 GR: For sure.
0:08:21.5 DN: But you also don't want to learn to build your entire schema around intervals.
0:08:28.7 GR: Yeah, this is a great question. At what point do we start teaching intervals? 
0:08:35.1 DN: And of course, in most curriculum, we start teaching them very early.
0:08:40.1 GR: Usually immediately after scales, typically...
0:08:42.4 DN: Yeah.
0:08:43.3 GR: Or key signatures. The typical arrangement is, you learn your letter names, you learn things on the piano, you learn half steps and whole steps, scales, maybe major key signatures or perhaps interval since it's a classic fundamental structure.
0:09:01.7 DN: And there's a lot of chicken and the egg here. How do you start, because you need some knowledge to talk about the other things? 
0:09:09.7 GR: Right. And we don't get to introduce scales without first talking about half and whole steps. Right? So we've already touched intervals.
0:09:19.3 DN: So I don't... If I still have not solved the problem for myself, except that I think the idea of spiraling your curriculum so that you keep revisiting subjects in more depth is the only solution I've come up with.
[laughter]
0:09:33.6 GR: Yeah. Which is hard to do, especially if you're in a one semester kind of fundamental sequence.
0:09:41.7 DN: Right, and yeah, when you only get control over one little tiny part of the education.
[laughter]
0:09:51.2 GR: Yeah. I've experimented. I've moved it around actually. I have experimented with teaching intervals after triads. The good thing about doing it that way is triads are pretty inherently musical things, and there are so many ways you can connect the teaching of triads to real music and to music that students are listening to, from your very first day teaching triads, and if you teach intervals after triads, then you can talk about the intervals as growing out of triads. Oh look, we already know our perfect fifths. We already know our major and minor thirds. I'm not sure I'd do it that way again, but I will say I found it very musical to do that way.
0:10:35.2 DN: Yeah. And the tricky part is teaching all the things without intervals up to that point. [laughter]
0:10:43.0 GR: Yeah, exactly right, exactly right. Yeah.
0:10:45.4 DN: But again, we can spiral, we can talk about them, and then we can talk about them in more depth.
0:10:49.9 GR: Yeah.
0:10:50.0 DN: And we can talk about them in more depth.
0:10:52.9 GR: Yeah.
0:10:52.9 DN: If we've learned scales, then we have that first step of being able to just identify a generic interval, and we can learn that we can count one, two, that's a second, one, two, three, that's a third. Even that is one of those tricky things that is probably hard for a beginner student, is to remember to include the note that you started on when coming up with the number for the interval.
0:11:24.7 GR: Yeah, for sure.
0:11:26.7 DN: Yeah, that's definitely a common fundamentals mistake. [laughter]
0:11:31.3 GR: It absolutely is. And even with someone experienced in fundamentals, if I say, "What's a third plus a third?"
0:11:39.3 DN: Oh, that is... The math then gets ridiculous because you're saying... Yeah, it's like saying two plus two equals five and...
0:11:45.1 GR: All right, yeah.
0:11:46.8 DN: Except in this case two plus two equals three, yeah. [laughter]
0:11:51.5 GR: Yeah.
0:11:52.2 DN: Here, everything you've learned at elementary school is wrong.
0:11:56.6 GR: Yeah, so let's talk about the pedagogy of generic intervals, so when we say generic intervals, we're talking about intervals just including the letter name, so we're not concerned about whether something's major, or a minor, or perfect, etcetera, just the distance on the staff.
0:12:13.3 DN: Right.
0:12:13.9 GR: And as you said, the first challenge there is the tendency to say, okay, yeah, E minus C should be two 'cause it's two below E.
[laughter]
0:12:26.0 GR: But of course, we use one-based counting for our interval system instead of zero based counting, and so it's three.
0:12:35.0 DN: And we just take it for granted.
0:12:36.5 GR: And we just take it for granted, yeah.
[laughter]
0:12:40.8 GR: Once you get past that basic challenge of, Oh yeah, we have to count the outer notes, both of them, then doing generic intervals is pretty easy, but it's not necessarily fast.
0:12:57.2 DN: Right. Especially if you're doing letter names, because then you have that... It's almost... It's easier to look at it on a keyboard or a staff, and see, because you have a very clear visual, but letter names means you have to have a schema for that. You have to have that pattern in your head.
0:13:16.9 GR: Yeah.
0:13:17.7 DN: Which I guess is one of the reasons why we hear a lot of advocating for use of keyboard.
0:13:26.1 GR: Although I actually think figuring out the generic interval, looking at a keyboard, is harder, because...
0:13:31.9 DN: Truth. Because on a staff...
0:13:33.2 GR: Because the keyboard, of course, by itself doesn't...
0:13:34.8 DN: And the reason why it's so easy on a staff, is because the staff is, and I love to remind my students of this, a tonal notation system.
0:13:42.7 GR: Oh, yeah. Very true.
0:13:43.2 DN: The tonality is built into that notation system.
0:13:46.5 GR: Yeah.
0:13:47.2 DN: And so, yeah, if you see it... If you see it on a staff, you know exactly what it is... There's no question and if you see a tritone on the staff. I tend to use in my classes, and I don't know if this is legit, but I tend to use tritone generically for that sound... Because out of context, you don't know whether it's an augmented fourth or a diminished fifth. But on a staff, you see right away, whether it's an augmented fourth or a diminished fifth.
0:14:19.2 GR: Yeah, yeah. On a staff, we're in the context of a key. Yeah, for sure.
0:14:22.8 DN: Yeah.
0:14:22.9 GR: So, ways we can get students to fluency with generic intervals... I think you've hit up upon something really important, which is that looking at it on the staff, versus working in letter names, can be two different things. And we need students to attain fluency in both of those. So, I certainly have ways that I like to try and help students get there. We're speeding up interval writing, generic interval writing, and identification on the staff. One of the classic tricks, of course, is to help students to notice that if both notes are on a line, or both notes are on a space, it's going to be an odd-numbered interval, no matter how big or small the interval is. And if they're not, then it's an even-numbered interval.
0:15:13.9 DN: And we've talked before about pattern matching... And I definitely know that I look for patterns on the staff.
0:15:25.2 GR: Yeah.
0:15:26.3 DN: It's more advanced concept to think about what a triad looks like in various inversions.
0:15:34.9 GR: Yeah.
0:15:35.0 DN: But I guess if we learn quickly to identify thirds and fourths... Or fifths and sixths as intervals, then we're more likely to be able to also see how those fit into patterns that we're likely to see in triadic... In intuition harmony.
0:15:50.1 GR: For sure. Yeah. Yeah. I like to do a silly game of... I put up my hand sideways with my fingers spread, so it makes a staff, and then I just take two other fingers and I flop in an interval, and after a beat I nod my head and the class calls out, "Fifth" or "Third" or "Second".
[laughter]
0:16:18.8 GR: But you know, it just... And then to have students drill each other that way on their little hand staff, just to pair up and, yeah.
0:16:27.8 DN: And not only is that very handy, because you always have it with you. Yeah, that's great. And I have also used... I've done similar things with the cinder blocks on the walls of my school.
[laughter]
0:16:45.8 GR: Where the blocks themselves are the spaces and the gravel is the other lines? 
0:16:50.4 DN: Yeah, yeah. You can find staff analogies all over the place. [laughter]
0:16:56.0 GR: Yeah, yeah. And just being able to see that, right? It's so much easier to see those intervals on the staff than it is to think about them in abstract letter names... An exercise that I use, that I learned from a student of a student of Nadia Boulanger...
[laughter]
0:17:19.8 GR: It's theoretically attributed back to Nadia Boulanger, is that she would talk about the idea of an infinite piano... It just spread infinitely to the left, low, infinitely to the right, high. And she would say, just take a finger and put a finger out, and now let the piano slide left or right under you and you can come to any note. And so, at first just imagine that... Just see your finger over C, and then see the keyboard sliding under it until your finger is at A, for instance. And so now we're going to set the keyboard sliding at kind of a slow rate, and we're going to say the name of every note that passes under our finger. So, we'll slide it and we'll say, C, D, E, F, as we're seeing the keyboard pass under. Great, easy enough. We get back to C, we come back down. So now, let's slide it a little faster. And let's say the name every of every note, we'll wind up skipping one of the notes that passes under our finger each time.
0:18:36.0 DN: Oh.
0:18:36.6 GR: And so now we're saying, C, E, G, E, D, F, A, C. And we do that coming down, C, A, F, D, B, G, E, C. And now we're saying our thirds right. And then... But the important thing in this is that you are actually, you're seeing the keyboard sliding under your fingers, that you're not just memorizing some abstract set of letters. And so her idea was to make late. So when you're thinking about your thirds or your fourths or your fifths, you're not just thinking about some abstract, oh, I know G is a fifth above C, but in knowing that you are also seeing everything that came in between it.
0:19:24.6 DN: Right. And you're connecting those two worlds that we were talking about, the alphabet world and the visual world.
0:19:32.2 GR: Yeah. Yeah.
0:19:33.0 DN: So that they're not separate concepts.
0:19:36.2 GR: Yes. Yes. And the great thing about all of the intervals, which maybe not everyone realizes, but there are many great things about all the intervals, [laughter] But one handy thing for this particular exercise is that for any interval, if you repeat that interval up or down enough times, you will get back to where you started.
0:19:56.8 DN: Right. Yeah. And we're still talking generic intervals.
0:20:00.7 GR: And we're still talking generic intervals. That's right. Because that is actually also the case with specific intervals. You will eventually get back where you started. It may have a different name. You'll get back where you started.
0:20:12.8 DN: Yeah. Yeah. Sometimes faster than you expected.
[laughter]
0:20:17.1 GR: That's right. Exactly. Yeah. Yeah. Tritone C, F-sharp, C done [laughter]
0:20:25.6 DN: A hypothetically harder concept, which is actually, in fact, easier.
0:20:29.6 GR: Right. Yeah.
0:20:30.6 DN: Major thirds or, yeah. Yeah. Well, not major thirds 'cause then they would get wildly complicated. You, wouldn't get back to where you're starting 'cause you...
0:20:38.9 GR: Oh no, you do very quickly. You do, yeah. C, E, G-sharp, C.
0:20:46.3 DN: But, no, because you're C, E, G-sharp, B-sharp.
0:20:46.7 GR: Oh right. To do this version, you have to allow yourself to re-spell, [laughter] something. That's right. Yeah. Yeah. The thing about that exercise is you can't do it for more than 45 seconds or you lose your class [laughter] Right.
[laughter]
0:21:02.6 DN: It's true. And I studied with several people, as I'm sure you did, you studied with Nadia Boulanger and, some of them, the ones who more distinctly tried to emulate her definitely posed challenges that left the class in the dust [laughter] at times.
0:21:26.8 GR: Yeah. Yeah. That might be a fun episode too. The, yeah.
0:21:32.2 DN: The Nadia Boulanger teaching Legacy. Gosh, she was so influential.
0:21:37.4 GR: Right. So many composers in particular studied with her. Yeah. So, okay. So I mean, generic intervals. I think maybe the other thing worth saying as you were talking about spiraling, with any of these concepts, students will not attain fluency and speed within the first day, 2, 3, 4, that they experience. It takes repeatedly coming back to something to build those connections, to build that fluency.
0:22:11.5 DN: And so how are they gonna build that fluency? And I think like the same way we learn language, you just have to use it constantly and probably engage them in ways where they need to come up with it quickly. I mean, the way that they hate is timed quizzes although that's valuable. Of course we love the fact that computers are a way of giving that kind of feedback at a rate that a student can handle and progress with the student. 'Cause computers are much more patient than we are.
0:22:56.0 GR: For sure.
0:22:57.0 DN: But also through games, and that competitive spirit.
0:23:00.8 GR: Along with that, another thing I love to do is take something that's fairly easy to sing and to have students sing it on generic interval names. Like happy birthday, for instance. You go, haha, unison, second, second, fourth, second, third, unison. Second, second, fifth, second. Fourth unison, octave, third, third, second, second. Sixth unison, second, third, second, second. And it's wonderfully hard. It's even hard for me. But it's certainly easier when you're looking at it on the page, but it can be, and I always will pick a song that most everyone knows like to do this, this is not how we want students to sight sing by thinking about the interval from the note they're on to the note they're not on. That can build up, that can cripple fluency in sight singing for life. If you're thinking about sight singing that way.
0:24:10.1 DN: And it's super common.
0:24:11.7 GR: And it is super common.
0:24:13.1 DN: I so often am doing sight singing with class and they're already in their third or fourth semester of, and they will get a big leap and they'll all choke.
0:24:30.2 GR: And they're trying to summon the interval to mind.
0:24:32.0 DN: Yeah. Because they're trying to think of the interval when I'm like, it's T, you know where T is just sing T.
[laughter]
0:24:38.6 DN: Yeah. Yeah, yeah. Yeah. I feel like this is going to be the hill I die on [laughter] is don't sight sing by intervals. I mean, there are times when the intervals are helpful, but they are rare and or where, we wind up needing to really think primarily in an interval context. But those situations are really rare in actual music. Yeah. Yeah. Anyone who wants to hear us opine more about this should go back to our very early episode on Sailfish systems.
0:25:16.9 GR: As if we're opinionated or something.
0:25:19.0 DN: No, I know, right imagine, imagine. Okay. So we've talked about generic intervals and that's the, "easy part" of teaching intervals where people, and I think most people kind of teach generic intervals the same way. It's a simple concept. They're not that many different ways of doing it. But where pedagogy really differs is in how we teach specific intervals. So I've seen four ways of doing this. And I'm... Just to enumerate them, teaching intervals by half steps, which is to say learning that a perfect fifth has seven half steps and four letter names, or five letter names, depending on whether you're coming outside. Teaching intervals by scales, which is to say that from scale, in a major scale from one up to any node in the scale is a major or perfect interval, and from one down to any node in the scale, is a minor or perfect interval. Teaching intervals by natural intervals, in other words, intervals from, if both of the notes were natural as in C natural, E natural, what would that interval be? And then, teaching intervals by scale degrees. So knowing that anytime I'm going from scale 3, 4 to scale 3, 6, that's a major third, and that can transfer across various keys. So those were the four I came up with. David, do you have any others that I missed in that list? 
0:26:48.0 GR: Not that I'm aware of, but those... And the thing is, except for the first one, I think you just need to know all of them.
[laughter]
0:26:56.7 DN: Right. So, okay. Yeah. And the first one being intervals by half steps, knowing that your major thirds have four half steps.
0:27:03.8 GR: Right. Oh God. I don't even know what that is. I would have to look and go. Right. Okay. I would've to count. I don't have that information in my brain.
[laughter]
0:27:14.5 DN: Yeah. It's funny. I don't either except from set theory. From teaching oral skills 4 so many times and, you know, just, yeah. Yeah. But, okay. So this first approach, teaching intervals by half steps, effectively the idea here is that you learn that any given interval has a certain number of half steps in it, right? And a certain number of letter names. So we learn our perfect fourth has five half steps and four letter names. Four letter names total. That's including the outer notes. And you learn this, most people who teach this way teach all the major and perfect intervals, and then teach how to alter from the major and perfect intervals to get any of the other intervals. And...
0:28:10.0 GR: That makes sense.
0:28:10.9 DN: Yeah. Yeah. I have to say, one of the things that I love about this approach, is you can teach intervals in a way that someone who has failed every previous quiz in your fundamentals class will still understand.
0:28:28.3 GR: Gotcha.
0:28:29.6 DN: Right? Because it's just, it's you find the note on the piano and you count your half steps.
0:28:36.4 GR: Right.
0:28:36.5 DN: And then you find the version of that note that matches the letter name, that's however many letter names apart.
0:28:43.5 GR: You know, I think the thing that's so tricky about this though, is that it requires so many transformations. It won't work if... It won't work just looking at a staff, unless you have an already inherent knowledge of how that staff translates to whole steps and half steps. In which case you're already advanced enough that maybe you didn't need this process. And if you're looking at the keyboard, it doesn't... Yeah. You're gonna have to do a lot of translation. You're gonna have to count 1, 2, 3, 4, 5, and then go, okay. But that's the third. [laughter] And it's... That's a lot of...
0:29:31.3 DN: Yeah, it is a slow...
0:29:33.3 GR: That's a of steps.
0:29:34.0 DN: It is a slow process because of all those transformations, right? 
0:29:38.1 GR: Yeah.
0:29:39.0 DN: I will say, and this was the method that when I saw that teacher, this was back in 2005, I saw a teacher teaching it this way, and I thought, this is the worst. I will never do it this way. But I also think if we skip teaching this concept, sometimes students, what this concept makes really clear is that when we're using intervals, what we're really doing is counting musical distance two ways. We're counting it by letter names and we're counting it by distance in half steps. And those are different. Even though we kind of merge them into one naming system. So I guess for me, this approach is one that I introduce in about 15 minutes, just to be sure students have this idea that like, and I introduce it usually by saying, okay, find me a white note fifth on the piano. And how many half steps are in there? And can you find me a white note fifth on the piano that has a different number of half steps. And of course there's only one white note fifth on the piano that has six half steps in it instead of seven half steps.
0:30:57.3 GR: Well, that is a good experiential learning process for them to find that one natural, as we call it interval.
0:31:06.1 DN: Yeah. Diminished fifth interval. Yeah.
0:31:07.7 GR: Yeah. That is different, rather than just saying, Hey, there is this one natural interval that's different.
[laughter]
0:31:15.2 DN: Right. Right. But for me, the important thing is that they understand that not all fifths are created equal, not all whatevers are created equal, right? This concept is a way for me of getting to why we need these specific interval names.
0:31:34.2 GR: So I love that. I love that as a tool to get yourself going. And then you've, and then they're aware of the concept. I'm not sure I would wanna personally dive too deeply in there, at least in a fundamental class.
0:31:50.5 DN: Yeah. And you know there are people who this is the way they teach intervals. And so if they really do that, then students memorize that major second, two half steps, major third, four half steps. Perfect fourth, five half steps. Perfect fifth, seven half steps, major six, nine half steps, major seventh, 11 half steps, right? Just...
0:32:12.1 DN: But I am with you that, to be fluent, that approach involves way too many transformations that just slow us down. So I think these other three approaches that we're talking about are effectively abstractions above that basic concept. That get you more quickly to a place of being able to identify your name intervals. So second one, intervals by scales, which is this wonderful trick that if you start from one in a major scale and you go up to any node in the scale, you're going to have a perfect or major interval. And if you do the same thing coming down, you're going to have a minor or perfect interval. And then everything is just a transformation by half step away from that.
0:32:58.9 GR: Which is also one of the ways that's closest to the way we may hear things. Wonderful.
0:33:04.2 DN: For sure. Yeah. And it's also, it's a wonderfully easy one to connect to oral training as well. 'Cause you can do the classic 1, 2, 2 is a major second. 1, 2, 3 is a major third and so on and so forth. Which of course is in building up students for, functional hearing. Or do do re, whatever language you wanna use of recognizing. Okay. Oh, where is my fa? Oh yeah. Do do fa there's my fa 'Cause I can just call do do mind and have, I've sung my Do do fa enough times that. Yeah.
0:33:42.8 GR: So yes, if we have a schema of what a major scale sounds like if we have a schema of, we keep the, I love this word now.
0:33:49.8 DN: Yeah. Thank you Lee.
0:33:50.9 GR: Yeah, exactly. If we have a schema of what a major scale looks like, we also have our answers.
0:33:57.6 DN: Yeah. And I think there you're getting to another of the reasons that I think all of these approaches, other than the first one we talked about of counting by half steps are maybe frankly stronger is because as we learned in our episode with Leigh VanHandel, a lot of learning is about making connections to things that are already known. And the greater number of connections, the easier a concept is to call to mind. And so yeah. As you're saying schema right. The technical term for that and this connects so directly to that schema of scales orally and in written theory.
0:34:39.8 GR: Yeah. And then we learn other fundamental concepts and fundamentals that will make this easier of when we learn key signatures, we quickly learn what notes are going to be in a major scale we can, and that is, that becomes an easy way to calculate things.
0:35:00.6 DN: Yeah. Now, one of the downsides of this approach is that there are notes for which there is no major scale or minor scale. For instance, David, what's a minor third above G-sharp? 
[laughter]
0:35:16.3 GR: Well, I can look at it on the piano.
[laughter]
0:35:18.0 DN: Yeah. But also you probably know right away, right? A minor third above G-sharp is B that's a pretty common interval. But if you've learned this approach, then suddenly you're like, oh gosh, do I know G-sharp major? Nope I don't.
0:35:30.5 GR: Yeah. I don't have a G-sharp major scale in my head.
0:35:34.2 DN: Or for instance, minor third above F-double sharp. Something that exists in the key of G-sharp minor.
0:35:39.6 GR: There are many situations in which this is gonna be cumbersome.
0:35:42.9 DN: Yeah. And in those cases, the classic approach is either you say, okay, I've gotta do a minor third above F-double sharp. So to do that, I'm going to cancel, hold off my double accidental, I'm gonna pretend it's F-natural. Oh yeah. Minor third above F-natural, A-flat easy. Okay. Bring back my double sharp. So I have to go up to accidental. So my, A flat becomes natural then sharp. And so my minor third above F-double sharp is A-sharp. One other challenge of intervals by scales, which is that if I'm working in a key, say I'm working in E-flat major, and I'm looking at, D to F in that key.
0:36:26.8 DN: And someone asks me what interval it is, if I only know my intervals by scales, I have to erase the E-flat major key and scale from my mind. And call to mind a different key and scale and...
0:36:41.1 GR: Yeah. That would become... That's a one too many things to do.
0:36:45.2 DN: Yeah.
[laughter]
0:36:48.7 DN: And problematic because it causes us, because we want to be thinking functionally always with whatever key we're in. And this causes us to have to let go of that to calculate an interval.
0:37:03.0 GR: Right. So that's why we have these other two methods that work much better in other situations.
[laughter]
0:37:08.5 DN: That's right. That's right. Yeah. Absolutely. So David, can you tell us about natural intervals? 
0:37:14.9 GR: I don't think that I prefer, I either of these last... Any of these last three methods, I think that you need to have all of them at your disposal.
0:37:25.8 DN: And it really... It comes back to what you were saying earlier about spiraling. That depending on our context as fluent musicians, we're going to use a variety of different techniques to recognize and create intervals. So natural intervals, usually what we're talking about there is learning, for instance, where all the major thirds are on the white notes or in letter names without accidentals, and then altering from there.
0:37:58.4 GR: Which teaches you some valuable tools anyway, that you should know what all those intervals are because they'll help you understand.
0:38:08.5 DN: And there's some great, really beautifully obvious visual things when you do it this way. So if we take our thirds, and if you see C, D, E on the piano, you'll notice right away there are two black notes between that. And our major thirds are white note, our natural interval major thirds all have two black notes between them. But if you take... But find a third on the piano that only has one black note between it, and that's going to be a minor third. And so if you're teaching interval qualities, if your primary way of teaching interval qualities is this natural intervals approach, then or when you're dealing with notes, other than the white notes, the classic way of doing it is to imagine the white note interval and to determine how it's altered based on that. So let's say I'm asked to write a minor third above F-sharp. I'm going to say, okay, I know my white note third F to A is major.
0:39:08.1 DN: And the given note is F-sharp that shrinks the interval by a half step, oh, good F sharp to A is minor. So you learn your intervals as alterations from the white notes.
0:39:19.0 GR: Yeah, and then that also ends up working well for core qualities and...
0:39:25.3 DN: Yeah, absolutely, and it's pretty darn quick, and it doesn't require a knowledge of scales or keys, which in this case can be a positive, because when we're working in the context of a key to figure out an interval, we don't have to erase that key context.
0:39:45.5 GR: Right.
0:39:46.2 DN: But we may have to erase an accidental which...
0:39:50.2 GR: Yeah and I think if you're working in a key with a lot of... If you're trying to do it visually on a piece of paper and you're working in a key with a lot of accidentals, you also then have to do a lot of cross-checking to make sure that you've accounted for all the accidentals...
0:40:08.0 DN: All the accidentals that you cancelled to figure it out. Yeah. This is... Yeah, for sure. Yeah. And David I think one of the things that you said earlier gives us a clue on how we can get past this challenge of canceling and adding accidentals, which as you were saying that you want students to know that, for instance, in a major scale, the third on one is major, the third on two is minor, the third on three is minor, et cetera, et cetera.
0:40:36.7 GR: Right.
0:40:37.4 DN: And which takes us to the fourth approach of intervals by scale degrees, which is to say knowing with all of the intervals whether a fifth on two, what kind of fifth is that? Well, in major it's perfect and in minor, it's diminished. And actually, in each of these, the complexity of how many things you know has gone up. There's a lot of information to remember, if we're doing intervals by scale degrees. You have to remember seven qualities or seven intervals, and so in one sense, it's harder, but the reality is that, I think most musicians who are fluent at these things are using this approach.
0:41:38.0 GR: And if I'm playing piano and I'm in a major key, I just know that a two chord is minor. I just know that. I don't...
0:41:48.2 DN: And with that knowledge comes the knowledge of the third and the fifth.
0:41:56.5 GR: And yeah... And I just know what those quality... And I don't have to think about them. They're just embedded in my schema, and I guess I do want to embed that schema in my students as well.
0:42:07.5 GR: Yeah. Yeah and I do things like I think many of us do right of... Especially with the smaller intervals of saying one to two is a major second, two to three is a major second, three to four is a half step, or one to three is a major third, two to four is a minor third of like actively singing various warm up patterns to make those things explicit and start to build up those schema. So this method of knowing intervals by where they are within... By scale degrees within a key, it's really wonderful and it's really fast, but it does require real fluency with scale degrees in keys. Knowing if I'm in any key and I have this note, what's the scale degree for that note or vice versa? What's scale degree two in the key of A major.
0:43:09.0 DN: Yeah And there are... I think there are challenges and how do you... How you develop that fluency. I think there are not challenges if everybody has a keyboard, because if everybody has a keyboard, you can have them play through it, and then they can see, "Oh, that's what I have to play."
0:43:31.4 GR: I'd also argue that for me, that particular skill, the ability to go between a scale degree and the name of a specific note in a key, or the name of a specific note in a key and a scale degree, that skill to me is the most important skill that I want students to learn in anything I'm teaching, in any written theory, in any oral skills, I want them to have that fluency of moving between functional identification of scale degree and letter name because it opens up sight reading and dictation, because as long as you can hear the scale degree, call to mind what the scale degree sounds like, or solfege, these are different names for the same concept or location within a scale, then you gain fluency in the oral side of things, and if you know your theory concepts by relation to solfege or scale degree. Then those become fluent and connected to hearing as well.
0:44:45.8 DN: So it's a broader schema that we're building, and the thing is that... So a lot of these are patterns and my goodness, we've had a great season of episodes, but so much of what we do is pattern recognition. So if you have this pattern of in your... If you have that pattern and you know that pattern and you can connect those patterns to notes, is what you're saying. Then you have the world at your fingertips.
0:45:32.6 GR: And, you do, literally at your fingertips. That's it. Whatever you can hear. If you can hear all the scale degrees you can write down or play.
0:45:41.3 DN: And I do. I remember having a teacher speaking of Nadia Boulanger, one of my teachers who studied with Nadia Boulanger. He could do things that seemed absolutely magical. And I just thought, I'll never be able to do that. But then some of this skill, some of my students look at it as if it's some magical skill. And I say, literally, I wasn't good at this before and I'm just trying to get you to be... There's no magic in this. This is just something that you can learn to do.
[laughter]
0:46:16.5 GR: Yeah. Yeah. I keep coming back to what you said at the beginning about spiraling because I think if on day one of teaching intervals we try and teach them by scale degrees, you lose the class. It's too advanced at that point.
0:46:34.4 DN: We can't teach them everything at once.
0:46:37.4 GR: At once. That's right. Yeah. And we have to, especially with intervals, gradually build it up, so that each step is a manageable step and not overwhelming. But I think, in that process as we've talked about, gradually connecting to schema that they've already mastered or begun to master. They connect to scales, to connect to their knowledge of the keyboard, to connect eventually to scale degrees and functional hearing. And when I think about teaching intervals this way, I hate it a lot less than when I think I'm going to teach them one way of doing it. But it's a... Pacing is a challenge too. You don't want to give them a new way until the prior way has become pretty automatic.
0:47:45.2 DN: I think it's a... Yeah, that's a good argument for really careful curricular design. And if you're in control of the whole curriculum, woo. Great. And if you're not in control of the whole curriculum, whoof. You've just gotta figure out how to fit it in.
0:48:04.5 GR: Especially if you're lucky enough to have your students over a more extended period of time, let's say you're working with them for two years or even, like middle school and high school teachers, three, sometimes four years there's a real opportunity to just sequentially layer these things up.
0:48:22.6 DN: And a little bit, there's some forgiveness in this too, that if you inherit students from another person who used a different method, this is not necessarily bad. This just means that they have that additional perspective [laughter] and now you can give them more additional perspective.
[laughter]
0:48:42.9 GR: Yeah. Yeah. And you know, when a student quickly knows what I hope they know, I don't particularly care [laughter] which process they used to get there.
0:49:00.5 DN: And it's just... It's more important when they're not quite getting there or not getting there quickly enough. And if they... To use a voice analogy, it's interesting because in order to build a consistent instrument vocally, sometimes you have to break down the strategies that they've already developed that aren't good long-term strategies. [laughter], there's a... Maybe this is not the place to talk about it, but young singers tend to raise their larynx as they get higher. And that's an intuitive strategy. It works kind of a little bit, but it is not a good long-term strategy. And convincing a body to stop doing that can be tricky. And it can be frustrating for a student who has learned to rely on that not so good strategy or on that less, that strategy that will take them less far.
0:50:11.4 GR: Yeah. Yeah.
0:50:15.3 DN: Maybe that was not a useful analogy.
0:50:18.3 GR: No I think it's a... But I think we all know cases of this in our own practice of where we may have had to rework something. I think in the case of these strategies for identifying and writing intervals, one of the good things is we don't have to convince students to give something up. We're just sharing an additional approach that can be faster and progressively more musical.
0:50:54.1 DN: And these things expand into other things. And as soon as I started talking about harmony, they're going to have to know that pattern with the exception, that of course the chords are gonna be major, minor, minor, major, major minor diminished.
0:51:15.8 GR: You're right. Yeah. Yeah.
0:51:16.9 DN: Plus theirs. [laughter] Yeah.
0:51:18.4 GR: And it's funny that you think I've never actually taught that as a linear pattern except in various warm up songs. Like one three, major third, two four, minor third. Whereas I've just always taught it as the major thirds are on one, four and five. Everything else is minor. And similarly. And then the expansion to the triads, major triads are one, four and five. Everything else is minor except seven.
0:51:46.3 DN: Right. Right. And although with intervals and perfect fifths or and fifths, it's fifths and fourths. If the two notes are not B and F...
0:52:06.2 GR: Yeah, this is the brilliant...
0:52:07.2 DN: That is perfect.
0:52:07.7 GR: We should just... We should just take a second and explain that shortcut because it's a wonderful shortcut, that for any perfect interval, both notes will have the same accidental.
0:52:16.9 DN: Right.
0:52:17.6 GR: Unless the two notes involved are F and B, in which case F will always have one accidental higher than B.
0:52:24.4 GR: Right. Or depending on... Yes.
0:52:28.6 DN: No. That's always true.
0:52:29.7 GR: Not depending on. [laughter]
0:52:30.9 DN: Yeah, yeah. For instance, if you have B flat to make a perfect interval, one accidental higher than F is natural. Yes, B flat to F perfect fifth, or F to B flat perfect fourth, yeah.
0:52:41.7 GR: Right.
0:52:42.4 DN: So yeah. A good shortcut. And just to wrap up David, what's your favorite interval? 
0:52:49.7 GR: Oh, what is my favorite interval? I can I...
[laughter]
0:52:55.8 GR: I really love a well-tuned fifth. Yeah, you know I love... This is so cheesy in the best way. A well-tuned major seventh.
0:53:10.2 DN: Oh, oh, all right.
0:53:12.6 GR: Yeah.
0:53:13.4 DN: Cool. That was not what I was expecting you. I was expecting a sacred...
0:53:17.0 GR: I wasn't expecting the perfect fifth...
0:53:17.7 DN: Major fifth, major sixth, or something.
0:53:18.7 GR: Oh, yeah, yeah, yeah. Yeah.
0:53:22.0 DN: Sixths are great though. Oh my gosh.
0:53:24.1 GR: Sixths are really great. Yeah, they are. They are. But there's nothing for me like the rub of singing a major seventh.
[laughter]
0:53:32.2 GR: It's just... It's just delicious. Whichever note I'm singing. I'm just... I'm just, yeah.
0:53:41.9 DN: Yeah. Well...
0:53:42.2 GR: A well-tuned perfect fifth I also love. Well, this has been fun. And we came out with a lot of ideas for future episodes.
0:53:55.7 DN: I know. Well, we know that. We already know in our own relationships that you are very good at staying on track and I am very good at taking us off.
[laughter]
0:54:05.7 DN: David, your creativity adds so much that...
[laughter]
0:54:13.6 GR: So if we rambled it's my fault.
0:54:15.9 DN: Otherwise I'll blindly follow my checklists.
[laughter]
0:54:20.9 DN: Well, this is why we're good together. All right.
0:54:23.1 GR: Yeah. Yeah. Awesome. And so listeners if you have a favorite way of teaching intervals that we didn't talk about, please let us know. And we'll be circling back to this concept when we talk about teaching intervals in ear training as well. So thanks so much for tuning in.
[music]
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Pedagogy of Accidentals with Paula Telesco

Dr. Paula Telesco walks us through some of the "gotchas" that come up when teaching accidentals, and shares some great musical examples for explaining concepts like enharmonic spelling, double accidentals, and cautionary accidentals.
 
Transcript 
[music]
0:00:21.0 Gregory Ristow: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:35.4 Leah Sheldon: Hi, I'm Leah Sheldon, head of teacher engagement for uTheory.
0:00:39.7 GR: And I'm Gregory Ristow, founder of uTheory and Associate Professor of conducting at the Oberlin Conservatory.
0:00:46.5 LS: Thank you listeners for your comments and your episode suggestions, we'd love to read them, so please send them our way by email at notes@uTheory.com. And remember to like us and subscribe wherever you get your podcasts.
0:01:00.5 GR: We'll be taking a deep dive into the topic of teaching accidentals today, and we're delighted to have Dr. Paula Telesco with us for this. Dr. Telesco is a professor of music theory at the University of Massachusetts, Lowell. Her research interests include music theory and oral skills, pedagogy, analysis of classical and romantic era music, the omnibus progression and her monism and musical cognition. Her writing has appeared in The Journal of music theory pedagogy, the Journal of musicology and music theory spectrum, among others. Most recently, her chapter on the pedagogy of accidental was released in the Routledge Companion to Music Theory Pedagogy, edited by Leigh VanHandel, who we just spoke with in December. Paula, thanks for joining us.
0:01:44.4 Paula Telesco: Well, thank you, it's great to be here. Thank you for inviting me.
0:01:48.8 GR: Yeah, we're delighted to have you. Tell us a little bit about yourself. You've been teaching at UMass Lowell for some time now. What all do you teach there? 
0:01:58.8 PT: Well, I've taught many things. Currently, I'm teaching a basic music theory. I also teach the non-major music history course. The basic theory I'm teaching right now is for non-majors. Well, they're non-majors, they're also music miners or people who want to get into the Music program, but they're not quite ready.
0:02:29.1 GR: Yeah. So, what we often call Fundamentals of Music, sorts of things? 
0:02:32.8 PT: Exactly. Yes.
0:02:33.9 GR: Yeah. Excellent, excellent. And I've to say, I really enjoyed your chapter in Leigh VanHandel Routledge Companion on teaching accidental. It reminded me of some things about accidents that frankly, I myself had forgotten.
0:02:47.8 PT: Well, thank you. Yeah, there's a lot more to know, certainly than students are aware of. The students who come into my class have mostly some background, and so they already think they kinda know accidental, but they don't. They know the basic things about them, but there are all these other things, the niceties of them that they're not aware of, so I wanted to make sure that they... I tell them, "This is the best theory deal in town." And I'm trying to give them as much information as I can.
[laughter]
0:03:27.2 GR: That's great. I think, one of the things I have experienced, I'm sure you've experienced as well, and Leah certainly in your teaching with the elementary, middle and high school students, I know we've talked about this, is that accidentals can be a really hard topic for students to first grasp. What are some of the things that students struggle with when learning accidental? 
0:03:50.7 PT: Well, for my students, the basic concept is not that difficult, it immediately starts getting difficult when you add an E sharp or E flat, something like that. And I tell them throughout the semester, we're gonna see why those kinds of notes are necessary. We're not just doing it just for the sake of putting a sharp next to the note E. So the black notes are always the easiest to understand, it could be this, it could be that, and we'll see why. And I tell them, I have lots of silly little analogies that I use. And so I always pick someone sitting in the front row and I say, "Do you have sisters? Do you have brothers? Do you have parents? Do you have cousins? And so on. And I say okay, so to their parents, this is their son. To their brother, this is a brother. To their cousin. So this person has different names depending on their relationship to other people. And in the same way, this black note has different names, depending on the context, it's relationship to the other notes and what key it's in and so on.
0:05:09.1 PT: So I start off with that kind of an explanation. One of the other problems is in the notation, and that's just to constantly reinforce that the accidental have to go on the same line or space as the notes, they can't be flying off into outer space because they often are being notated way, somewhere not close to the note, so that's always an issue that comes up and you have to make them aware that an... Another thing I tell them too, throughout the semester, is that the purpose of notation, or at least one of the important purposes, is to make music as easy as possible for the performer. If you have to learn a different system every time you play a piece of music, you're never gonna get very good at it, so it has to be very consistent. When someone is reading music, they have to know this is how it looks, and when I see this, this is what I play. I need to know if there's an accidental in front of the snow or I probably am not gonna play the right notes.
0:06:25.0 GR: Yeah. Leah, you and I were talking, was that just yesterday, we were chatting about [chuckle] true beginner students when they first see accidental, and can you just say a little bit what you were saying to me yesterday? 'cause I thought he was so wonderful.
0:06:40.5 LS: Yes, so I have the opportunity to teach beginning instrumentalists, and sometimes their very first, their mix-up just comes even between, identifying between is this a sharp or is this a flat, and accidentally calling an F-sharp and F flat. Just some of the very basic terminology or for example, the sharp F, since they see the sharp sign first or flat B, just getting that down can be a challenge, especially for beginners or younger musicians. I also have some students who are older instrumentalists and have played for a couple of years, but started on a non-piano instrument, and they don't have the keyboard to reference. So sharps and flat, they don't have that visualization of the black keys, and it doesn't really mean anything to them, unless we are intentionally explaining to them that G-sharp is a half step higher than the note G, so some of those very basic things that maybe sometimes we take for granted as musicians is really abstract to them.
0:07:56.0 PT: Yeah, I know that not all my students have access to a piano, there's pianos in the building, and some of them do go and use them, but I always keep pulled up in my bazillion tabs in my browser, 'cause I'm always projecting a MIDI keyboard and I post links for them, and I say, "You really wanna be using this keyboard," and so throughout the semester, I'm always flipping to the keyboard so they can see whatever it is we're talking about, the sharps and the flats and the half steps and whole steps and everything, and that is really very helpful. And what you were saying, Leah, about what comes first? I know that if a student comes in with... If they've... Some of my students are playing in the marching band, so they're used to looking at music, but not everyone is, and so again, I just stress that if the accidental comes after the note, you're gonna play the white note before you realize you were supposed to play an accidental, so we read from left to right. We have to see the accidental first if we wanna have a fighting chance of playing the right note.
0:09:15.4 LS: Absolutely.
0:09:16.9 GR: That's great. That's great.
0:09:18.7 LS: And I find in most cases, the students know what to do, it's just, it's more about that they've memorized what to do rather than actually understanding the theory behind it or the relationships between the notes. So I'm always a proponent for using the keyboard and referencing the keyboard. Some of my students I inherited without having heard that, so it's been fun to go back and re-introduce that.
0:09:41.3 PT: Yeah, yeah.
0:09:42.1 LS: Yeah, definitely. I think we probably all come across students for whom F-sharp means a particular fingering and not necessarily relationship to notes around it.
0:09:51.8 PT: Right, right. And now the keyboard is really invaluable for learning all kinds of things.
0:10:00.0 LS: So, along the same lines, even those of us with experience, we can find that accidental have delight Fledge cases. So what are some of the things that even knowledgeable or more advanced musicians get wrong when writing accidentals? 
0:10:19.1 PT: Well, one of the fossil things is certainly an older practice. If you are going from a double sharp to a single sharp, you would put the natural sign first and then the sharp. I realize in a lot of contemporary music that that's no longer the case. So if a person plays lots of contemporary music, they might not be aware that an older music, it had been done that way. Flats, you just go from a double flat to a single flat, you don't put the natural before it. I will say, even though they're not advanced musicians, probably without knowing which accidental goes where. If you have a cord and you're having to write accidentals, a very common problem at least with my students, is I have to keep reminding them, "You can't put accidentals on top of each other because you're not gonna be able to clearly see which one is which." So the lowest note that accidental is gonna go furthest to the left. If you've just got two notes, and obviously the other one is closest to the note on top, as you start adding notes in, you have to alternate closest farthest, closest, farthest away, if you had four notes, for example.
0:11:43.4 GR: Yeah. Those rules are great. They're actually a little more complex in what you described. I happen to have implemented this for a software program, and so that's one of the algorithms I love. I don't know, is it worth talking about it, they're very nerdy, but our listeners might enjoy the nerdiness.
0:12:02.5 PT: Sure, sure.
0:12:03.7 GR: Eritrean.
0:12:04.5 PT: Yeah. 'Cause I know sharps and flats of different...
0:12:08.2 LS: Yeah. Exactly. So I just can't see...
0:12:09.7 PT: Hanging down pieces.
[laughter]
0:12:12.3 GR: Hanging down pieces versus pointing up pieces. Exactly, and so this is... Yeah, this is at the heart of it. So when you're talkin about typography and the shape of characters, some characters have descender which are things that go below the line, and some characters have a ascender for things that go higher than the lower case letter standard height. And so when we think about all of our accidentals, we have two accidentals that have both ascender and descender that's the sharp sign and the natural sign, those are the tallest accidentals. We have two accidentals that have only ascender and that's the flat and the double flat. And we have one accidentals that has neither in A center nor a D center, and that's the double sharp. And so the rule is that if you have... If you have a conflict between... How do you do this? At the interval of a seventh, you can have any two accidentals written directly above each other from a seventh or larger. So you could have... What's one that might actually happen in music at a seventh? For instance, you've got a A-flat up to G-flat with no problem, but you'd also have a sharp up to G-sharp, obviously much less common in music, even though both have an ascender and both have a descender.
0:13:38.7 GR: At the interval of a sixth, you can have the upper accidental with no descender and the bottom accidental with an ascender, so for instance, you could have a flat up top and a sharp down bottom. At the interval of a fifth, you can only have a... Let me just be sure I'm getting this totally right. Yeah, at the end...
0:14:04.6 PT: I'm certainly learning something here.
0:14:07.9 GR: [laughter] Yeah, yeah. At the intervals of a fifth, if the top accidental doesn't have a descender, so if it's a flat, a double flat or a double sharp, and the bottom note has no ascender, that's only the double sharp, then the two can be written together. So effectively, at the interval of a fifth with double sharps, you can write them together or double sharp on bottom and a flat on top. But I can't think of any time, you'd ever see a double sharp on bottom and a flat on top in the same chord. Heaven help us. So that gives us writing them for two notes, but then chords often have more than two notes, and so in that case, the rule is to start with the highest accidental, closest to the note, and then to alternate from highest accidental to lowest accidental going out to the left, away from the chord. So imagine that we had an F-sharp major chords balding close position, like F-sharp, A-sharp, C-sharp, then the accidental closest to the chord would be that top C-sharp. You go down to the next available lowest accidental, the F-sharp, and then to the A-sharp. And now if you have a seventh, let's say we had a C-sharp.
[music]
0:15:23.0 GR: No, lets pick a better one. Let's pick... Because I want an accidental on bottom and an accidental on top. Oh, my apologies for this but it'll work, a C-flat dominant seventh chord. So C-flat, E-flat, G-flat B-double flat. At this point, you can write the C-flat and the B-double flat, those accidentals directly on top of each other, that C-flat is your highest. So next we're going to go to the next available lowest, which would be that E-flat, and then the next one out, would be the G-flat, and so... That's the full rough routine. And if anyone is as nerdy about this as I am, the book to read is Elaine Gold, who is the chief typesetter for... She had booze or she had Oxford. She's at one of the major British music houses, and her book is called Behind Bars: The Definitive Guide To Music Notation. And I geek out on this stuff like crazy, so...
0:16:22.4 PT: Oh, I'm gonna have to check that out.
0:16:24.5 GR: It's delightful. It's every possible edge case you could ever think of, and she's... Yeah. So anyway. Yeah, that was a fun little diversion, but...
[laughter]
0:16:37.4 GR: I think Paula for me as well, It's just a matter of... Especially in music fundamentals, from students who are first writing triads and intervals of just reminding students that if they just know like... If it's anything smaller than a seventh, space those accidental out to the left.
0:16:53.2 PT: Yeah, yeah. Yeah and for our purposes, for intervals, I just always tell them the lowest note that accidentals furthest to the left, the upper note, it's closest to the note. When we get to triads, I didn't know exactly all of that so, but I still just tell them... I don't really specify where the middle one should go, I tell them the top and the bottom, and so you just have to make sure they're not overlapping, same as notes. If you're writing a second, they have to touch but they cannot overlap or nobody knows what note it is.
0:17:34.4 GR: Yeah, yeah. And there are all sorts of rules for which way the second should go in a chord cluster, but let's not dive into that crazy mess.
[laughter]
0:17:46.8 GR: These are the kinds of things as I'm talking with... Who was I talking with it about this recently? It doesn't mater. I was talking with someone about this. Maybe, was it you, Leah? I was talking about these rules and how maybe any more of these rules don't matter as much because largely, we're all working with music notation programs and they will help us arrange the accidentals and do all those kinds of things. And unless you're going to become a professional music typesetter or someone who programs notation programs like me, then you probably don't need to actually know these kinds of rules.
0:18:25.0 PT: Yeah. Well, I have Sibelius, my copy is very old, but it still works and in the manual it comes with it, they even say something about, "Don't worry about that, Sibelius knows how to do it, and you're better off not even thinking about it, we'll just do it for you."
0:18:49.3 LS: Yes. Notation programs have become our calculator. [chuckle]
0:18:52.9 PT: Right, right.
0:18:53.6 GR: Yeah, yeah. And I am so glad for it because I remember having to look up the rules for which way the second should go when I was writing seventh chords as an undergrad and yeah.
0:19:06.3 PT: Yeah.
0:19:06.9 GR: We spoke, I guess about a month and a half ago now with Melissa Hoag, who wrote a chapter on putting the music in music fundamentals in the Routledge Companion. And one of the things I loved about your chapter on Accidentals in the Companion was that you give us two really great examples of pieces that show almost all of the edge cases and likely places for confusion in accidentals, Beethoven's, Waldstein Sonata and Chopin's Nocturne in D-flat major Op 27, number two. I thought it would be great if you could take us through these rules that you outline, along with some examples from the Waldstein, And I'm here at my piano so I can plunk out some of these as we chat about them. Does that sound like a good plan? 
0:19:55.5 PT: It does, it does. And as I'm sure you are very familiar with, one of the biggest issues is time. And so the more you have to flip around to find different examples, you just waste a lot of time. So I honestly don't remember what came first. If I just happen to notice doing, 'cause I've used Waldstein for lots of stuff, if I just sort of noticed all the different accidental usages, and so I thought, bingo, this is what I should do.
0:20:35.2 GR: And it's a great piece for... If listeners don't know, I'm just gonna play a little bit of the beginning to kind get it into their ears.
0:20:40.0 GR: Please do.
0:20:41.1 PT: Sound good? Okay. Here, it is.
[music]
0:21:04.9 GR: And so on and so forth. I often call this the climb every mountain Sonata because the opening progression is the same. Right.
[music]
0:21:18.0 PT: Oh how funny.
0:21:22.5 GR: [laughter] Right.
0:21:24.0 PT: I never realized that. Oh, that's great.
0:21:28.0 GR: You know, for music theater lovers out there.
0:21:30.5 PT: That's great.
0:21:31.1 GR: Yeah. So, and it's...
0:21:33.2 PT: And it's also got what I really like is the descending tetrachord progression too.
0:21:37.8 GR: Yes. Yeah. Yeah. And there's so many wonderful things about the second theme of the Sonata, right? Normally, of course, a Sonata... This is in C major, normally a Sonata in C major would have a second theme in G major, but this Sonata has its second theme instead in E major.
0:21:55.3 PT: E major.
0:21:57.4 GR: Which means Beethoven's writing, normally you'd be writing just an F-sharp in your second theme, but now Beethoven has to write a ton of accidentals. So it makes sense that this is a perfect choice for this.
0:22:06.1 PT: Yeah. And because it's in C major, you're not dealing with a key signature where you have to think about is that just canceling out something in the key signature or is that adding something in? So, yeah. So even just in the first page or two, you can find so many things. I always start in measure two with the F-sharp and I say, it's on the fourth beat, the first eighth note, and it's repeated. And I say, here's an example. Once you write an accidental, it's in force for the whole measure in that register on that line or space in that clef, bar line cancels it out if you want. So that's why you don't need to write it twice. If you wanted F-sharp in the next measure, you'd have to write it again. Then in measure four, there's the little grace note and we talk about what a grace note is and it's a C sharp, and then immediately it has to be canceled out.
0:23:09.9 GR: So we have that C-sharp, we have...
[music]
0:23:12.8 GR: And then we have C natural.
[music]
0:23:17.3 PT: And again, here we are only in measure four, but I can already tell them or ask them 'cause what I do too is I play in measure two, I play those as F naturals. And maybe you wanna do this. And then F-sharps to say, "Listen to the difference. What if Beethoven wrote F natural?"
0:23:35.7 GR: So here it is with F natural, not what Beethoven wrote.
[music]
0:23:44.8 GR: Oh, that feels so weird.
0:23:46.5 PT: Yuck. [laughter]
0:23:49.1 GR: And here it is with the F-sharps.
[music]
0:23:57.0 PT: Yeah. So already, I introduce the concept. We can't get into secondary dominance in a one semester course, but the concept of a leading tone is gonna keep coming up. So, as with accidentals, and what's the difference, the F-sharp is pushing more strongly to the G. G is on a downbeat. It makes a nice strong arrival right on the downbeat. Similarly in measure four, it's a little grace note, but it's a half step below D, it's leading to D, it's a leading tone, and then it gets canceled out if you play the C natural for the grace note. Not as good.
[music]
0:24:46.7 PT: Yeah. Okay. Yeah. Then in the next measure, well there's our flats. Oh. And guess what? We have a B flat in two registers, so we must include a flat in both registers. However...
0:25:01.5 GR: Yeah. And so this is... So if we just outline the chord, so we have this C major chord at the beginning, then we have a G major chord with B on bottom. And then the kind of third big chord of this piece is this B-flat chord you're talking about in measure four. Where we have B-flat, F, B-flat. And indeed Beethoven notates the B-flat in both octaves is not enough to notate it just once.
0:25:23.5 GR: Yeah. But I also just point out, like, can you hear the music? It seems to be just being pulled down, because the B-flats don't fit in C. But anyhow, so yeah, you've got two B-flats, one in each register, and then you don't have to write 'em again for the rest of the measure because they're enforced till the bar line, when you cross the bar line, oh, he has to write 'em again, 'cause now we're in a new measure, looks just like the previous one. So, we talk about that. By the time I get to measure what is this gonna be, 10, we see that in the right hand, there's a B natural and it's the first note of the measure, and there's no flats or sharps in the key signature. So why in the world did Beethoven actually really the typesetter, the copyist, whatever, why did they put a B natural there? And we look back and say, "Oh, well, two measures ago there was a B-flat in the right hand," and this flies by." And when you're playing that fast, you might not remember that B's are naturals. You just played a B-flat one second ago. So this is saying, "Hey wait, caution, courtesy. I'm doing you a favor. I'm telling you, no, no, no, no. Play the B natural, don't play the B-flat again." So, we've now introduced... We're still only in measure 10, and now we've introduced cautionary accidentals.
0:27:08.6 GR: And interesting to note as well that a misconception I see a lot is the belief that cautionary accidentals have to be notated in parentheses.
0:27:17.8 PT: Parentheses, yeah.
0:27:19.2 GR: And they don't, they can be notated just as normal accidentals. Yeah. And then you mentioned...
0:27:24.0 PT: I read some... Oh.
0:27:25.5 GR: No, please go ahead.
0:27:26.0 PT: I read something very interesting about, and I've read a lot about notation and something I hadn't thought about. And it's really the same in language. It's really the editors, the publishers type setters who really have determined what notation should look like or what... How punctuation and language should be used. Because it does have to be consistent. And if Beethoven is in one place and someone else is somewhere else and they have no interaction whatsoever, one person could notate things one way and one person could do it another way. So it really has to be up to the publisher to make sure that when they publish music, it's always gonna be consistent. So yes. It is true that sometimes there are parentheses around cautionary accidentals and sometimes there are not. So that's not completely, consistent.
0:28:30.9 GR: You mentioned...
0:28:31.4 PT: But no, there doesn't have to be.
0:28:32.4 GR: As we were just starting to chat about the Waldstein, you said it has a descending tetrachord progression, and we've just heard that first beginning part, which is that moment. Can you just talk about what the descending tetrachord is? And some people might know this as a lament bass as well.
0:28:49.6 PT: Yeah. And that's what I always call it that, 'cause that's one of my favorite things. My whole thing about the omnibus progression is it's coming out of this lament bass. So we start with C for two measures, then we go down to B for two measures, then B-flat for two measures, then A, then A-flat, and we go A-flat G, A-flat, G with an ending on the dominant.
[music]
0:29:17.4 PT: So that is that chromatic descent in the bass.
0:29:23.0 GR: Going through a fourth, otherwise known as a tetrachord. Yeah.
0:29:28.4 PT: Right. Right.
0:29:29.6 GR: I think often called the lament bass because well, we see it in, especially in the Baroque era.
0:29:34.6 PT: Every lament.
0:29:35.0 GR: Yeah, in lament songs. Dido's lament probably being the most famous example of That.
0:29:40.9 PT: Yeah. And in fact, I'll just also add as an aside, we have an early music ensemble, and I'm the founding director. And so, on our concert just a couple weeks ago we did Monteverdi's Lament of the Nymph. Which is a beautiful piece if you know that. I played the little harps accord part. And the shepherds are the bookends of the piece. But the main lament sung by the Nymph, the left hand, it's just that descending bass the entire time, A, G, F, E, over and over and over again. And I've looked at lots of laments and Baroque operas and you know, they all... They might go like A, G-sharp G F-sharp F or just A, G. I mean, what am I saying? They might go chromatically or diatonically, or a little of both, but pretty much they all do that.
0:30:46.0 GR: Yeah. My other favorite one is Hit the Road Jack.
0:30:49.8 PT: Exactly. Exactly. And I don't know if you know Ellen Rosand, she called it the emblem, The emblem of lament. Oh no, I'm... Anyhow, she wrote about it too.
0:31:05.4 PT: Yeah. You mentioned another word, which I'm betting many people will not have heard, which is the omnibus progression, which is this wonderful...
[music]
0:31:14.7 GR: Sorry.
0:31:15.8 PT: You got it.
0:31:16.8 GR: Don't try and play an omnibus while talking, which is this wonderful, reversible...
[music]
0:31:27.0 GR: Crazy chromatic progression. Can you maybe just say a little bit what that is? 
0:31:33.0 PT: Well, they are dominant seventh chords. Well, you have to voice them so that when you are playing them, you have, if you're going outwards, the right hand is going up, the left hand is going down, that two voices are moving chromatically, like in a wedge by half step. And then, they change voices. And then two of the other notes are moving outwards chromatically. And that keeps going. And you will eventually come back to your original chords. And then there's always a minor six four chord stuck in the middle of every two dominant chords. And it's a great, great progression. And I found that because... Or I wrote about it because I had been doing some research long ago, and I think it was something in Hayden and somebody was writing about this crazy progression. And I actually already knew a little about it, but it had not been written about much at all. And so I thought, "Oh, well, that's the omnibus progression." And then as I looked further, I thought, "Wow, there's not many people who seem to be aware of this." And they talk about it like it's just, "Oh, this is this very chromatic progression here."
0:33:08.2 PT: And so it's in tons of, I mean, lots of people have now written about it. But that's how I started getting into it. And you can also substitute diminished seventh chords for some of the dominant sevenths. And Don Giovanni, the opera has a passage like that, or a couple passages like that. So it's great. It's great. It's the bus to anywhere, you can go to any key from there. [laughter]
0:33:38.0 GR: Yeah. 'cause it repeats at minor thirds effectively, right? 
0:33:41.6 PT: Yeah.
0:33:41.7 GR: And so... Yeah. And you pass through... Anyway it's... Yeah. That's a delightful progression. And I think, you start... Once you sort of know it as a thing, you start hearing it all over the place, right.
0:33:50.5 PT: Everywhere. Yeah.
0:33:53.0 GR: Beethoven especially, I think like, the second movement of the fifth Symphony, which is the beautiful cello, a cello variation movement.
[music]
0:34:02.0 GR: Yeah.
0:34:04.2 PT: And then he gets us over to C major.
[vocalization]
0:34:16.6 GR: So he goes to an A-flat dominant seventh.
0:34:19.5 PT: Right. And then to C Major.
0:34:20.8 GR: But then he turns that into the C Major. Exactly.
0:34:25.7 PT: Yeah. I'm very impressed that you can play all these things off the top of your head.
0:34:30.8 GR: I grew up listening to a lot of Beethoven. But what I'm saying about is when he gets back from C Major, 'cause he does that same thing.
[music]
0:34:58.3 GR: And then we're back to A-flat. Right. But it's that classic.
0:35:03.2 PT: Yeah.
0:35:10.0 GR: And oh my gosh, in the context, I can do it but then I forget. Right. Oh, to E major to the passing six four to the diminished seventh to the dominant seventh, like wedges us back to A-flat major.
[music]
0:35:21.7 PT: Yeah.
0:35:22.0 GR: Yeah. They are. They are all over the place and they're just, they're delightful. So, okay. This is a lovely diversion from our...
[laughter]
0:35:32.4 GR: From our various...
0:35:32.8 PT: Lots of accidentals in there.
0:35:34.1 GR: Tons of accidentals. Yeah. Yeah. Yeah. That's another one. These third relationships in Beethoven. Right. A-flat major to C major, up a major third. And similarly in the Waldstein, C major up to E major up and they are just all over the place in this wonderful ways.
0:35:54.0 PT: And that's what allows so early on, it's like measure 42 or something. I have these measures more or less memorized. Well, I'm off, 45, no, I'm right, 42, 43, where we get the double sharps, the F-double sharps, 'cause we're going to E major at that point. There's many other things that have already happened that I would be pointing out, but yes, if you were going to G major, there would be no F-double sharps.
0:36:26.1 GR: So in that moment on that, we hear... So it's basically the second theme is this motive. And in the second time Beethoven does it, it's decorated with these lovely triplets.
[music]
0:36:42.4 GR: And in that moment of decoration, we have this beautiful E major chord, but we have this little lower neighbor, so it's G-sharp on top, but Beethoven doesn't spell this middle note as G natural. He spells it as F-double sharp instead. And the reason for that is.
0:37:02.9 PT: He's decorating the G-sharp because it is an E-major chord and it's acting again, is that little leading tone. Another thing I point out, which I really think for many of them connects more. So I'd say, let's re-notate this. We're gonna have G-sharp, G-natural. G-sharp A, G-natural G-sharp G... How many accidentals are we gonna need for those six notes as opposed to one F-double sharp? That really connects with them 'cause that's when they're all right away going, "Oh, oh." You know? So yeah, it just makes it a lot cleaner.
0:37:48.8 GR: Yeah, which I have always found introducing double accidentals in a fundamentals class. And inevitably students say, "Wait, do we actually need these? Are these real things? You're making this up, right? Surely you're making this up." But you know, what a beautiful example of, "Oh, no, no, we're not making it up." And yeah, it is so much easier to read than had we used single accidentals for that passage.
0:38:12.6 PT: Yeah, and one of my big things in teaching theory is to always explain the why. Not just, "Well, here's an example, and then we can look over here and we can see how he does something else over here." I always want to make sure I explain to them why, because this is a pet peeve of mine and you might not wanna include this. [laughter] But when people say things like, "Well, he could do it because he was Bach." It drives me crazy because I said, "No, there's a reason for it. There's a musical reason. You just don't understand the principle behind it." It's not because Bach said up, I don't need these rules. I'm gonna do what I want." I mean, that's just such a total misunderstanding. So I try to make very clear, or people very often say, "Well, Deb, you see used parallel fifths and octaves.
0:39:13.3 PT: Well, but that means you don't understand why we say you shouldn't use parallel fifths and octaves. It has to do with individual voice parts. Deb, you see is writing just sort of sound color chords. He's not writing individual voices when he's got parallel chords. So it's a different effect altogether. It's a different musical reason. It's not just because a composer is allowed to do it because they're good. So yeah. I always, as much as possible with the limited understanding they may have at any given moment, try to make them understand there's a reason for all of this.
0:40:00.8 GR: Yeah.
0:40:00.9 PT: It all makes perfect sentence as you learn more about it. I tell them it's kinda like math. Many people see math as being a beautiful thing. And I said, "I see theory as being beautiful. The more you know, the more you can appreciate."
0:40:16.0 GR: So one example that I love that you pull out is when in one measure we have an accidental, say, spelled as an F-sharp, and in the next measure we have it spelled as a G-flat, which seems like a waste of ink, right? 
[laughter]
0:40:34.5 GR: But can make a lot of musical sense. I think it was around measure 125, which is over in the development.
0:40:39.8 PT: It is. It's 125, 126.
0:40:42.0 GR: Yeah. And so in this moment, this is where... I played through the exposition last night, just to remind myself of it. I'm going to play very slowly this moment in the development. So we've got this E-flat minor chord...
[music]
0:41:00.5 GR: And then this F-sharps dominant seven...
[music]
0:41:08.9 GR: Which goes to be minor. But that wonderful moment of...
[music]
0:41:13.9 GR: And then this almost sounds like movie music to me every time. Just that shift.
[laughter]
0:41:22.3 GR: Yeah, I think especially in... Yeah, in context, we are really hearing that as E-flat minor. Once we've heard the F-sharp major, at least for me retrospectively, I hear that E- Flat minor is D-sharp minor instead. Right. And it... But, yeah.
0:41:43.9 PT: Yeah, there's a true and harmonic change there. That's again, beyond my students. So all I say is, "Well, this is this chord here, it's spelled this way here." And then the next measure, he wants an F-sharp chord. So he has to spell it according to what notes fit in each one of those chords. Because our basic triad spelling rule, it's gotta be every other line or space note, every other letter name, because again, it's gotta be consistent. That's what a triad is. So that's how he has to spell it.
0:42:23.7 GR: Yeah. That's...
0:42:25.7 PT: So I can't get into anything about in harmonics with them, but yeah, that's always fascinating.
0:42:34.0 GR: But you previewed it in a nice way by looking at those passages and... Yeah.
0:42:40.9 PT: Yeah. And in fact, I was gonna mention when you started talking about the second theme, so measure 35, there's a good example in measure 36 actually of a B-sharp. And again, the idea of like, do we really need a B-sharp? Why can't we call it a C? Well, if you look at the other notes, it's a G-sharp triad, and the triad rule is every other letter name. So if you add G-sharp, C, D-sharp, people wouldn't know what that is.
0:43:15.8 GR: Yeah, and this is...
0:43:16.1 PT: So you have to spell it.
0:43:18.4 GR: Yeah. This is that... So at the beginning of the second theme...
[music]
0:43:23.3 GR: This chord where we have the G-sharp, B-sharp, D-sharp, yeah. And if it appeared as G-sharp C natural D-sharp, it would look very strange to our eyes.
0:43:33.8 PT: Yeah, and again, you want notation to be as easy as possible for everyone to read and play without having to learn something new every time they play a new piece.
0:43:46.5 GR: Yeah, yeah.
0:43:47.9 PT: Yeah.
0:43:48.0 GR: I also love... This is a piece that obviously you can come back to many times throughout theory studies, right? And of course, we get the classic descending thirds progression here, slightly altered. Otherwise is was a Pachelbel canon chord progression or descending five, six, right? 
[laughter]
0:44:05.3 GR: But on the fourth chord of it, instead of a boring minor three chord, we get this...
[music]
0:44:17.4 GR: Actually in the case of Beethoven, a dominant seventh there. That's really wonderful.
0:44:18.6 PT: Yeah.
0:44:19.6 GR: Yeah.
0:44:20.2 PT: Yeah.
0:44:21.6 GR: Yeah, excellent. So Paula, this is great. I think one of the things that I came away with from reading your chapter was... Oh, here's... I can make these concepts so much more concrete now if I... Especially if I introduce them with say Waldstein right alongside. And then you give us that second example of the Chopin D-flat major Nocturne Op seven number two that has almost all of the same sorts of things. And I was just thinking like, "What a beautiful, in a way, lesson plan you've written for the next time I'm introducing accidentals that I can do the Beethoven Waldstein.
0:45:04.0 PT: Thank you.
0:45:05.2 GR: And then say, "Here's the Chopin and find an example of all of these things and why are these notated that way?" So it's just a beautiful lesson plan.
0:45:16.3 PT: Thank you. Well, and the Chopin has a few things the Beethoven doesn't, like the double flats, but also it's much thicker and it has things that the students have simply never seen. Let me see, where do I have a Chopin? I thought I had it all pulled up in front of me, you can tell me the measures maybe. But where...
0:45:45.3 GR: I don't have nice Chopin in front of me, I'm getting it now. [chuckle]
0:45:48.5 GR: Oh, okay. Were you have, for example, in the right hand, the pinky is playing the same note, we'll say it's a B-flat, and the inner voice is coming up chromatically. And that would be a B-natural against it. So again, the accidental only applies in the register, and here is a case where you actually would have a B-flat against a B natural, and then in several measures later, you have an A-sharp against an A natural in the same register. So of course, you've got to have both of those accidental. So those are things you wouldn't find in the Beethoven.
0:46:32.4 GR: Yeah, yeah. And the other thing of course about this piece is it has a key signature which the first move of the Beethoven doesn't have. And so that brings up some other challenges of canceling out accidentals in the key signature, using A natural to cancel out accidentals in a key signature. Whereas in the Beethoven, the natural is always returning it to the key signature.
0:46:52.7 PT: Right.
0:46:53.6 GR: Yeah. Well, it's been fun chatting about accidentals. We also... In email we're chatting a little bit about a way that you teach rhythm using rhythm clocks. Can you tell us a bit about that? 
0:47:05.5 PT: Yes, I love my rhythm clocks. [laughter] It's a perfect device because with 12 hours on a clock, you can divide them in half and thirds and quarters. And so I use chopsticks. I have a little video posted and I teach them tapping patterns. I use takadimi and counting syllables. And I tell them, "You gotta do both. Takadimi is great for learning individual patterns, but if you're playing with someone, you have to count. You have to be able to stay together." And so I start out just by saying, "A beat isn't just an articulation point. A beat has a duration, just like a minute has a full duration of 60 seconds. And we can have a half a minute and a third of a minute and a quarter of a minute and so on. And beets are exactly the same way." So instead of numbers on my clock, well I have numbers, but then I put like on the outside the takadimi syllables and on the inside the counting syllables, and I have different clocks.
0:48:18.6 GR: So each clock represents one beat, basically. Is that right? 
0:48:22.3 PT: Yes, yes. And so one clock is just at the top and D at the six. And I say... So and I talk about it in seconds. So it's 30 seconds for the half a beat and 30 seconds for the second. Ta is 30 seconds, D is the other. So you wouldn't say ta D 'cause you have to hold it for the whole 30 seconds. If you're playing a note and you let it go, the conductor is gonna say, "What happened?" So you're holding it for that full duration. And then I can divide and then we say one end two end then I can divide in three parts, kind of like a peace sign 20 seconds each. And that's gonna be ta-ki-da ta-ki-da. One triplet, two triplet. We divide in four parts. We get our ta-ka-di-mi or one anda.
0:49:14.8 PT: And then especially for showing unequal divisions like ta-di-mi, ta-di-mi. Ta is the first 30 seconds, the second 30 seconds is divided in half into di-mi. So I like to do as much visual stuff as possible. I teach a lot in approaching things visually because it really helps. In fact, I'll even give you a different example that just happened yesterday. I teach intervals differently than probably the majority of people. I don't teach them as numbers in the scale from one to three and all that. I do everything starting by looking at the keyboard and looking at the white notes. And I say, for example, all of your white note seconds are major except E-F, and B-C. Those are the minor. I mean, once we actually talk about intervals, those are the minor seconds.
0:50:17.3 PT: So if you know your white notes and there's only seven of them, you can figure out any second. If I put C and D, I know that's a major second. If I raise 'them both to a sharp, well then I immediately know that's a major second. I don't have to think like, "Oh wait a minute. That would be in the key of C-sharp and what's got a sharp on it and what doesn't. That's a lot of steps to go through. So anyhow, yesterday was our last day of class and some of my students, again, they have some background and I said, "I just want you to know that the way I've taught you intervals, I do the same thing with triads and scales." And I said, "There's another way that you would read if you looked at most theory books and this is how they do it. And it just seems to me you're taking way too many steps and you're not really seeing it. And this one kid spoke up, he said, "That's the way I originally learned it." He said, "This way is so much easier." So, and I know when I was listening to, I don't remember if it was Leigh or Melissa talking about... I think it was Leigh, the connection with math.
0:51:33.2 PT: And actually Nancy Rogers wrote an article and I cited and something that I wrote, that really the best predictor is pattern recognition ability. Which is very important in math, but that's...
0:51:47.8 GR: So just in case listeners haven't heard that episode when we spoke with Leigh VanHandel.
0:51:52.7 PT: Oh.
0:51:53.4 GR: She spoke about how the SAT or ACT math scores turned out to be a really strong predictor, even stronger than like a typical music fundamentals placement test of how students will do in a theory curriculum.
0:52:08.0 PT: Right, right. So to recognize... I mean, music is all about patterns. I tell my students, every major scale is a transposition of C-major, so if you see C-major on the keyboard, you know where the half steps are, you know your white notes can all be transposed up and down, and you just keep the half steps and so on. So it's that ability to recognize patterns that whether you look on the keyboard or then on a staff, that's really very helpful for students, so I try to do everything with a visual component first. And now I've forgotten the question you actually asked to me.
[laughter]
0:52:53.3 GR: We were talking talking about rhythm clocks. But yeah, what a beautiful insight and...
0:52:57.5 PT: Yeah, 'cause it's a visual.
0:53:00.1 GR: Yeah, into teaching intervals and triads. Yeah, yeah. And so, now you started to say you use chopsticks, and I was very curious, how do the chopsticks relate to the rhythm clocks? 
0:53:08.9 PT: Okay, so I teach my students to conduct, and of course, I teach them to conduct with the right hand. With chopsticks, we're using two so we have to use both hands. The beginning of the beat is always on the left hand. And I say, "If you're in marching band, what foot do you start on?" And they always say, "The left foot." And I say, "Okay, so we're gonna start our beat always on the left hand." And so I tap on the board, but I also have a video. And so for example, ta-di would be I tap down ta-di-ta-di.
0:53:42.2 GR: Okay. And so for...
0:53:42.6 PT: So that's our...
0:53:43.6 GR: Yeah, so for our listeners, with your left hand you're tapping ta on the desk and you're tapping di, with your left hand you're tapping your right hand holding a chopstick. So it's your alternative in the desk and then the right hand chopstick. But the right hand is just standing there. It's just sort of waiting to be tapped by the left hand.
0:54:04.6 PT: Right, right. And then if I'm doing ta-ki-da, same thing, I'm just holding the right one there and I hit down with the left ta-ki-da and I tap on the right chopstick twice, ta-ki-da ta-ki-da. They're fine. With takadimi is really hard. So I do it very slowly because I say, "Okay, you gotta tap down with the left, now tapped down, the right has to do something. Now you tap down with the right." So we've got ta-ka, you come back up with the right, you're hitting underneath the left and then you go back down. So you're going ta-ka-di-mi ta-ka-di-mi. That one is really tough for them to do, but when they get it, 'cause I say when you do it fast it's fun, ta-ka-di-mi ta-ka-di-mi. And so they do do like to do that. They have to get it, but then when they get it, they really like it.
0:55:00.7 PT: So we do... Again, it's a one semester course. There's no time. I mean, I wish we could do oral skills, but there's simply no time. So the only oral skills I do is with rhythm. And I tell them, "You gotta feel rhythm. You don't read about rhythm, you feel rhythm." And I make them march and things like that. I don't make them do proto notation. I've tried that and it's way too difficult 'cause it really needs practice. And some of them are just very uncomfortable because they're not music majors. They don't wanna have to notate something. So I do that, but I show them like if we're doing Yankee Doodle, I'll have them march and I say, "Okay, I'm gonna recite it. You just march where you feel the beat. We'll all start on our left foot." And everyone of course marches exactly together.
0:55:55.1 PT: And I say, "Look, it's like magic. You all hear the same beat." And then I say, "Okay, now as we recite it, how many syllables do you hear per beat Yankee doodle when they realize that each beat had two parts to it. And then we can ta-di our way through it, ta-di ta-di ta-di ta-di ta-di ta-di ta ta with my frog in my throat, so. And then, I can show them in proto notation what it would actually look like. So I give them enough that for those people who actually want to learn how to do it, they can see it and they can always add. And sometimes I post things for them. I say, "You can try and do this on your own." But I don't require it 'cause when I did, it was really kind of a disaster.
0:56:47.1 PT: So I thought, "Okay, okay. I'll do it. But I'll show them how." But I do go through lots of nursery rhymes 'cause they all have very similar repeating patterns, whether it's Humpty Dumpty or Yankee Doodle or Baa Baa Black Sheep or Want A Penny To A Penny, so that they can at least feel with a tapping pattern what that rhythm feels like. And then they can look at it too and know, "Okay, when I see if I'm in... I mean this obviously later after we've now talked about time signatures, if I'm in 4/4... 'cause I actually start this like right on day two just to start feeling patterns without any big explanation. So if I'm in 4/4 and I see four 16th notes, oh that's ta-ka-di-mi ta-ka-di-mi. So they know what that rhythm feels like. They know what it sounds like. I wish I had some training like that when I was first in college because... When I encountered... I played piano, but if I came across a difficult rhythm, I mean, I could sit and sort of mathematically figure it out, but I didn't know what it sounded like. So this is great that they can hear the sound of these patterns, feel them actually produce it just with chopsticks or some kids have drumsticks but... So yeah, I like my rhythm clocks.
[laughter]
0:58:19.3 GR: Great. And if you're okay with it, we may post a little video of your demonstration of the chopsticks for people to see. Would that be okay? 
0:58:25.8 PT: That's fine.
0:58:26.0 GR: Awesome. Great. We'll do that.
0:58:28.5 PT: Yeah.
0:58:29.3 GR: Yeah. Good. Well, Paula, this has just been really delightful chatting with you. I feel like we could pick any topic from Music Fundamentals and you would have wonderful tips for us on how to teach that. Just clearly you're coming from a wealth of experience doing that. And I so appreciate you taking the time to speak with us.
0:58:46.9 PT: Well, thank you so much. I would... Anytime if you wanna talk more about any of those topics, I'd be happy to do it 'cause I've been doing this for a long time. [laughter] And again, to piggyback just on something that, again, I think it might have been Melissa, when she talked about putting herself in the student's position in terms of what they know and don't know. Having taught for as long as I have, I've encountered probably most of the common errors that anyone is gonna make. And so, you figure out not only how to correct it, but why are they making that mistake? So that I try to get always to that underlying reason and how, what can I do to preempt that mistake before it even happens with anybody. So I've thought about those kinds of things a lot.
0:59:43.7 GR: That's great, yeah. And thank you for sharing them really so.
0:59:50.0 PT: Well thank you.
0:59:51.6 GR: Excellent.
0:59:52.1 PT: It's been fun. I love to talk about theory.
[laughter]
0:59:56.8 GR: Me too. Me too.
0:59:56.9 PT: So do we.
[music]
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Memory, Learning and Theory Pedagogy with Leigh VanHandel

Dr. Leigh VanHandel joins us to talk about the science of memory and learning, and how it can help us better structure our teaching. We also chat about her new book, the Routledge Companion to Music Theory Pedagogy, which recently received an Outstanding Multi-Authored Collection award from the Society for Music Theory, and about the Workshops in Music Theory Pedagogy series she coordinates.
 
Links:
Leigh VanHandel's faculty page at the University of British Columbia
The Routledge Companion to Music Theory Pedagogy: 
Workshops in Music Theory Pedagogy
Ask Dr. Van
uTheory
Chapters:
00:00:20 Introductions
00:01:45 Editing the Routledge Companion to Music Theory Pedagogy
00:07:56 How math pedagogy research can inform our teaching of music theory
00:12:34 Long term, short term and working memory.
00:15:24 The relationship of working memory and visuo-spatial skills
00:19:00 How learning happens, neurologically. (Schema forming)
00:21:21 The implications of schemas for how we teach
00:24:13 The curse of expertise, and working memory
00:32:30 The value of memorization vs. deriving concepts
00:34:30 Using schema to teach for fluency
00:44:58 Strategies for identifying and helping students with working memory limitations
00:50:20 Reducing cognitive load to help students focus on what they're learning
00:55:31 Workshops in Music Theory Pedagogy series
00:59:50 What else are you up to, now that the book is out?
1:00:00 Where can we follow you?
1:03:18 Wrap-up
 
Transcript:
[music]
0:00:21.2 David Newman: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:34.5 Gregory Ristow: Hi, I'm Greg Ristow, founder of uTheory and associate professor of conducting at the Oberlin Conservatory.
0:00:40.3 DN: And I'm David Newman. I teach Voice and Music Theory at James Madison University and I write code and create content for uTheory.
0:00:48.7 GR: Thank you, listeners, for your comments and episode suggestions. We love to read them. Send them our way by email at notes@utheory.com and remember to like us and subscribe wherever you get your podcasts.
0:01:00.1 DN: Our topic for today is music theory and working memory and joining us to talk about this as well as her new book, The Routledge Companion to Music Theory Pedagogy, is Dr. Leigh VanHandel. Dr. VanHandel is associate professor and chair of the Division of Music Theory at the University of British Columbia. Her primary research areas are music theory pedagogy, music cognition, and the relationship between music and language. Her research is published in Music Perception, the Journal of New Music Research and the Journal of Music Theory Pedagogy. She is co-director with Gary Karpinski of the Workshops in Music Theory Pedagogy program, a week-long summer intensive where teachers can learn from six experts in the teaching of music theory. Leigh, it's an honor to have you join us.
0:01:46.2 Leigh VanHandel: It's an honor to be here. Thank you so much.
0:01:48.6 DN: And especially right after you won this award at SMT for, what is the... The award was for? 
0:01:54.7 LV: Outstanding Multi-Author Collection.
0:02:00.5 DN: Fantastic.
0:02:00.6 LV: Yeah. So The Routledge Companion to Music Theory Pedagogy had an insane number, 68 authors and contributors. And so I think that qualifies as multi-author. [laughter]
0:02:17.6 GR: It's a delightful book, I have to say. We had a chance to speak with Melissa Hoag a couple of weeks ago and Stefanie Dickinson just about a week ago. And I have been just really loving going through the articles in it. It's a really... I think so many pedagogy textbooks come from one author's perspective and I've just been delighted by the variety of perspectives offered. Could you maybe talk a little bit about the origins of the book? 
0:02:50.7 LV: Yeah, sure. So I'd been approached by Routledge about putting together some essay collection and the Norton Music Theory Pedagogy book was in its final stages. We knew what the format was gonna be, we knew who the authors were gonna be. And I had that moment where I went, "Well, why do we need another one of those? What can I do that's gonna be different?" And it was literally a shower thought, you're in the shower, you're washing your hair and you go, "Well, wait a minute, what if, what if I did this crazy thing where instead of these long essays, we put together a bunch of lesson plans and made something that's practical and useful and immediately relevant to people?" And so I pitched that to Routledge and I don't think they knew what to make of that idea at first, but somehow I managed to convince them to go along with this crazy idea.
0:04:00.0 LV: And I sent an email out, some people I targeted specifically, I also sent emails to the SMT mailing list and things like that and just said, "Send me your best lesson plan. Send me the lesson plan that you look forward to teaching every year that works every time you do it." And people responded. And I wasn't sure what the response was gonna be. I thought maybe I'll get 40 and maybe I can choose 30 of them or something. I got over 220.
0:04:41.1 GR: Oh my gosh.
0:04:41.4 LV: Yeah. [laughter] And so I kept having to go back to Routledge and going, "Okay, so what are the limitations of the print again? What... How many... [laughter] How many pages am I allowed to have?" And there were just so many amazing, amazing lessons and it was so exciting to go through all of them and figure out what to include and it was just... The contributors were amazing, that they were willing to share their best lessons and let people see what they do and then allow people to replicate it also. So it was just... It was an amazingly big project, but it was also really, really rewarding and in a very nerdy way, a lot of fun.
0:05:33.5 GR: And also there are the wonderful companion materials that so many of these lessons have as well, can you talk a bit about that? 
0:05:42.8 LV: Yeah. So I think that was another innovation for the book is that, authors, when they talk about assignments that they might give or scores or analyses or whatever, they provided the materials and I created a website where all of these materials are on the website and you can go and say, "Oh, here's the assignment that this person uses after making that... After doing that lesson." And so there's links to recordings and there's all of this material that people can use to make these lessons happen. And that was really the goal was I wanted to make it as easy as possible for someone to read the chapter and implement the lesson in the way that the person was recommending. And there's... I also wanted it to be accessible to specialists in music theory, but there's a lot of non-specialists who are teaching music theory.
0:06:45.3 LV: There's a lot of schools these days that are hiring the bassoon/theory or trumpet/aural skills instructor and having them have these resources and materials was really important for me and having them be able to use them easily and right away. So that was the goal behind the supplemental materials was just making everything available as much as possible for everyone.
0:07:14.5 GR: That's great. We've been saying on the past few episodes, we are just in love with this book, I have to tell you. I'm [laughter] decidedly a fan and really have just been thrilled to, I mean, as you say, to have this window into these really excellent teachers' best lesson plans. It's just delightful.
0:07:35.8 LV: Yeah. Yeah. It's... I'm incredibly proud of the volume and I'm also incredibly grateful that I was allowed to come up with this crazy idea and see it through to completion and even more grateful that it's being recognized because that's just... That means a lot to me.
0:07:56.3 DN: So I have loved talking with you and Betsy Marvin about your work in music cognition. And your chapter in this on music theory and working memory opens by talking about the connection between success in math and music and how math pedagogy research can inform our teaching of music theory. Can you talk about that a bit? 
0:08:17.9 LV: Sure. So I wrote an article in, I guess, it was published in 2012 in the Journal of Music Theory Pedagogy about what music theory pedagogy can learn from mathematics pedagogy. And I have a really good friend who is a excellent mathematics teacher at the university level and he and I would have conversations about how people learn math and I... And he was also a musician. And so we started seeing relationships between these things. And so I just took it and ran with it. What happens is that the best predictor for how someone is going to do in a freshman level music theory class turns out not to be how good of a performer they are or how good of an ear they have, whether they have absolute pitch or anything like that, it's their score on the math portion of the SAT or ACT, depending on which exam they take.
0:09:21.9 GR: Wow.
0:09:23.0 DN: Wow.
0:09:25.5 LV: Yeah. And there's... I think there's a lot of work that needs to be done on why, but the article basically says, "Look, assuming that there is this relationship between these things, how can we borrow how we understand mathematics is best taught and adapt that into music theory pedagogy?" 'Cause mathematics pedagogy is a very, very well-funded field. Music theory pedagogy is not. So when we can steal research from anywhere, we should, I think. [chuckle] So I did a lot of reading on how people learn mathematics. And in order to make the relationship between fundamentals and math, you have to go back to first principles of mathematics, which is basic principles addition and subtraction and things that. And of course, the problem is most people learn those things when they're very young.
0:10:30.9 LV: And so the learning process, people are usually concerned that it's a little bit different. There's actually evidence that adult learners go through the exact same processes that children do just at a slightly faster rate. Not slightly, just at a faster rate. And so if you have someone who is still struggling with mathematics when they enter college, they go through the exact same processes learning basic math as a third grader does essentially. So then I thought, "Okay, if that's the case, then we can take these principles and apply them to our adult learners in freshman theory or so on, who are trying to learn these very complicated systems of music theory."
0:11:22.1 LV: And one of the challenges is that mathematics is a well-formed system. If you add four plus four, you're always gonna get the same thing. Music is what's called an ill-formed system, which I find hilarious [laughter] because sometimes in one context, the answer to something is this and sometimes in another context, the answer is this. And so it's actually even more complicated than learning mathematics in that way. So yeah, so that got me thinking about what are the different processes that we go through when we're learning to do basic mathematics? How can we apply that to basic music theory skills like spelling intervals or chords or scales? And all of that got me thinking about the cognition of teaching and learning and about what are the best, most efficient and effective ways of teaching this material to adult learners. And then that led into the working memory stuff and that led to the chapter in the Routledge Companion.
0:12:35.3 GR: That's great. And in that chapter, you talk about three kinds of memory. You talk about long-term, working and short-term memory. Can you tell us a bit about these? 
0:12:45.7 LV: Sure. So long-term memory is essentially the facts, the declarative knowledge or the procedural knowledge that you have stored away in your head and it's material that's there and is available for retrieval and you don't have to walk around rehearsing that information all the time. It's there. You can... If you wanna make the filing cabinet analogy, you can go to the filing cabinet, pull out that information when you need it, and then put it away and you don't have to constantly be thinking about it. Short-term memory is our ability to hold a certain amount of information in our memory for a short period of time.
0:13:27.7 LV: So short-term memory is the thing that kicks in if you are trying to remember a phone number or if somebody tells you, "Okay, turn to page 221 and look at example 4.3," you're holding 221 and 4.3 in your head and you have that in your short-term memory. Working memory is when you are holding a short amount of material in your memory, but you're manipulating it. And so if I said to you, "Here's my phone number," and then you had to remember it long enough to run over and write it down, that would be short-term memory. If I said to you, "Here's my phone number, now repeat it to me backwards," that would be working memory because now you're having to manipulate that information in some way. Or if I said, "Add one to every number of my phone number," or something like that, that would be having to manipulate that information.
0:14:25.3 GR: And how consistent is, do we... Is there a base level of working memory that everyone has, or do we vary in our ability to use our working memory? 
0:14:39.0 LV: The answer to both those questions is yes, [laughter] which seems contradictory. But in the 1950s, there was a psychologist named George Miller and he did a famous memory study in which he determined that the short-term memory limits for most people are, as he described it, five plus or minus two items. So there's a range in which most people fall, but some people have more abilities and some people have fewer abilities. And so yes, the answer to both questions is yes. There's a limit, but there's also variation within that.
0:15:26.1 GR: Yeah. And then you talk in your article a bit about the relationship between working memory and visual spatial skills or visual spatial skills. First off all, what are visual spatial skills and what is that relationship? 
[laughter]
0:15:41.9 LV: So yeah, visual spatial skills are the ones that are hardest to describe. It's essentially like direction finding, the ability to rotate a figure. If you've ever taken an online test or something that where it says, "Here's an F and here's another F," but it's rotated and you have to say which direction it's been rotated or something like that. It's essentially the ability to manipulate spatial information. And your podcast listeners can't see it, but I'm rotating my hand around in circles in very bizarre ways right now because I talk with my hands. So it's that ability to manipulate spatial information, keeping one version of something in your head and then manipulating the other one to see how it changes. My theory, and I have not yet had a chance to test this and I really, really, really want to, my theory is that visual spatial memory comes into play in music theory fundamentals, especially when we're talking about things like interval inversion and things that or chord inversions, because students have to be able to spatially manipulate chord members that are out of order basically.
0:17:05.4 LV: If they're in open position or if they're inversion, they have to be able to go, "Okay, I have a G on the bottom and then I have an E, and then I have a C. Wait a minute, how do I rotate those around in my head to get them in the right order?" And I've encountered a number of students in my career who struggled with that in a way that was more than I would have expected them to. And so I have this crackpot theory that I really wanna test at some point, which is that if you have a visual spatial working memory deficit or memory deficit, then things like chord rotations or open position or things like that might be a little bit more challenging.
0:18:00.6 DN: There's a clear example of that if you're playing on the piano because it does, it feels very much... It looks like a rotation, how you position your right hand, for example.
0:18:12.6 LV: Yeah, yeah. And that's actually a really good point because one of the ways you can combat that if it's happening is through some other sensory input. Sometimes if somebody has trouble doing that mentally, the kinesthetic reinforcement of thinking about a piano keyboard, if it's something they're familiar with, if they're struggling with the piano keyboard as well, this just adds another layer to the complication. But if it is something that they're familiar with, then that can be a kinesthetic reinforcement of the rotation or representation of the rotation and can help them figure that out. But if they're having that trouble, yeah.
0:18:56.0 DN: Alright. So in the context of these kinds of memory, how is something learned? How can we solve this problem? 
0:19:08.3 LV: That's a great question. So when we are learning material, the first thing it does is it goes into our working memory and our short-term memory. If we're manipulating it, it's working memory. If we're processing it for knowledge, it's short-term memory. But as it's becoming knowledge and as we're trying to get it into our long-term memory, we're creating what's called a schema. And a schema is basically an interconnected network of basically all of the things that we know. And this is a gross simplification, but there's this network where when a new piece of information comes in, our brain goes, oh, wait, that's connected to this and to this and to this. So I'm going to put that there, and I'm going to build these connections out to this other material so that this piece of information partially recalls these other pieces of information when I pull it up. So you can have isolated bits of knowledge. The example I always give is, you can tell someone who's a non-musician over and over that the key of A major has three sharps. And you can repeat that enough to them that they'll be able to repeat that piece of information back to you.
0:20:30.3 LV: And that is now a piece of knowledge that they have. It may even be living in their long-term memory if you've said it to them often enough. But they have no context for what that information means or what they can do with it. So the schema is the network that helps you figure out, oh, okay, the key of A major has three sharps. I know what those three sharps are because I know this information. I know what that means in terms of scale because I know this information. And I know what that means in terms of intervals and chords because I know this information. And all of those things are connected. And that's the goal that we want to get people to when we're teaching them fundamentals is we want them to have this schema where every bit of information that we're giving them reinforces every other bit of information.
0:21:27.9 DN: That is cool.
0:21:29.1 GR: I think, just right away about the implications for how we teach as well, just how important that means it must be to think about when we're introducing a new concept, proactively tying it into things that we've already covered and making the back connections and setting up the forward connections as well.
0:21:51.9 LV: Absolutely. Absolutely. That's the critical thing. Some students are able to make those connections on their own. And they're the ones whose schemas are pretty robust. If someone's schema is shaky to begin with, they need that explicit connection to be made for them. And even if they don't need it, it helps. It helps them to go, oh, this is how this connects to the material I already know. It helps reinforce that material. And like you said, it helps lead forward to whatever other way we're going to expand that information in the future.
0:22:28.8 DN: And this is a little off topic, but it makes me think of how does one deal with remediation? But a good description of what you're trying to do is trying to help find where the holes in someone's mental map are and maybe help patch them.
0:22:47.1 LV: Yeah, exactly. Exactly. I've been teaching fundamentals for a really long time because I absolutely love it. But one of the things that happens is if a student is struggling with some material, they're usually not struggling with that material. They're struggling with one of the steps on the way to it. And so you have to investigate their schema a little bit and figure out where are they having that struggle? Where are they failing to make that connection between something and then help them make that connection. And I can't count the number of times I've spent time with a student doing that. And when you finally find that fundamental misunderstanding or that thing that never quite clicked for them and you work through that with them and then they go, oh, wait. And then all of a sudden, you see the metaphorical light bulb go on over their head and they go, wait, now I get it. And this means this and this means this. And they get really excited because suddenly all of these things fall into place. And quite honestly, those are the moments that I love. I love watching that light bulb go on and I love watching them see that connection and see this connected world of fundamentals opening up in front of them and them seeing how to navigate through that path. And those are the wonderful, wonderful moments.
0:24:15.0 GR: That's great. That's so great. I think for me, sometimes one of the challenges of that and probably for a lot of teachers is, and you talk about this in your article, is the curse of expertise. This idea that especially when we're teaching basic concepts in our field, we know those so well that it doesn't tax our working memory at all. Could you maybe give an example of this and help us with how we can work through that curse of expertise as teachers? 
0:24:47.2 LV: Sure. Sure. So yeah, so the curse of expertise is basically when you've gotten good enough at something that you don't remember what it's like to not be good at it. And as a result, what that means is that you forget how many steps a non-expert has to go through to get to that point. So my favorite example of this is, because we are all experts, we do not have to tax our working memory at all if we're trying to remember how to spell common chords, for example. If somebody says to us, what's a D major chord? We go DF Sharp A. There's no... Yeah, exactly. And we don't have to use any cognitive load on that. There's no working memory burden. It just pops out, right? And it pops out immediately. What we forget is that for someone for whom this is new material, there's a tremendous number of steps that they have to go through because the number of steps that are involved in figuring that out, if we don't already know it, are really quite big. So if you go, okay, what's a D major chord? Then somebody would have to go, okay, so wait a minute, which notes are in, if a D is the root, so it would be A, B, C, D, E, F, G, A.
0:26:09.3 LV: Okay, D, F, and A. So I'm going to have some kind of a D, some kind of an F, some kind of an A. Now they want major, so major, let's see, where is that on the circle of fifths? Okay, that's two sharps. What are the order of sharps? So I'm going to have F sharp and C sharp. And wait a minute, what were the notes of my chord again? I had a D and an F and an A, and I had F sharp and C sharp. Oh, F, F sharp, F sharp. Aha, it's DF Sharp A, right? And I'm exaggerating a little bit for comic purposes or demonstrative purposes, but those are the steps. And if any one of those things is not really that solid, if they had to spend more time thinking about the key signature and the order of the sharps and whatever, by the time they came back to what were my notes that I had, they might have forgotten which the notes were, if they don't have those things set together as a chunk. And so it's really a quite working memory intensive task that we're asking someone to do if it's not already in your schema. Whereas we just go, DF sharp A, no problem. So one of the horrible things that I've asked people to do in presentations on this is I've said, okay, we are all experts at the A, B, C, D, E, F, G system, so let's take that away. You're not allowed to use A, B, C, D, E, F, G. We're now going to use H, I, J, K, L, M, N, right? 
0:27:52.9 GR: Yeah. As I see you're counting them out on my fingers, yeah.
0:27:55.1 LV: Exactly, exactly. And think about your fundamental students who are doing the same thing on their fingers, A, B, C, D, E, F, G, right? They're experiencing the same thing.
0:28:06.3 GR: Or even worse, they're doing C, D, E, F, G, A, B and struggling with the wraparound after G.
0:28:11.6 LV: Yeah, exactly, exactly. So then in this exercise that I do, I say, okay, we've got H, I, J, K, L, M, N, those are our new note names. Let's keep the conceit of root, third, and fifth of a chord. We'll alternate to spell chords and so on and so forth. Wrap around when you reach the end and don't write this down. Do it in your head. And so then I'll give them some examples and I'll say, okay, in that system, what if I is the root? How do you spell the chord? 
0:28:45.7 GR: I, K, M.
0:28:50.0 LV: Yes.
0:28:50.7 DN: I, K, M. But yeah.
0:28:53.9 LV: But you have to count it out on your fingers.
0:28:56.1 GR: Yeah, exactly. Yeah, people can't see that, but yes, I'm sitting here and yes, absolutely counting out on my fingers.
[laughter]
0:29:01.1 LV: Yeah. And then if H is the third.
0:29:09.0 GR: M, H, J.
0:29:12.1 LV: Yes. Why was that one harder? 
0:29:14.0 GR: Because I had to wrap around. I had to work backwards from H, which is the start of the alphabet, and I couldn't wrap backwards because I couldn't remember what the end of the alphabet was, so I had to go all the way forwards to the end of the alphabet and then count backwards.
0:29:32.6 LV: Exactly. Exactly. So yeah, so that's a really challenging exercise. And then I make it harder. I add different things in where you have to... So you have to spell the chord and then you have to look at what I call a target word and figure out how many letters the target word has in common with the chord that you just spelled and manipulate the chord in some way, which is essentially the process of figuring out your letter names, thinking about the circle of fifths, thinking about what the order of sharps and flats is, and then applying that to what you're doing. It's really a humbling experience for a lot of experts. Some people don't find it that difficult, but they're still taking 10 seconds per chord to do it, whereas if I say, what's a D major chord, you go DF sharp A, and it takes you one second.
0:30:35.2 LV: And so where this creeps in is that as expert musicians with our cursive expertise, we forget the number of steps that someone has to go through in order to solve these problems that we're giving them. And so we go, oh, okay, here's 10 intervals. You can do this in a minute, forgetting that we can do that in a minute because it's six seconds per interval. But they're having to go, okay, so wait, they want a major sixth above E. Okay, so six, E, F, G, A, B, C. Okay, so it's some kind of a C. Now, let's see, major six. Oh, god, what's the key signature for E? And all of a sudden, now we're already at 20 seconds for this one interval, whereas we look at that and go, C sharp, done, next. Right? So one of the things that we have to think about when we're designing assessments or when we're trying to assess fluency is, we have a different level of expertise than our students do. We are able to come up with this information much faster because it's in our schema. That is the goal for the students. We do want them to be able to have that material, that available.
0:31:56.6 LV: But if they're just learning it, it's going to take them time to get there. And so we have to allow for, for example, more time than we think on timed tests. We can't go by how fast we can do it, basically. And then we also have to remember that it is really going to help the students if we make those explicit connections that help them develop that schema so that they can then develop that expert recall that we want them to have.
0:32:29.4 GR: As you're talking about this, I'm thinking a lot about this idea of a schema and the interconnections between pieces of information within that schema. I wonder, does this tell us anything about the value of memorization versus saying understanding processes for deriving ideas? 
0:32:53.6 LV: Yeah, it does. So if you are memorizing information, yes, you're getting it into your head and you're able to pull it back out. But it's usually not connected to other information as well as it should be. A good example of this is think about someone who's memorized a piano sonata or something like that, any piece of music. What happens if they make a mistake and have to stop? They usually have to go back to the beginning of some section because that's where they've created a mental, here's where this starts and I have to go through. It's harder to pick up in the middle. And that is if they memorized it by rote, right? I do this thing after I do this thing after I do this thing. And then if you stop in the middle and go, okay, what comes next? They go, I have to go back to the beginning and work through all of this. Whereas if you have the information memorized, but you have it connected to other information, then you can go, okay, this is where I am. This is what comes next and start back up from where you left off. And the same thing happens in spelling chords or intervals or whatever. If you get a problem and suddenly you get distracted and then you go, "Wait, where was I?" Oh, right, I remember this. And then pick back up and go where you left off from.
0:34:31.6 GR: And in a topic like music fundamentals where we do want students to eventually gain that fluency and ease and speed that really only comes at the point that a lot of these things are, as you said, immediate knowledge accessible in long-term memory. Does that have implications then for how we teach to get them to that speed? 
0:34:58.1 LV: Very much so. You're about to open up a rant on how we teach intervals. Is that okay? 
0:35:03.9 DN: Please. Yes. Yep.
[laughter]
0:35:09.2 LV: Okay. There's a number of different ways that people think about teaching intervals and one of the ways that people teach intervals is by teaching students to count whole steps and half steps. The benefit of teaching whole steps and half steps is that it's a algorithmic process. The bad thing about it is that it is not connected to any other piece of information. If you get a student who is going, okay, every time I see a major third, I'm going to count four half steps, then they're not necessarily learning how these things connect to one another or how these are connected to the bigger schema. So I cringe internally a little bit when I see people teaching intervals by whole steps and half steps just because it's memorization of an algorithm, not of, not adding it to the system. And so there's a number of different ways that you can take students who are relying on doing that and move them towards more sophisticated understandings of how these things relate. Obviously, one way of thinking about it is if you're asked to spell a major third above F, you can think of F as the tonic of the scale and then go, okay, what's my key signature? How does this relate? And so on and so forth.
0:36:52.4 LV: And that works, but the problem with that method is what happens when the bottom note is a D double sharp and you don't have that as a tonic and so on and so forth. Then when that happens, what expert musicians do is they go, oh, okay, let's see, you're asking me for... The interval I always give when I give this example is a minor sixth above D double sharp. And that is because pretty much nobody has that interval stored in their memory anywhere. And so you actually have to think about it. What happens is if we meta-cognate about how do I solve that problem, expert musicians do what's called decomposition. They go, all right, D double sharp. No, I am not thinking about D double sharp. Mentally, I'm covering up that double sharp and I'm thinking about D. Now, let me think of a minor sixth above D. If we have it in our memory, we go, okay, minor sixth above D is B flat. Otherwise, we go, now I can think of the scale of D and now I can think of D minor and figure it out that way. And I go, "Okay, now I know that this is B flat." But my interval was above D double sharp. Now I re-manipulate that and I go, I'm going to raise my D by two half steps. I'm going to raise my B by two half steps. And now my answer is D double sharp to B sharp, which is a ridiculous interval and nobody should ever encounter that in their lives, but it's a good example how we can move people through a strategy.
0:38:34.4 LV: If somebody is spelling the interval by counting half steps and whole steps, they have to remember that there are eight half steps in a minor six and then they have to count up from D double sharp. And if they're just counting, there's a really good chance that they're going to land on C and go, oh, my answer is a C and that's not a minor sixth then other problems come about. If they're just relying on that scale method, then they're going to run into trouble because they're going to have to think about what the key of D double sharp is and nobody should ever have to do that. The more sophisticated steps are these decomposition steps, which is where you take a piece of information you already know and manipulate it into the piece of information that you need to find out mixed with this idea of immediate recall.
0:39:32.3 LV: We couldn't immediately recall a minor six above D double sharp, but we probably could because we are expert musicians immediately recall what it was above D. We did the immediate recall for that and then the decomposition to manipulate that information. What we want to do is when we're teaching students to spell intervals, we want to move them as close as we can to that immediate recall. But we also want them to have the other strategies in place for when the immediate recall doesn't work. And I talk about this some in my 2012 article. What we want to do is we actually want to show students that these strategies work because if they're stuck on using half step and whole step method to count intervals, it's because they don't trust their schema to give them the right answer otherwise. They're going back to the version of this process that they think is the most reliable for them. One of the things that I do in the classroom when I'm doing this is I very, very deliberately talk about process for every single question that I ask them. When I was in the theory classroom, I had teachers who would point at you and go, "What's a major third above A flat?"
0:41:09.7 LV: And you had to answer immediately and then point at the next person and point at the next person and point at the next person and bark out intervals. You had to answer as quickly as you could. And A, it was terrifying and intimidating, but B, if you got the wrong answer when he was barking at someone else, if you even were practicing these intervals along or if you were just sitting there in terror waiting for your turn, you didn't know why you got the wrong answer. One of the things that I do is I will always say, okay, so what is a minor third above F? I'll let people think about it for a second and then I'll call on someone. If someone goes, oh, it's A flat, how did you get that answer? And if they say, I just knew it. I'll say, okay, what if you didn't just know it? It's great that you knew that, but what if you didn't just know it? How could you get that answer? And then make them go through the steps of saying, well, I could have thought of the F minor scale and realized that the F minor scale has four flats and that A flat was one of them, so the third above F is going to be A flat.
0:42:25.8 LV: Okay, great. What's another way? And then somebody will go, well, I thought of the F major scale and then lowered the third by a half step. Okay, great. I'll do that so that the students who are struggling with these processes see how that works. And more importantly, they see that students are being successful with those more sophisticated strategies because ultimately what it is is they don't trust the strategy yet because it's not quite... Their schema isn't quite built up enough so that it's working for them. You have to work on the schema, but you also have to work on that confidence. And so that's where making that schema explicit, making those connections explicit is super, super helpful. Ironically, the other type of student that this helps, it helps the student whose schema is not fully formed yet. It also helps the overachieving perfectionist student who has the immediate recall, but has to double and triple check to make sure that their answer is correct. And so they end up spending way too long on every answer. If you get interval quizzes back where two-thirds of the questions are answered but they're all correct, you've got someone who is double and triple checking their answers to make sure that they're correct, which means that they're not getting through as many as they should 'cause they don't trust their process.
0:44:03.9 LV: Having those students see, okay, I'm using this process. This other person used this process. They got it right. I should trust my process more. I should trust my schema more. Also helps those perfectionist students who are afraid of making a mistake.
0:44:23.0 DN: I love this reminder that perhaps we need to be mindful of what our goals are and that the goal is not necessarily to know the piece of information, but to build the schema.
0:44:39.7 LV: Exactly. Exactly. That is the piece of... Building that schema is the thing that's going to help students moving forward. Having the isolated bit of information that a minor third above F is A flat will be useful in some circumstances, but does not help them with anything else really going forward.
0:44:58.3 GR: And related to that, you talk in your article on working memory a lot about ways that we can use our knowledge of working memory to improve our teaching. I wonder if you could talk about some of the strategies you identified, specifically identifying and intervening with working memory issues and also reducing cognitive load.
0:45:22.6 LV: Sure. When I present on this, the question I always get is, okay, how do we figure out who's having those working memory problems? The easiest way to tell if someone is having a working memory problem is, I think we've all had students who brain dump a whole bunch of information on the top of a task store in assignments. They'll write out the note names and they'll draw the piano keyboard and they'll draw the circle of fifths and they'll do all this stuff on the test. And the reason they're doing that is because that is reducing the burden on their working memory. They've now offloaded this information onto the page so that they have something to reference and they don't have to do the mental calculation each time. Those kind of things are crutches, basically, and they will help the students at the beginning and then they will hinder them as they move forward because they are not developing quickly enough the schema that they need and they're relying on this offloading of information. And they're doing it because they're having trouble developing that schema. This actually relates to both working memory and schema and cognitive load because essentially, they're trying to lighten the load on their cognitive burden in order to calculate these things.
0:46:50.5 LV: That's one way of identifying them. Obviously, another way is if a student is struggling with material then they probably have some weak link in their schema somewhere and you have to spend a little bit of time with them to drill down into that. But there's other cues as well other than performance on assessments. So if students are exhibiting trouble in processing information simultaneously or keeping information in their heads or forgetting what the next step is in a complicated process, for example, if they're like, okay, wait, wait, wait, what do I do after I do this? It has to be a constant thing. But working memory deficits are also implicated in things like ADHD or other attention deficit disorders. It's not the cause of it, but it's implicated in it. And so they might be easily distracted, especially if an activity is challenging, they might try to avoid completing the activity just because it's become hard for them and they don't want to acknowledge that it's hard for them. So they go, oh, look, a squirrel and they get distracted by something. So students who have ADHD or other neurodivergences like that, they tend to exhibit behavioral problems.
0:48:38.0 LV: Students with low working memory exhibit some of the same symptoms, but they typically don't exhibit any of those behavioral problems. So if there's no other issues, then working memory might be implicated in something like that. So the thing is there's no real way that we can train our working memory. So if you listen to National Public Radio for any period of time, you'll hear ads for Lumosity or something like that, train your brain kind of things. And studies that they fund talk about how this helps you with your working memory or with brain processing and so on and so forth. Independent studies find that that's really not the case. The tasks that something like Lumosity are asking you to do, you can get really, really good at those tasks, which are things like swipe on the direction of the center bird or things, there's these different exercises that Lumosity gives you. You can get really, really good at swiping in the direction that the center bird in a group of five birds is facing, but that's not going to help you spell chords. [laughter] So there's no transfer from the type of task that something like that is asking you to do into music theory fundamentals.
0:50:11.3 LV: You have to practice music theory fundamentals, and you have to develop that schema of music theory fundamentals in order to get better at it. And you mentioned cognitive load, and that's a really, really important thing for instructors to think about because if a student has a working memory deficit and you are standing in front of them going, okay, so everyone, let's turn to page 88. Let's look at example 12. I want you to identify passing tones, neighbor tones, appoggiaturas. If you're listing a whole bunch of things, by the time you're done with that list, they've forgotten what page you asked them to turn to because they've been trying to keep all of this material in their head as you've been going, and that's when you get the what page, what example, what are we doing? And so this is one of those universal design for learning principles that it's better for everyone not just people with working memory deficits. If you give instructions very, very clearly, if you provide time for processing, if you write it on the board so that they can reference it when they have questions, it's the cognitive load of... If the cognitive load of the task you're asking someone to do is very high and you're dumping more information on them as they're trying to do that task, they're going to fail at the task.
0:51:48.7 LV: There's going to be some an interrupt, whether they've forgotten the instructions, whether they've forgotten the task or how to do the task. So there's a lot of principles in learning about the best way to reduce cognitive load on students so that they can put most of their cognitive load on the task that you're asking them to do. Clear instructions, instructions that are in the same place as the question. So for example, don't design an exam where the instructions for a question are on one page and the question is on the next page because then they're flipping back and forth and they have this split attention issue where they're not able to read the instructions and immediately look at the thing that they're being asked to do. The other thing, I've observed people in the classroom where they will play music during some kind of a test. Music unrelated to the test, they will play music during the test. And their feeling is, well, students to listen to music when they study, so I should do this when they... But that's a huge cognitive load drain because students with working memory issues or with attention issues are going to be distracted by this thing that you're doing.
0:53:17.6 LV: And so that's always something I did, don't play extraneous music while students are concentrating on something. And one of the things that I figured out also was, if students are doing a test and I have a musical example that I wanna play for them, for example, it's really intrusive of me to go, okay, everyone, turn to example three. I'm going to play the example now and then play the example because they were in the middle of a task. They were in the middle of something and they had their thought processes going and they had all of that stuff where they were trying to remember, okay, I'm doing this and I'm doing this and I'm doing this. And suddenly I barge in and go, okay, pay attention to this now. So what I'll do is I'll tell them I'm going to play this music example at 10 after, at 15 after, at 20 after, and I will give you 30 seconds notice before each time I play it. And so when it gets to that point, I will very quietly say, okay, finish up whatever task you're on. I'm going to play this musical example in 30 seconds.
0:54:25.9 LV: That gives them time to make notes to themselves or finish that thing and then get that gone so that they can now concentrate on this new thing. And it's worked really, really well because one of the things I noticed when I was not doing that was that students would leave questions blank or half completed because they forgot that they were working on it. They looked at it and they went, oh, I've got an answer there that must be right and then moved on to the next question. And I don't see that as much anymore when I'm mindful of directing their attention in specific ways and carefully asking them to finish up what they're doing and now let's pay attention to this.
0:55:14.2 GR: Yeah, I'm learning so much just talking with you now.
[laughter]
0:55:15.0 GR: This is wonderful. I have the sense we could go on talking for hours, but of course, time is always...
0:55:24.7 LV: That's probably my fault. I'm sorry.
0:55:27.8 GR: It is such a gift to us. Really, it's just delightful. But for people who would like to learn more from you, there's certainly that opportunity. You and Gary Karpinski coordinate the Workshops in Music Theory Pedagogy series. Could you tell us a bit about that, about who that's for and if people want more information about that, where they can find it? 
0:55:50.4 LV: Yeah, absolutely. So the Workshops in Music Theory Pedagogy have been a workshop series that's been hosted every three years. They've been hosted by Gary Karpinski at the University of Massachusetts at Amherst. Gary has retired and he's asked me to step in as director. So this year is his last year. We're co-directing this year and we're moving them to the University of British Columbia. And they are June 26th through 30th of 2023. The workshops consist of four faculty that are brought in who are expert music theory pedagogues and it's a week-long workshop where each faculty member talks about their strategies and things that they're specialists in. And then there's also small group workshops with each faculty member each day so you can choose who you want to go work with and get more information and feedback from each person. So this year we have six faculty. It's Gary Karpinski, me, Michael Callahan from Michigan State, Nancy Rogers from Florida State, Jena Root from Youngstown State, and Jenny Snodgrass from Lipscomb University. And so it's an amazing, amazing group of music theory pedagogy scholars who are going to have a ton of information that they can share with people.
0:57:29.3 LV: We're in the process of finalizing the registration like financial stuff, just getting the ability to have people make payments. But there is a website that you can go to which is just workshopsinmusictheorypedagogy.com and that will take you to the UBC website where the information is and that website will eventually include links for registration and housing and meals. And basically, you just live on campus for a week and do these workshops, these interactive workshops. And it's a wonderful type of nerd camp which is perfect for people who are... Like grad students who are studying to be music theorists, music theorists who just want to hear other people's perspectives. It's wonderful for faculty who maybe are non-specialists in theory who are being asked to teach music theory. Every single time it's offered, we get somebody who comes in and goes, I'm the flute instructor. I've just been told I'm teaching aural skills in the fall. What do I do? And it's the perfect...
0:58:44.0 GR: What about high school teachers who maybe are starting to teach AP theory or something? 
0:58:51.1 LV: Absolutely. Absolutely. Yeah, that's actually a great population for it as well because if you're a music ed person you had theory classes but you probably haven't had them in two or three years and now you have students who want to do an AP class and you're terrified, come to us. Come to us.
0:59:11.8 GR: Great. And we will link to that site in the show notes as well.
0:59:16.0 LV: Excellent. Excellent. Yeah, so it's really exciting that it's being hosted in British Columbia now. Late June in Vancouver is an absolutely stunning time to be in Vancouver. And I know a lot of people are planning on taking a couple of extra days at the beginning or at the end to do some sightseeing around Vancouver's area and I'm super excited to have it in here and to be part of it now.
0:59:52.1 DN: Cool. [laughter] And aside from that, what else are you up to these days? 
0:59:58.5 LV: Well, I'm still relatively new at UBC. I started in September of 2020 in the middle of the pandemic, so to me I feel that first online year didn't really count. I feel like I'm still figuring out how things are going here but I've managed to get a really good music cognition lab going and so I'm doing lots of music cognition research. My main interests there are meter, rhythm and tempo and so we've been running a whole bunch of experiments on perceived rhythmic complexity and rhythmic patterns and what makes people feel something is complex. And yeah, so that's probably the primary thing that I've been working on recently is that project.
1:00:54.8 DN: Cool.
1:00:54.9 GR: I just can't wait to hear what you have to say as well.
1:00:58.7 DN: I know we need to have you on again. [laughter]
1:01:00.7 GR: This has been just such a delight talking with you today. I wonder if listeners are interested in keeping up with what you're up to, where can they find you? 
1:01:10.2 LV: So they can search for me on the University of British Columbia website. I have my own website. You'll eventually find it if you search for Leigh VanHandel Music Theory. It'll probably take you right to it. On that website, you'll find information about my research lab. You'll find information about the Routledge Companion to Music Theory Pedagogy. There's also a blog that I have that I call Ask Dr. Van where I get a lot of emails from middle school students who have to do some a research project where they email a faculty member and ask a question. And so I started answering the questions and then putting them up on the website with the identifying information redacted of course. And some of the questions are really great, really sophisticated that take multiple iterations of questions to answer. And some of them are just wonderful questions why is Stairway to Heaven the best song ever? 
[laughter]
1:02:19.3 LV: And I had to sit down and figure out how to answer that question. So that's really fun also looking at that and seeing that even younger students are really interested in music and what it means to them and how they think about music. Some of the questions are theory oriented. Some of them are cognition oriented. And it is really fascinating to see that kids are thinking about this and hopefully these are the students that we can get interested in it, keep them interested in it and they're going to be our fundamentals theory students and our music theory and cognition students in the future.
1:03:06.6 GR: Excellent.
1:03:07.3 LV: And people can also email me, leigh.vanhandel@ubc.ca.
1:03:13.4 GR: Awesome.
1:03:14.2 LV: So if anyone has questions, they can email me.
1:03:16.8 GR: Great. Well, thank you again for joining us. Really just such a delight to learn from you. I feel I've come away from this with 100 ideas that I'm going to have to just sit down and process as I start to incorporate them into my teaching. So really thank you.
1:03:31.8 DN: Thanks so much, Leigh.
1:03:32.0 LV: Thank you for having me. This was a lot of fun.
1:03:38.5 DN: Notes from the staff is produced by utheory.com.
1:03:41.2 GR: uTheory is the most advanced online learning platform for music theory.
1:03:45.4 DN: With video lessons, individualized practice and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm and ear training.
1:03:56.9 GR: Create your own free teacher account at utheory.com/teach.
[music]
 

Music Fundamentals Games with Stefanie Dickinson

Dr. Stefanie Dickinson joins us to share some of the music fundamentals games that she uses in her music theory classroom.
 
Links
Routledge Companion to Music Theory Pedagogy
Dr. Stefanie Dickinson’s page at UCA
The Power of Play with Jed Dearybury (Notes from the Staff Episode)
Dalcroze Solfege Games with Greg Ristow (Notes from the Staff Episode)
uTheory.com
 
Show Notes
0:00:21.2 Introductions
 
0:02:27.1 Value of play in teaching and learning
 
0:06:02.4 Key Words - for key signatures
 
0:08:47.0 360 Degrees - for scale degrees
 
0:10:30.4 Balance Beam - for rhythmic values and notation conventions
 
0:13:38.2 Meter Cards - for identifying time signatures
 
0:16:44.8 Notation Bloopers
 
0:20:15.0 Triad Bingo (can be extended to other topics)
 
0:23:01.6 How do you help students who are struggling to get beyond the despair factor?
 
0:25:18.0 Interval Train
 
0:26:57.5 Value of competitive games in teaching fundamentals
 
0:32:43.1 Phone Numbers Game (aural skills, scale degrees/solfege)
 
0:38:32.1 Extending games for other topics
 
0:40:04.6 Wrap-up
Transcript
[music] - These are the notes from the staff where we talk about our point of view, and we share the things we're going to do, `cause the path to mastering theory begins with you.
 
0:00:21.2 Greg Ristow: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
 
0:00:33.4 David Newman: Hi, I'm David Newman, and I teach voice and music theory at James Madison University, and write code and create content for uTheory.
 
0:00:42.9 GR: Hi, I'm Greg Ristow, I conduct the choirs at the Oberlin Conservatory, and I'm the founder of uTheory.
 
0:00:49.0 DN: Thank you listeners for your comments and episode suggestions. We love to read them. Send them our way by email at notes@utheory.com, and remember to like us and subscribe wherever you get your podcasts.
 
0:01:01.6 GR: Our topic for today is music fundamentals games, and joining us to share some of her favorite games is Dr. Stefanie Dickinson. Dr. Dickinson is associate professor of music theory at the University of Central Arkansas. Her primary areas of research include the music of Liszt's late experimental period, issues in analysis and performance, and music theory pedagogy. She has presented her work at regional and national meetings of the Society for Music Theory and College Music Society, the International Conference on Music and Gesture, and others. And her articles can be found in Gamut, College Music Symposium, the Festschrift Liszt 2000, and most recently in the Rutledge Companion to Music Theory Pedagogy, where she's written about games for teaching music fundamentals, which is what we're going to talk about today. Stefanie, welcome.
 
0:01:49.4 Stefanie Dickinson: Thank you so much. It's a pleasure and honor to be here, and I appreciate the opportunity.
 
0:01:54.4 GR: We're thrilled to have you. So you're teaching at University of Central Arkansas. What all do you teach there? 
 
0:02:00.0 SD: I teach only music theory. I have two sophomore theory and two sophomore aural skills classes in the fall, and then spring I go on to teach some upper level electives. I teach the form class. We have an introduction to linear analysis, and then in the summer I teach music theory pedagogy class.
 
0:02:19.5 GR: Well, I loved your chapter, so I'm so excited to talk about games, and especially music fundamentals games.
 
0:02:27.1 DN: So a theme we've come back to several times on this podcast is the value of play in teaching and learning. Listeners may remember our episode with Jed Dearybury, author of The Playful Classroom, or the episodes where Greg and I talked about Dalcroze solfege games and about music theory songs. So we've talked a lot about this, but before we dive into specific games, I wonder if you could talk about the value of games in teaching and how you came to use them in your own pedagogy.
 
0:02:52.5 SD: Sure. I think that games are very, very valuable, potentially at every level of instruction, but specifically for fundamentals. And I think it's just due to our competitive natures and our desire to succeed and our desire to win that really heightens our awareness for learning. And games are such a fun environment where we can really push ourselves, but we do not have the risk that we do when we take exams. So I think this resonates with students, and we've all been playing games since we were tiny children. The fact that the games speed up our thought processes really mirrors the way that students will use these fundamentals in the real world. And I found that students, when they first come into a fundamentals class, they think that they just need to be able to master the concept. They don't realize that they actually need to master it and have, in fact, instant recall, because a lot of our students are music education majors. And they're not thinking into their future when they're standing in front of their band sight reading a piece, and they don't realize that they don't have five minutes to count the flats and to look at the next to last one to determine the key signature.
 
0:04:11.6 SD: So games are just a great way to build up that speed and just build up the real world skills that they're going to need. And also, these games particularly came to me when I was trying to think of a different modality for drill and practice, because we know that drill and practice is absolutely essential to mastering fundamentals. And of course we can do drill and practice exercises in class, and then we can give our students written homework. We can send them to an online website or use a computer app, but games are just fun and interactive and competitive. And one thing that I was very enthusiastic about was having my students see how their classmates perform in this situation. So some of the students who would be struggling would be able to see the students who had already mastered the concept, and they might realize, "Hey, my classmate has mastered this, so I can do it too." So I was interested in that aspect.
 
0:05:13.8 GR: I love that. That's great. That's great. Leigh VanHandel's new book, The Rutledge Companion to Music Theory, I've been finding absolutely delightful as I've been working my way through the various chapters. We had the chance to speak recently with Melissa Hoag about her chapter on putting the music in music fundamentals. I absolutely loved your chapter on these music theory games, and I thought it might be fun if you took us and the listeners through some of these games. And maybe for the ones that aren't too visual, David and I could go head to head on a question or two and see who wins. [laughter]
 
0:05:44.4 DN: You just want to show how good you are.
 
0:05:46.9 GR: Don't you? [laughter]
 
0:05:50.6 SD: Well, most of these games are visual based, but I'll see if I can think of a few questions.
 
0:05:55.3 GR: Sounds great. Sounds great.
 
0:05:56.6 SD: That will allow a little competition here on the podcast. [laughter]
 
0:06:00.5 GR: Excellent.
 
0:06:02.4 SD: I tried to think of games for quite a few different aspects of fundamentals, and I'll tell you about my Key Words. Each has a little kitschy kind of title, each game does. And one I'd like to call Key Words, and it just involves identifying key signatures. And there are three rounds for this game. The students are given 15 cards, and each card has a unique key signature. And for the first round, the students are just given a word. So I like to start with a very simple word, maybe like beg, B-E-G, or fad, F-A-D. And the students who are usually working in teams shift through their cards, and then they just place one key signature for each letter. So they might, for example, have F major, A major, D major for fad, F-A-D. Of course, I don't really specify whether they should use A major or A flat major for the A, their choice. Of course, some of our words have two letters, so that then the complimentary key signatures can be used for those. But it's really a simple kind of game.
 
0:07:13.5 SD: And then we go to round two, where I will say a sentence, and only one word in the sentence is actually a word that you can spell with key signatures because obviously we're limited on letters. So I'll give you a few sentences.
 
0:07:29.1 GR: Nice.
 
0:07:30.8 SD: And see if you can tell me which word that you would be able to spell with the cards.
 
0:07:34.0 DN: Okay.
 
0:07:35.2 GR: Okay.
 
0:07:35.6 SD: And so this is just to add another dimension, so it kind of creates a bit of a riddle. All right. My sister just earned her first scout badge.
 
0:07:46.4 GR: Badge.
 
0:07:47.3 DN: There you go.
 
0:07:50.0 SD: Great, great. And then you would have practice with five different major key signatures, or I could specify minor key signatures.
 
0:07:56.1 GR: Oh, so then once they get the word, do they have to write out the key signatures or find their key signature cards for those? 
 
0:08:02.5 SD: Yes, they find the key signature cards and they'll have one card for each letter in the word.
 
0:08:09.3 GR: Got it.
 
0:08:10.3 DN: Yep.
 
0:08:10.4 SD: But we usually play this at a table and they'll line up the cards on a table.
 
0:08:14.7 GR: Nice. Yeah.
 
0:08:16.2 SD: Yeah. But one of the catches is each team only has one attempt, you have to be sure that you're accurate. So another sentence might be, do you drink decaf coffee? 
 
0:08:23.9 DN: Decaf.
 
0:08:26.5 GR: Oh, good for you.
 
0:08:30.4 SD: Great. Yeah. And that would give you practice with another five key signatures.
 
0:08:36.8 DN: Coffee comes close.
 
0:08:36.9 GR: Yeah. I was trying coffee. [laughter]
 
0:08:37.8 SD: It does. I'll give you one more so we can break the tie. My friend's favorite movie is Dead Poets Society.
 
0:08:46.4 GR: Dead.
 
0:08:46.5 DN: Dead.
 
0:08:47.0 SD: Oh, that's a draw. [laughter] I think it's time to go on to another game. [laughter] So there's one that I call 360 degrees and the emphasis here is scale degrees. So I'll have students divided into teams and you can have, I suppose, two to four teams just depending on the board space available in your class. And this is a good way to get students out of their desks and I'll have each team line up. I'll have one person go to the board at a time, but before they go to the board, I'll call out three pieces of information; a clef, a key, and a scale degree. A clef, a key, and a scale degree. And then I'll let students think about that for a minute. And then I'll say go. And the first person on each team closer to the board will run to the board and write the clef, the key, and then the scale degree of that specific key. So unfortunately we can't play that one on the air.
 
[laughter]
 
0:09:58.2 GR: Yeah, it doesn't work too well aurally. So in other words, you would say something like bass clef G major 6.
 
0:10:05.3 SD: Exactly.
 
0:10:05.4 GR: And so someone would draw the bass clef, draw one sharp, and would write the note E on that staff.
 
0:10:13.1 SD: And so, of course, treble and bass clefs are relatively easy. You could throw in some C clefs. [chuckle] That would be a lot of fun, I'll tell it to them.
 
0:10:23.5 GR: Yeah, writing key signatures in C clefs can be fun too because they have a different shape depending on the C clef.
 
0:10:30.4 SD: Absolutely, absolutely. And this is also practice, of course, for writing key signatures and having the correct placement and the correct order. Another component of that game. One of my favorites I call Balance Beam. So I'll have one student from each team go to the board and write on a horizontal plane numbers 1-14. Actually, it could be any number that work, but the game that I like to start with has 14 different rhythmic values. And then I'll call out a rhythmic value for each number and my students will write that rhythmic value, no beams. So, for example, let's say numbers 1-3 each have eighth notes. Number 4 is a quarter note. Number 5 is an eighth note. Number 6 is a dotted quarter. 7, 8, 9 are all eighth notes. 10 is a quarter note. 11-14 are eighth notes. So they're just looking at what might seem to be just a random assignment of note values.
 
0:11:40.2 GR: And at this point not beamed at all...
 
0:11:43.4 SD: Not beamed at all.
 
0:11:45.0 GR: Just individual notes.
 
0:11:46.6 SD: No, because that's part of the competition. So I have five rounds. I really can get a lot, a lot of competition out of this one visual. So round one, I asked the teams to beam the rhythm in 6/8 and of course include bar lines. So, and again, I give each team only one chance. So they have to really think it through and check themselves. So for round two, I have the teams beam the same notes correctly in 3/4 and, of course, check on the bars. Round three, I asked the teams to beam the same rhythmic pattern in 9/8. And, of course, this time they have to move the bar lines. And then round four, I asked the students in 9/8 to replace each rhythmic note value with a rest value. And then for the last round, I asked them to do rhythmic transposition. So I'll have them change the rest values from 9/8 to 9/4.
 
0:12:50.8 GR: Change all of the values from 9/8 to 9/4.
 
0:12:52.9 SD: Right.
 
0:12:53.7 GR: Got it.
 
0:12:55.3 SD: Exactly. But I specifically work with rest values at first because I think it might be a little tougher than the actual note values. Although that's certainly a possibility.
 
0:13:03.3 GR: Yeah. That's great. And I can see all sorts of ways you could extend this as well, depending on which notes you changed to rests, it might be that in some meters you would normally combine those rests to form a longer value. Whereas in other meters, you'd want to keep them separate to reflect the metric structure.
 
0:13:23.8 SD: Right, and that's certainly a very important point, yes. And in addition to teaching beaming, we can also teach the proper combination of rests. Absolutely. Then I go on to Meter Cards. Each team receives two sets of cards, and on one card, there is a rhythmic value that's the equivalent of one beat. So for example, in 4/4, this could be a single quarter note. It could be two eighths. It could be an eighth and two sixteenths. It could be a dotted eighth and a single sixteenth. It's just the value of a single beat. And then I have another stack of cards with the numbers two, three, and four. Now, of course, these refer to meters or beats per measure. Usually I just start with the more common two, three, four, though you could certainly add others. And then the students basically have to figure out what the meter is when I combine one card with a rhythmic pattern with another card with a number.
 
0:14:30.4 GR: Can you give us an example of that? 
 
0:14:33.3 SD: So perhaps we can do a little competition here.
 
0:14:35.8 DN: Yeah, I'm still trying to envision this.
 
0:14:38.3 SD: Okay, so I would like for you to tell me the meter or the time signature for your first card, which is a quarter and an eighth, the equivalent of a beat.
 
0:14:52.0 DN: Gotcha.
 
0:14:53.5 SD: And then the other card, which tells you that there are four of these per measure.
 
0:14:57.5 DN: So 12/8.
 
0:14:58.4 GR: So 12/8.
 
0:15:00.5 SD: Exactly, exactly.
 
0:15:00.6 GR: Four compound beats, yeah.
 
0:15:02.2 SD: Now, of course, simple meters are pretty easy to do, but then when I choose a compound meter, then there's a extra step of students having to think about how the time signature reflects not the beats per measure, but the divisions per measure.
 
0:15:24.5 DN: Great. Okay. Yeah, the part that I hadn't grokked at first was that there would be compound meter beats. Yeah, and it always seems like it's a difficult thing to explain in fundamentals why a compound meter is what it is.
 
0:15:42.8 SD: It really is. It's always a challenge. And I think it sometimes helps for students to see a single beat isolated on a card as opposed to just looking at example thinking that the divisions are the equivalent of beats.
 
0:15:58.2 GR: Yeah. And I think also it's nice, right, because so often we say in 6/8, 9/8, 12/8, the dotted quarter gets the beat. But of course, all sorts of other things can form a beat. And so, I like that idea of getting them to think about the rhythm words as being beats within those compound meters. And, of course, you could make some really hard ones. You could do a dotted 16th, 32nd, 16th, right, at which point we're in, and the number three, at which point we're in 9/16 time, where you can get some really crazy ones in there. Yeah.
 
0:16:36.6 SD: Right, right. And usually that's the process. You start with the easier ones and then work your way to the ones that are more challenging. I think perhaps my favorite is the Notation Bloopers Game. [laughter] And this is just to reinforce conventional notation, which I think a lot of our students are just not aware of. They take conventional notation for granted. So I'll give my students a slip of paper that has just a short melody on it, and I'll ask them to identify the mistake. And it's just really fun to come up with these mistakes. They might be as subtle as a bass clef with the dots in the wrong place. So instead of surrounding the F line, they might surround the D line. And usually that takes a while for students to identify that. And this is a fun game to play with teams because you've got the interaction of the team members as they look for the mistake. Another favorite of mine, see if you can identify this mistake. So picture this, I've got a bass clef with dots in the proper position, right? And then next you see 4/4. After that you see two flats; B flat, E flat. And then for simplicity's sake, let's say that you see four quarter notes, a bar line, and a whole note. What's the mistake? 
 
0:18:19.6 GR: I'm cheating a bit because I've seen it in your book, and I have to say I had to read the answer. [laughter] And then I was like, oh, of course. [chuckle]
 
0:18:30.0 SD: So a bass clef, time signature of 4/4, two flats, B flat, E flat, followed by four quarter notes, a bar, and a whole note, with a, let's say, a double bar.
 
0:18:42.5 DN: You've transposed the time signature and the key signature.
 
0:18:47.8 SD: Exactly. [chuckle]
 
0:18:48.0 GR: Excellent, David.
 
0:18:51.3 SD: Exactly.
 
0:18:51.4 DN: I had to look... I had to visualize it. [chuckle]
 
0:18:54.6 SD: Mm-hmm. It's a lot of fun. And you could do other things like using wrong stem direction, incorrect beaming. And another one of my favorites is a mistake that my students make very often, which they'll have a melody with an upbeat, but then in the last measure, they'll have note values for the complete value of the measure. So they've forgotten to compensate for the upbeat. That usually takes a minute too.
 
0:19:23.0 DN: Although I... Yeah. I get to some of these things and I think, well, I've seen professional scores that feature this or feature... And, of course, I do a lot of early music, so I've seen the F clef on different lines.
 
0:19:40.3 GR: Everywhere. True.
 
0:19:41.1 DN: But I've seen the G clef on different lines.
 
0:19:44.5 SD: That's a great point. That's a great point. And that's a good conversation to have with students, that this, what we call conventional notation is not universal. I just had a discussion today with my sophomore students about using a Dorian key signature in a Bach chorale. So the key of G minor was notated with just one flat.
 
0:20:07.2 DN: And Bach does this...
 
0:20:08.0 GR: All the time.
 
0:20:08.5 DN: All the time.
 
0:20:11.1 SD: Right, right. So many Baroque composers. And then another game we play is Triad Bingo. So I just made these bingo cards. Let's see. With intervals, I usually do B-I-N-G-O. For triads, sometimes bing or just sometimes bingo, but... And instead of a traditional bingo card layout, you would just have single chords, just a row of single chords under each letter. And then I'll call out a letter and then a chord quality, and the students will have to find that chord quality. Usually, we just circle them. And, honestly, I only make one version of the card for each class. So everyone's looking at the same card, because it's just chaos running around looking at different cards and reconfiguring your brain.
 
0:21:06.9 DN: Oh, yeah.
 
0:21:09.9 GR: Okay. So it has been a while since I've played bingo. So just to be sure I'm picturing this correctly. So at the top are these five columns, B-I-N-G-O, and then underneath them you said qualities or letters or both? 
 
0:21:30.1 SD: Qualities.
 
0:21:30.2 GR: Okay.
 
0:21:30.3 SD: Qualities. So, for example, under... Let's say, under B, I might have an F major triad. Maybe a D minor triad. A C augmented triad. And then a B diminished triad.
 
0:21:43.9 GR: Got it. And so you would call something like B augmented, and...
 
0:21:47.9 SD: Exactly. Exactly.
 
0:21:49.8 GR: And then they would put a chip on the one augmented card in that row.
 
0:21:53.0 SD: Correct. Yes.
 
0:21:55.4 GR: Okay.
 
0:21:57.1 DN: And so if you're all using the same card then, there's a definitive point at which someone should have won.
 
0:22:04.4 SD: Yes.
 
[laughter]
 
0:22:06.8 DN: I'm wondering if I could do this with aural skills, except that I fear I would get premature victories.
 
[laughter]
 
0:22:15.0 SD: Oh, you do. You do.
 
[laughter]
 
0:22:16.7 GR: I'm sure. Yeah.
 
0:22:18.4 SD: But once you declare a premature victory, you are out of the game.
 
[chuckle]
 
0:22:23.9 GR: And you could easily turn that game... Is that what you were saying, David, that you could turn that game to an aural skills game by calling column B and then playing a diminished chord? 
 
0:22:33.5 SD: Absolutely.
 
0:22:34.5 DN: Yeah.
 
0:22:35.2 GR: Uh-huh. Yeah.
 
0:22:37.9 SD: I use the same format on intervals, on triads, on seventh chords. There's so much you can do with it. And also, you could add that aural component to the triads and seventh chords.
 
0:22:46.8 GR: Mm-hmm. Nice.
 
0:22:49.5 SD: Yes. But you really need to state up front that premature declarations of victory...
 
0:22:55.8 GR: Eliminate you from...
 
0:22:57.7 SD: Will result in elimination from the game.
 
[laughter]
 
0:23:01.6 DN: I love the fact that you mentioned that, of course, it lets some of the students see that other students are doing well, that they understand it, and, therefore, that it is understandable. I have seen some students react to this with despair that their colleagues just know these things and they don't. And I wonder how you handle the despair factor.
 
0:23:37.2 SD: [laughter] The despair factor is definitely present, whether it's written theory or aural skills, definitely. It's uncanny. I had this talk today with my students. In my sophomore aural skills, we do an error detection exercise every day in class, and I have some students who are just not passing them. And so, we had to have a little chat about everybody has their weaknesses, and there's some things that you can do now very well, but you were not able to do them at some point before. So none of my students were born reading treble and bass clef. They had to learn those. And I think it's important to tell students, as I'm sure you all know, that sometimes people are more comfortable with the written side of theory. Sometimes they're more comfortable with the aural side of theory. And they're all important. And it's just a matter of developing skills. And sometimes you even have to ask for help. And, of course, we as functioning adults in the real world, we call people for help all the time. We have physicians and mental health professionals and electricians and plumbers and people with professions that we just cannot live without them.
 
0:24:58.4 SD: So it's really difficult sometimes for my students to ask for help. They think they should just naturally be good at a skill, but that's why we do skill building. And it's just so valuable to know your weaknesses, to know where to focus your time and your effort. I have one more I'd like to share with you. I call it interval train. And this actually is not original. I think we did something like this when I was an undergrad a long time ago. [chuckle] And this is also a game that could have an aural component, but I'll focus on the written, the visual right now. So I'll have each team at the board, at a board, and I'll give them the starting note. And then I'll tell them the name of an interval and a direction. So let's say ascending minor second, and then they'll write the next note, and then I'll just go through a series of 5-12 intervals. And whoever gets to the correct final note first is the winner.
 
0:26:08.6 GR: I love it.
 
0:26:10.8 DN: It's a very modus novus...
 
[laughter]
 
0:26:15.4 SD: Yes, it is. And then, of course, you can sing... You could try to sing the melody that you created. And, of course, you could play those aural skills by playing the intervals. That'd be a great way for them to reinforce the written with the aural, which is always important, of course.
 
0:26:35.1 GR: And you could make it a name the tune then as well by... If you pick... Give the intervals for some tune, say...
 
0:26:42.5 SD: Absolutely.
 
0:26:44.0 GR: F sharp, perfect unison, ascending minor second, ascending major second, descending major second, and we're off to Ode to Joy.
 
[laughter]
 
0:26:51.7 SD: Great. It's great. Great addition.
 
0:26:57.5 DN: I wonder... And I... It's really cool to me how you've... Sort of all of these games leverage a competitive spirit to especially get out that, as you said, that immediate recall that... And I know... One of my colleagues instituted time tests on all of her fundamentals classes and Theory 1, and they would just have time tests every day. And the students kinda hated them, but at least it... Time test does not leave you time to count up the letters and figure out... Of course we know you can do that. That's not the issue. The issue is that you'd be able to see it and immediately recognize it. And so, you've leveraged this competitive spirit. I wonder, and maybe this is... I just wonder if you have games that are less competitive. Are there collaborative games? Do we have ways of... Or is that less useful? [chuckle]
 
0:28:11.1 SD: I'm sure there's a place for that. Certainly. There's some times when you, as a professional musician, you want to take time. You want to enjoy the discovery maybe of analyzing a piece, and when taking time is appropriate. But with these games, as you mentioned, my primary concern is that students just go beyond understanding, that they actually have an opportunity to, essentially, prepare for the real world where you don't have time to think about what the F sharp major scale looks like. [chuckle]
 
0:28:54.6 DN: And I've had some students, I think, who don't always understand that right away. I definitely had a conversation with one the other day who said, "Well, when you make me do it so fast, I can't... When I do the homework, I have plenty of time. So I don't understand why I didn't do well on this test." "Well, you... It's 'cause the homework... You're obviously doing it very slowly. But you can't do it slowly." [chuckle]
 
0:29:21.9 SD: Right. Well, I'll reveal a secret here. It seems like sometimes the students think that the primary purpose is to win the game. And I usually offer some kind of interesting reward. It might be if we have a games day, then the team who wins has their lowest homework replaced by an A. So that's something that everybody, everybody is interested in. So they think that the primary objective is to get that homework grade replaced. So that's really what they're focused on. And they're gonna just try to get through each of these exercises as quickly as possible and pull their resources together, when actually my primary goal is for them to build up their speed and recall.
 
0:30:13.8 DN: It's nice to think about motivation in this sense too, because I do find it frustrating sometimes that our students come to us increasingly motivated by grades and less motivated by the desire to learn. It feels like that's happening anyway. And, of course, this doesn't necessarily encourage motivation to learn, but it does provide motivation that is not grade-based, necessarily.
 
0:30:49.3 SD: Motivation to win can also...
 
0:30:50.1 DN: Motivation to win.
 
0:30:50.8 SD: Double as motivation to learn when you don't realize you're learning. And I agree with you that sometimes it seems like their motivation is more about getting the grade that they want, which is kind of sad. And I think sometimes it's just our place to remind students to think about why it is that they're studying music. Why do you want this music degree? Do you really want to get an A, or do you actually wanna learn the material? And not to say that in a harsh way, but just to be the voice of reason, the person who reminds them that this amazing thing that we study, that we all love, music, is a wonderful and complex area. And I often make the analogy with my students between their relationship to music and, say, their relationship to maybe a significant other. When you first meet someone and fall in love, of course there's that period when you want to know everything you possibly can learn about them in a brief period of time, because you really cherish that person. And if they love music, then they really need to have an attitude of wanting to learn as much as they possibly can. They might not like everything, but just like you don't like everything about another person, don't like everything about a friend. But it's just checking their perspective, I think, is part of teaching, especially music majors.
 
0:32:33.9 GR: Great. I thought it might be fun, reading your games, I thought, we should share more games just with each other 'cause I think...
 
0:32:43.1 SD: I would love to hear some of your games.
 
0:32:43.1 GR: Yeah. I was thinking, too, just as as students, the younger we are, the more learning tends to have games in it. And as we go through the grades and into college, there tend to be fewer and fewer games. But, boy, the second I hear, "Let's play a game," I'm there. [chuckle] So, anyway, a game I thought would be fun to share, I do this game with a lot of my students, but especially with any time I'm teaching aural skills. And I usually teach using scale degrees, and... But you can do it with solfège just as well. And so the basic idea is if you map the numbers one, two, three, four, five, six, seven, eight, nine and zero onto a scale, you can get like one, two, three, four, five, six, seven, eight, and then you can have nine as a high two, and you can have zero as a low seven. And of course, you could do the same thing in solfège. And so then... I love this game because it involves students' cell phones. And how many times in class do we find ourselves thinking, Oh, I wish that student weren't on their cell phone or saying, Hey, would you put away that cell phone? And how rarely do we get to say in class, All right, everyone, take out your cell phone? 
 
0:34:06.7 SD: Oh, that's a thrill right there. That's a thrill for a student.
 
0:34:09.8 GR: So I ask students to take out their cell phone, and they convert their telephone number to scale degrees using this system. And then I ask for volunteers to sing their number...
 
0:34:27.7 SD: Oh, wow.
 
0:34:28.5 GR: Not on the numbers or solfège, but on a neutral syllable, la, la, la, etc. And the first person to successfully make their cell phone ring wins the round.
 
[laughter]
 
0:34:47.5 SD: Oh, that's fantastic. Oh, wow.
 
0:34:53.1 GR: And we practice... Before we do this, I say, now, it's very possible you're going to dial a wrong number. And if someone picks up, you're not allowed to just hang up on them. You have to say, "Oh, I'm so sorry, I misheard a number," before you hang up.
 
[laughter]
 
0:35:15.2 SD: Wow, that's fantastic. I love that game.
 
0:35:18.6 GR: Yeah. I have way too much fun with it.
 
0:35:22.1 DN: It has great potential for embarrassment.
 
[laughter]
 
0:35:23.7 SD: It does, it does. And that's the way I've memorized my credit card numbers, by converting them to scale degrees.
 
0:35:30.4 DN: Oh, this is how we've memorized... Greg and I have both memorized Pi this way.
 
[vocalization]
 
0:35:41.6 SD: Awesome. That's fantastic.
 
0:35:44.1 DN: We've got different rhythms 'cause...
 
0:35:45.9 GR: We do. And I actually... I wrote a fugue on Pi. Maybe I got... Yeah. Anyway. Yeah. Musical nerdiness.
 
0:35:51.6 SD: When there's that element of humiliation, then it really heightens your hearing.
 
[laughter]
 
0:35:58.0 GR: Right? Absolutely. Yeah, yeah. Another version of this I like to do is... It's harder to do now because it's hard to find the yellow pages, but I'll hand out a different page, I'll cut out pages from the yellow pages, and I'll hand each student their own page from the yellow pages. And they're to pick a company listed on the yellow pages and to write a jingle with the company's phone number. And depending on the level of the class, they might also... They might set it to a rhythm and meter or they might also add harmony and accompaniment and create a... Kind of create a thing about it. And the best jingles are ones that don't say the name of the company, but that they give you some hint about what the company does. And then the students like... And I'll usually give that as a homework assignment, then the next class, students will perform their jingles for the other students, and they'll try and figure out what the company might be.
 
0:37:00.8 SD: How fun.
 
0:37:03.2 GR: Anyway. So some of my... Couple of my favorite games.
 
0:37:06.1 SD: That's very creative. That's very creative.
 
0:37:09.4 DN: I haven't really done competitive games in my classroom. I'm feeling embarrassed that I haven't. But I've done, I guess, collaborative things where we have a challenge, and I'll let people form groups and work with their group to pass the challenge, like executing a good four against three or five against four or four against five. And the... That's proved useful, especially if you have somewhat diverse groups of students go off together, because then the ones who can do it will... They'll get peer learning. But I guess that doesn't really count as a game. [chuckle] Unless you let them come back and have a competition.
 
0:38:11.0 SD: Well, it's a fun activity outside of lecture time or structured time. Those are always fun.
 
0:38:19.2 GR: Yeah. These are really great, Stefanie. Thank you so much for sharing them with us.
 
0:38:23.9 SD: Thank you so much for having me. It was lovely meeting you both. And I enjoyed hearing your ideas too. I'll have to put some of those to use. I enjoyed that.
 
0:38:32.1 GR: Yeah. I can't I can't wait to use some of these as well. And I think we... David and I, when we did our episode on Dalcroze Solfège games, we were talking how any game there... Any game is like a seed that can be developed into so many other versions of that game, depending on...
 
0:38:50.9 SD: Absolutely.
 
0:38:51.6 GR: What you're working on. I could see these being extended, say, to Roman numerals, for instance, or to various other things, so...
 
0:39:00.8 SD: Definitely, definitely adaptable.
 
0:39:03.6 GR: Yeah, yeah. Right. And a question for you. I know you mentioned in your chapter in the Routledge Companion to Music Theory Pedagogy that you tend to do a games day, like it'll just be like we used to have field day in school where we just play games outside. Is it like that kind of a feeling? 
 
0:39:21.7 SD: Sometimes, I'll have a fundamentalympics.
 
[laughter]
 
0:39:30.4 SD: And I find that those are good for review, your test time. Also, if I'm away at a conference, it's a great lesson plan for a substitute to come in and do. But also, of course, the games are modular. So it's always good to review a previous topic each class, so by just having a quick game, that be a wonderful way to reinforce a topic that you've already covered but your students are still working on that mastery.
 
0:40:03.9 DN: Great. Fantastic.
 
0:40:04.6 GR: Yeah. Awesome. Oh, this is... Yeah, I'm just really delighted that you've shared these with us and that we'll share them with a broader audience, and, yeah, hopefully, we'll have a whole bunch of Key Word and Notation Blooper and Triad Bingo contestants out there in the world.
 
0:40:25.3 SD: That will be great. And I'm so glad that that you find these helpful, and I hope... Certainly hope that your listeners will too.
 
0:40:32.2 GR: Excellent. Well, thank you so much, Stefanie.
 
0:40:33.8 DN: Thanks so much.
 
0:40:34.6 SD: Thank you.
 
[music]
 
0:40:39.8 Speaker 4: Notes from the Staff is produced by utheory.com.
 
0:40:42.8 GR: UTheory is the most advanced online learning platform for music theory.
 
0:40:47.4 S4: With video lessons, individualized practice and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm and ear training.
 
0:40:58.2 GR: Create your own free teacher account at utheory.com/teach.
 

Putting Music in ”Music Fundamentals” with Melissa Hoag

Dr. Melissa Hoag joins us to talk about ways we can make the teaching of music fundamentals musical, fun and effective. She shares tips from her chapter in The Routledge Companion to Music Theory Pedagogy, and takes us through her list of six best practices for teaching music theory fundamentals.
Links
Melissa Hoag's faculty page at Oakland University
The Routledge Companion to Music Theory Pedagogy, ed. Leigh VanHandel: https://www.routledge.com/The-Routledge-Companion-to-Music-Theory-Pedagogy/VanHandel/p/book/9781032174136
Lana Lubany "Sold" (Harmonic minor scale at beginning): https://www.youtube.com/watch?v=mIGxMtWXjS0
Renaissance Composer Maddalena Casulana: https://en.wikipedia.org/wiki/Maddalena_Casulana
Bruce Haynes: Performing Pitch: The History of "A": https://rowman.com/ISBN/9780810841857/A-History-of-Performing-Pitch-The-Story-of-A
uTheory: Online Music Theory and Ear Training
Show Notes
00:01:04 - Guest Introduction: Dr. Melissa Hoag, Oakland University
 
00:02:01 - Why is teaching music fundamentals hard?
 
00:03:18 - Can you talk about your own experience teaching music theory fundamentals?
 
00:05:14 - What topics do you include in music fundamentals?
 
00:06:37 - What do we get wrong about teaching fundamentals?
 
00:09:18 - How do you put actual music in your music fundamentals classes?
 
00:14:31 - Do you still have time for drill & practice if you're spending so much time with real music?
 
00:15:35 - Importance of letting yourself be fallible in front of students
 
00:17:21 - What are ways you connect fundamentals to sound?
 
00:18:30 - Composition exercises in fundamentals & engaging students creatively
 
00:23:47 - How do you approach teaching a topic that you know so well, that you can't remember what it was like to know the topic?
 
00:27:06 - The value of the piano keyboard in teaching & learning music fundamentals
 
00:30:10 - Six Best Practices for teaching music fundamentals
 
00:30:30 - #1: Repetition Counts
 
00:35:20 - #2: Consistency and Rigor Matter
 
00:38:20 - #3: More Assessment Opportunities are Better than Fewer
 
00:39:27 - #4: Prompt Feedback and Specific Grading Are Import for Learning
 
00:41:02 - #5: Involve Students in Finding Examples
 
00:43:31 - #6: Have Fun!
 
00:45:36 - Final thoughts? We should acknowledge that we're talking about Western, tonal music fundamentals, and that there is much more to the world, and we value that and are curious about that.
 
00:46:58 - Wrap-up
Transcript
0:00:21.2 David Newman: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
 
0:00:34.3 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and associate professor of conducting at the Oberlin Conservatory.
 
0:00:40.7 DN: Hi, I'm David Newman and I teach voice and music theory at James Madison University and write code and create content for uTheory.
 
0:00:48.4 GR: Welcome to our second season of Notes from the Staff, and a quick thanks to all of our listeners for your comments and episode suggestions. We love to read them, so send them our way by email at notes@utheory.com, and remember to like us and subscribe wherever you get your podcasts.
 
0:01:04.3 DN: Our guest today for the first episode of our second season is Dr. Melissa Hoag who is Associate Professor and Coordinator of music theory at Oakland University. Dr. Hoag's writings have appeared in the Journal of Music Theory Pedagogy, Music Theory Online, Music Theory Pedagogy Online, College Music Symposium Notes and others. She is a scholar who thinks deeply both about music theory and how to teach it in relevant ways, from her 2013 article on strategies for success in the first year music theory classroom to her 2018 article on relevance and repertoire in the 18th century counterpoint classroom, to her recent chapter in the Routledge Companion to Music Theory Pedagogy, which we'll be discussing today on Putting the Music in Music Fundamentals. Melissa, welcome.
 
0:01:53.3 Melissa Hoag: Hi, thank you so much for having me.
 
0:01:55.3 DN: We're so glad to have you here.
 
0:01:56.8 GR: Melissa, I have to say, I absolutely loved your chapter on putting the music in music fundamentals, that's in the Routledge Companion to Music Theory Pedagogy. This is a book that we're gonna be coming back to a number of times throughout the season. Its structure is just delightful, it's like a whole bunch of lesson plans or ideas from teaching from a bunch of different authors. One of the things that you said in your chapter that I think is absolutely true is that teaching music theory fundamentals is really hard. Why is it so hard?
 
0:02:27.3 MH: First, I completely agree with you that the Companion to Music Theory Pedagogy that Leigh VanHandel edited is just really wonderful, and I've already used a lot of the ideas from that book myself, so I'm glad that you'll be talking about it some more this season. I think teaching music Fundamentals is hard because most of us who teach this material just think of it as part of who we are as musicians, we don't remember not knowing those things in many cases, and we find it hard, I think, to take the time to recapture what it felt like not to know things like scales or key signatures, or what a tonic is, and I think that's really the hard thing, and then I think some people also maybe consider it not as interesting as teaching analysis. I think some people might feel that it's dry or just something they have to get through to get to the good stuff.
 
0:03:27.5 GR: And can you tell us a little bit about your own experience teaching music fundamentals you... What classes do you teach there at Oakland?
 
0:03:34.4 MH: So right now I teach and have taught for a long time, Music Theory 1, which does include fundamentals. We have a separate fundamentals class for students who really have absolutely no background in music, like maybe they sing well, but they don't have any background with note reading or anything, but everyone gets a very thorough introduction to fundamentals and Music Theory 1. And then of course, I teach a bunch of upper level classes and graduate classes, but the fundamentals part of Music Theory 1 goes for the first 10 weeks, so it's most of the semester and of course, before that, before I came to Oakland, I also taught fundamentals at Indiana University, Purdue University at Indianapolis, otherwise known as IUPUI.
 
0:04:28.2 MH: So I taught it then as well, and that was to non-majors, and so that was a different kind of approach, but I really use a lot of the same techniques for teaching college level music majors, some of whom are music minors, and teaching those non-majors, I don't see them as particularly that different in terms of trying to engage them, the level of rigor might be a bit different, I don't wanna let things go very much when I'm teaching college majors just because they're gonna have so much more theory following it, whereas a non-major taking music fundamentals, you wanna give them a broad overview and some experience, but I really adopt the same general idea as far as how to engage them in the topic.
 
0:05:14.8 GR: For you all, what's included within music fundamentals? What do you cover in that first, say, 10 weeks of the first semester.
 
0:05:21.9 MH: So for us right now, it is very western tonal-focused. That's a topic I'll talk a little bit more about later. We're in the process of trying to find ways to broaden that a little bit, or at least acknowledge that that is the focus instead of calling it music fundamentals and acting like it's all music. You know what I'm saying? So for now, because that is the focus of our major, it is a western tonal music focus in our major, we start with, of course, note reading, we do that very quickly, because most of them don't know the other clefs alto and tenor. We do do those because it's a college level fundamentals class, and then major and minor scales, and we do quickly acknowledge the different modes and stuff like that, but we don't require them to know them just because it's enough for them to know major and minor, and they'll get to the modes later on, and then we do intervals, a very basic introduction to meter, and then we do triads and seventh chords, and that's pretty much what comprises our fundamentals unit for that first year of Music Theory.
 
0:06:40.2 DN: What do we get wrong about teaching music theory fundamentals?
 
0:06:43.4 MH: Well, I think we get... I think many people can get it wrong by teaching it in a dry way, like just showing scales, just making students write scales, just drilling things, which obviously you do have to do some drill, of course, there's just no way out of it, but having students just do these really dry exercises without making them sing... I should say inviting them to sing without engaging their musicianship and even in a class of non-majors, some of those students probably took the class because they had choir in high school, or they sing in their church choir and they wanted to take this music class or they play in a community band or a rock band, and they just wanted to know more. So they've got some musicianship, most people do, and just finding ways to plug that in, and then of course, applying it to musical examples. I try to include just as much diversity of repertoire as I can, I use like band music, I just... I think the mistake really goes back to looking at it as something we just have to get through to get to the good stuff, and then not applying it to real music and not inviting students to engage their own musicianship. So that's kind of... That's kind of been my experience.
 
0:08:20.3 GR: That really resonates with me. My first real teaching job was at a community college on the north side of Houston, and I taught pretty much every semester a music fundamentals class, and the first time I taught it, I taught it as though I was preparing those students as quickly as possible to go into say theory one at a major conservatory and I wasn't too concerned about doing anything musical. It was like, we are going to master these music theory fundamentals. And it didn't go so well, I have to say, and that was a real learning experience for me. And gradually over the five years that I was teaching there, I introduced more and more activities of making music, of approaching music that students are actually listening to as opposed to say the things that I had studied in my own undergraduate and graduate training and... Yeah, it brings us really nicely, I think back to the subject of your article, which is putting the music in music fundamentals. So maybe you can go in that direction a bit. What are some of the ways that you do that in your own teaching?
 
0:09:24.7 MH: So for me, one thing I started doing a few years ago is just their first assignment on the LMS, the learning management system, for us it's Moodle. So I will put an assignment module on Moodle and ask students a series of questions, and those include things like their preferred name, 'cause sometimes the registered name is not how they prefer to be addressed, and what their pronouns are and who their studio teacher is in case I ever need to get in touch with that person about their progress, but then I also ask them their three favorite pieces they're listening to right now. And it can be any music, there's... And I say that in the question like, there's no guilty pleasure type of judgment implied here, it can be a video game music, it can be film music, it can be a pop song, it can be something you're playing in lessons or something you've studied in band, anything. And so then as soon as I have that, I slot those things into the various topics, 'cause I have playlists for all my topics on Spotify, and that way we can either start class by listening to one of their songs or one of their examples, and I'll just have them think like, well, what meter is this? Let's conduct it. Does this fall into one of the meter types we've studied?
 
0:10:45.5 MH: Or what kind of scale are they singing at the beginning of that example or... Just a lot of different techniques and approaches like that, and like you said, using music that the students are listening to is a really good way to engage them. And it's impossible to overstate how much they love it when you play one of their favorite songs, it just... They're so happy. Like I have the super quiet girl who is a trumpet major, and she is... Especially for a trumpet player. She is just so quiet in class, she does not ever speak unless I call on her, and if I call on her, like if I can tell it looks like she knows the answer, then her face gets red but she'll answer and she knows the answer. So anyway, I was playing her this piece that she's working on in her lessons, this trumpet piece, and she was just so happy that we were playing that piece, and I just asked a couple of basic questions like, what harmony is arpeggiated there at the beginning? Is it at triad or at seventh chord, is it major or minor? And it just took like five minutes out of class, but it really helps the students feel engaged and it helps them feel like you care about what they're interested in. And it's also a really easy way to diversify what you're teaching, because at least I cannot keep up with what the young ones are listening to.
 
0:12:16.6 MH: I don't really listen to that stuff. It's not that I don't appreciate it, I just can't keep up. So it helps me stay more current as well with pop music and film music and stuff like that. And then sometimes I'll just do a quick search too on Spotify, people have all kinds of playlists and they're of various quality, like if they say it's like compound triple meter, it may or may not really be. Or if they say it's a... You have to definitely vet them, but I found some really good examples. Like this Palestinian American singer, Lana Lubany, I'm not sure if I'm pronouncing her name correctly, but there's this song Sold, and it has a harmonic minor scale right off the bat, and it's this really cool... It has like... She's plugged into her Middle Eastern roots, but it's a pop song and it's in English, and so it was really a beautiful example of a harmonic minor scale. And so I played that and then I had students kind of echo it after I played it a couple of times at the beginning, and then we figured out together what kind of scale it is, and then I had them notate it and sing it on solfege, which I just kind of, guess sort of fold in organically, even though it's not, I don't give them aural skills exams in fundamentals, but I still fold in solfege because I believe in solfege.
 
0:13:45.4 DN: For which those of us who teach aural skills are grateful for it.
 
[laughter]
 
0:13:51.1 MH: Well, yes, 'cause they are learning it also in aural skills in that class, but even when I taught it to non-majors, I still had them sing just some basic solfege because it's just so helpful. So that's just kind of an example. And then I try to also include, if I don't get these from students, I also include like... Of course, I include works by Western classical composers as well. I try to always have an example by a woman and an artist of color... Or composer, artist of color. I just try to be as broad as I possibly can within the confines of, yes, we're still talking about major and minor tonality as the focus of what we do, just having them sing as much as they can too as I already mentioned.
 
0:14:33.7 GR: Can I ask a devil's advocate kind of question, which is, if I do it... If I take this time to bring real music into the curriculum, will there still be enough time for them to actually do the drill and practice they need to master these topics?
 
0:14:47.7 MH: Oh, yeah. [chuckle] See, that's what I do. It actually doesn't take a ton of time to do the student's favorite examples, and to me, I view that as such a valuable use of time because students are applying that knowledge and they're viewing it as contextualized, which I think helps them learn it better and retain it longer because they see it as more relevant. And then of course, my students always have an assignment due the next class period, and it's not graded necessarily, they only have one graded homework per week, but they always have something due, and I call on people just... And I said, look, we're all gonna make mistakes. If you don't know the answer, it's fine, but if you don't know it because you didn't do the homework, that's different, then you should be embarrassed, but you have to try to at least make an attempt.
 
0:15:47.0 MH: And if you don't know it, that's fine. And I always make sure if I make an error, I own it. During the first week of class, I messed up writing the circle of fifths or something. And I said, I have a PhD in music theory, and I just messed up the circle of fifths, and none of you need to be embarrassed about any errors. I said, it's just something that is going to happen, and it's just music theory it's not... We're not learning to do open heart surgery, no one will die if we make a mistake, it is important to learn music theory, but we can all take some of that pressure of perfection off of ourselves. I don't know if it sinks in or not.
 
0:16:30.5 DN: I find that so valuable to lead by example and... Yes. To show my fallibility.
 
[laughter]
 
0:16:39.4 MH: For sure, of course. It's so different from at least my undergraduate experience, it's so different. I mean, everybody was afraid of my theory teacher. I loved her, but most of the students did not love her. They were terrified of her.
 
0:16:57.6 DN: Well, and it's incredibly daunting if you see someone who just seems to be impossibly good at something, and then how do you envision yourself being able to grow into that if you know that this is someone who didn't used to be able to do this, and they learned to do this.
 
0:17:15.9 MH: Exactly. So it's important to make it seem attainable, I guess.
 
0:17:20.4 DN: Yeah.
 
0:17:20.7 GR: You mentioned you have the students sing a lot on solfege, and one of the things that you talked about in your chapter in the Companion to Music Theory Pedagogy, was that importance of connecting the ideas to sound can you talk about various ways that you do that? Obviously we've talked about using musical examples, they already know, so they have a good sonic image and singing as well. Are there other ways that we might do that in our teaching?
 
0:17:45.9 MH: For me it really... It's all about singing. I've also had students do different things with rhythms and stuff like that, even like in Aural Skills 1, when we do rhythms, just like a dry rhythm exercise. Sometimes I'll do things like if they do it well as a group, then I'll have them count off one, two, three, four, and they'll just go measure by measure, which definitely makes it more challenging. And so that's always a fun thing to do, just as far as connecting it to sound, I've had students like when we've done compositions and stuff like that, which we tend to get to a little later. Although when I taught it for non-majors, I did have them do some little composition assignments, which is an interesting thing, like just write a little jingle in major, and it doesn't have to be perfect 'cause they really know enough about chords yet to match them to the melody. But that was kind of an interesting little experiment and then just... I played some of those and had us sing some of them, and again, they kind of muddle through, some of them I've never sang.
 
0:18:56.0 MH: And that's okay, I'm like, "Just do your best." But like little composition assignments, if it really is just in fundamentals and especially if it's for non-majors, I think it's really fun to have them take some risks like that. In our fundamentals unit, we just don't have time to do that. 'Cause we are going to get to that by the end of the semester, they'll be writing a phrase. And then in the second semester, a period structure. And I think we're gonna have them write a little pop song verse or something like that this year, for the first time in theory 2. But if you're teaching non-majors and you have a whole semester especially, or even majors and you have a whole semester dedicated to fundamentals, I think that would be a great thing to connect it with composition. And especially if you have the keyboard skill yourself to kind of make whatever it is sound really good, [laughter] to support it. And I don't mean that in a negative way, but if you can take their idea and be like, "I see what you're going for." And give it a progression.
 
0:20:03.5 GR: Give it a good harmony. Give it a good... Yeah.
 
0:20:06.0 MH: Exactly. Then that's really fun for them. They really love that, when you can do something like that. Even with Counterpoint class, if you can play their minuet in a really convincing way, even if there's some stuff going on, it helps I think.
 
0:20:30.6 DN: It reminds me of a project I did with a bunch of middle school kids, where we collaboratively wrote a musical.
 
0:20:39.0 MH: Oh, cool.
 
0:20:40.6 DN: And that was obviously a totally different structure because it was a summer camp kind of deal, and we had lots and lots of time, but I got lyrical ideas from them. And then I would get melodic ideas from them, but they didn't have to know... They didn't have to be great at creating melodies because they could give me a melodic idea and I could take it and say, "Oh right, we could do this with that, that would be cool." I hadn't thought of doing that, but that's of course, brilliant that I could, in a fundamentals class, I could still use the same techniques so that they have ownership and that they see the utility of it, which is exactly what you're advocating. That's so awesome.
 
0:21:28.8 MH: Yeah. I think they really connect with that.
 
0:21:31.8 GR: And our students are, they're creative people, right? They are musicians, they're artists, or they're taking that class, even if it's a class for non-majors because they have an interest in music. And I love these ideas for engaging that creativity.
 
0:21:46.6 MH: Yeah. And it's also much more fun for the instructor to... You know what I mean?
 
0:21:52.8 GR: Yeah.
 
0:21:54.6 MH: Who wants to just drill scales and... You have do those things, you have to. But making it a challenge to find these creative ways of engaging them. And so Greg, what you were asking, is there time to drill those things? We always have some time at the end of the class to do that. And then like I said, I give them an assignment, and then we go over that the next time. So they do that drill somewhat out of class too. And then with the homework assignments, we have a pretty regular schedule where they're due on... We have Tuesday, Thursday, Friday for freshman theory. So they will hand in an assignment on Tuesday, and I do everything I can to get it graded and handed back by Thursday so that I can collate common errors and address things. And especially if they have a quiz on that Friday, 'cause Fridays are days when we have quizzes five times a semester, so. But that kind of keeps us on track and it... That way you grade it with a quick enough turnaround that they remember doing the assignment, hopefully, and can think back to what they might have done wrong. And that way you're using some of the time outside of class by having those little practice assignments due every class, not for a grade, just I'll call on random people.
 
0:23:20.7 DN: We are fans of offloading some of that drill work to software. [laughter]
 
0:23:26.0 MH: Yes, I know. I know you are.
 
[laughter]
 
0:23:31.0 MH: That is a wonderful thing.
 
0:23:32.8 DN: Which of course only works if students do it.
 
0:23:35.0 MH: Right, I know.
 
0:23:38.0 DN: Of course, nothing works if students don't engage, that's why engaging students is so important.
 
0:23:41.4 MH: Yes, they do have to actually do the work. Yes.
 
0:23:46.5 GR: One of the things you said at the start of our interview was that it's hard to teach music theory fundamentals for a lot of us because they're already so deeply ingrained that we can't remember a time when we didn't know them. As an instructor, how do you approach a topic when you're formulating how you're going to present it given that that stuff is already so deeply ingrained for you?
 
0:24:08.8 MH: I just try to keep in mind what things look like from their perspective, from some of their perspectives. Some of them have more experience than others, of course. Students who already play the piano have a very different perspective. But I try to imagine what it would be like if you're a voice major and you've never taken piano lessons and you don't have any of that tactile knowledge. I just try to keep that in mind instead of expecting them to immediately import that knowledge, which is impossible to do immediately. And of course, they're taking keyboard at the same time, but it's not... They're not gonna be at the same level as another student who has already had years of piano lessons, for example. So I just try to put myself in their shoes as much as I possibly can, instead of living inside my own head or teaching to the students who are gobbling it all up. And again, I try to use a lot of... That's why I use examples that students give me.
 
0:25:16.4 MH: And I try to also use, again, especially with voice, some vocal music like the Renaissance composer, Maddalena Casulana. Her stuff is really beautiful, and she was the first woman to call herself a composer and to publish music that we have record of. And so that's an interesting thing. And it's Renaissance choral music, so it's very triadic. So that's a good opportunity, we've analyzed two of her madrigals this semester. And so that's a good way to engage, just making sure that you have music that addresses different performing forces, of course, but especially for those singers who might feel a little bit more behind. Not all of them, but just some of them who come in without that note reading knowledge, they might be very, very good singers and they just... They don't have that knowledge yet to back it up. They've never played a triad, so it's a foreign concept to them. They don't have any kind of tactile embodiment with knowledge of that. So showing stuff like that in different performing forces for those students helps a lot. And also just having them not just arpeggiate them but sing it in groups, make them build the cord as the class, sing it as a class.
 
0:26:36.9 GR: Each person singing one note of the... Yeah.
 
0:26:41.4 MH: Yes. And we even do the thing where it's major, augmented, major, minor, diminished. And so the augmented is kind of weird, but at least it's a way to make it more applicable to everybody, 'cause I don't... I also don't teach it in a keyboard lab or anything, I'm just in a regular classroom. So if you're in a keyboard lab, that's helpful, 'cause students can at least see the geography of some of these things.
 
0:27:06.1 GR: Can you talk a little bit about the value of keyboard instruction a bit more in terms of learning music fundamentals?
 
0:27:13.5 MH: So for me, it's such a valuable aid because you can see the whole keyboard, you don't have to learn any special fingerings to make a note sound. To play a scale coherently, you do need special fingerings, but to play... It's not like guitar or a bassoon or something where you have to know the fingerings. It's just so valuable for being able to say, "Oh yes, that is a whole step. Between C and D, we skip exactly one pitch." And for that reason, it's just so valuable to have students take keyboard at the same time because it... Of course, it's an important skill because most schools have pianos and pianos are widespread, right? It's a good thing because if students have those skills, they can use that skill in their eventual professions, but it's just such an invaluable support to Music Theory learning. And our keyboard curriculum is similar to our theory curriculum, but a little bit slower because it takes time for students to gain those tactile skills, being able to just feel the geography of a triad, of a second inversion triad, and it's just hard to overstate the importance.
 
0:28:27.7 GR: As you say, along those lines, I think what you're getting at is something that I see all the time when I'm teaching fundamentals, which is that students naturally tend to assume that the musical staff is an accurate representation, just in terms of the vertical space between notes, of how far apart notes actually are. But because there are whole steps between some letters and half steps between others, that vertical distance on the staff doesn't always reflect the same distance, and that... You see that creep up when students are writing scales, when they're... Any topic for music fundamentals, you have to use some tool to think back to the exact distance and not just the generic distance between letters. And of course, the piano shows us all of those, plus it shows us the letter names because of the arrangement of white and black notes on it, in a way that other instruments don't. The guitar, yeah, you can see all the half steps, but you can't see where the octaves are on the guitar in the same way you can on piano.
 
0:29:33.3 MH: Yeah, absolutely. And being able to see the difference between B-C and F-G. Perfect example. Yeah, exactly what you're talking about that on the staff they look the same, but they're not the same because on the keyboard, you skip a note between F and G. So for that reason, it's just so important, and whenever I've talked to prospective students, "Try to get some piano lessons before you come to college, wherever you go, it can be a helpful thing."
 
0:30:08.8 GR: I want to come back to your article in the Companion to Music Theory Pedagogy, because you listed at the end... The thrust of the article is putting the music in music fundamentals. But then at the end, you had this just delightful list of six best practices for teaching music fundamentals. I don't know if you could just talk a little bit about each of them. So the first one you listed was repetition counts.
 
0:30:34.1 MH: Oh yeah, I think I remember writing about that. So basically, fundamentals never leave the whole first year of theory. On every assessment, they will have to write some intervals. And they tend to get a little meaner by the end of the year, like some augmented ones in tenor clef and stuff like that. At the beginning we're a little more gentle, but there's just always fundamentals on every assessment. They don't know which ones they'll be for sure, but even after we're finished with the fundamentals unit, they will have scales, intervals, cords, meter questions like, "Here's a rhythm with no meter, provide the meter. Or re-notate this incorrectly notated rhythm to reflect the... " Those kinds of questions. That's one thing, we never stop. And we just always, on the LMS for every quiz or midterm or finals or anything, and fundamentals, that includes everything. So they know that any of those things can come back at any time and... 'Cause when I first came here, some of the upper level students were real foggy on things like intervals, and I thought, "OH, no. This can't be." So that's why ever since then they just know that it's gonna come up forever. [laughter]
 
0:31:56.7 GR: I love that. And I have to say that... But yes, I have also had the experience of coaching a student who is several years past their first semester of music theory, and just saying, "Hey, what key are we in?" And this look of abject terror comes across their face [laughter] and followed immediately by the same look of terror on my face for a completely different reason. But just... Yeah. I think also about... Probably many people are familiar with Ebbinghaus's forgetting curve, which is this theory, I think it goes back in the 1960s, that the moment you learn something, you have 100% chance of getting it right, and that quickly plummets with time. But each time you're asked that question again, it's a moment of learning that pops you back up to a hundred. And the curve falls at a more shallow rate with each moment of review. So I do love that idea of bringing back those fundamentals at many points throughout that first year, because you do... When you do that, significantly decrease the rate of forgetting, conversely, increase the rate of retention for those topics. That's great.
 
0:33:07.9 MH: Yeah. And the way I explain it to students is, "We just... We don't want you to be afraid of anything. I don't want you to end up conducting the local high school's Jazz ensemble at 7:00 AM where you have five French horns and an Oboe d'amore and three saxophones, and you have to help them with the transpositions. You know what I mean? You have to be able to deal with these things and not be intimidated because students will smell fear." And that's how I put... I just say... 'Cause we've been doing instrumental transposition this week, which they're always like, "Why? Who allowed this to happen?" There's always these reform ideas. [laughter] Anyway, I always make the joke about the local high school's 7:00 AM Jazz band with some ridiculous smattering of instruments that are all transposing at different intervals or something, but they all wanna take Jazz band, so.
 
0:34:10.5 GR: I've actually referred students to Bruce Haynes' book, Performing Pitch, The history of "A".
 
0:34:22.9 DN: Such a great book.
 
0:34:24.6 GR: Because inevitably, if you start talking about why we wound up with all these different transpositions, the students get super interested in it. And like, "Here, if you want 350 pages on it, go right ahead."
 
0:34:41.0 MH: Yeah, absolutely. And I'm always like, "Well, the saxophone was the last one, so blame [0:34:45.3] ____ at all sax." Because those are by far the worst... E-flats? Are you kidding me? Was that really necessary? Couldn't you have done something better than that?
 
0:34:58.4 GR: And for me, I'm just like, "But that's just a bass Clef transposition, right? It was like, I'm just...
 
0:35:01.9 MH: See, I don't ever think like that.
 
0:35:04.0 GR: Yeah. I have the old conductor clef training where it's like, I'm reading the E-flat part in treble clef, if I just imagine the base clef then it transposes itself for me.
 
0:35:11.8 MH: See, I'd rather just think down a major six. I'm self-punishing like that. [laughter]
 
0:35:19.8 GR: Yeah. So the second one on your list of best practices was consistency and rigor matter.
 
0:35:24.6 MH: Oh, especially like, yes. And again, this goes back to when I first came and I was so disturbed by students who were gonna be graduating and didn't have a good grasp of any of this stuff, and they knew it, and they were like... They were upset. They didn't wanna feel like that. So starting with the first year then we just were just very specific about the sharp has to be centered on the line. And I'm not a big notation stickler, but it has to be clear, it has to mean what it means. It needs to be on the correct line. And it doesn't have to be a beautiful sharp, but it needs to be like accurate. And just being very consistent, if the rhythm is supposed to be this, that it needs to be that, don't be lackadaisical with those things and really hold them to it and they will meet that.
 
0:36:32.0 MH: Or if your standards are way up here, students will at least approach that, but if your standards for consistency is mediocre, then they will approach that too. So if you can do that in a fun and inviting and engaging way without... You don't wanna, again, while being fallible yourself and admitting that everyone makes mistakes, but then at the same time, being consistent and holding a reasonable level of rigor for their actual eventual gaining of those skills. At least for me, at my school. [chuckle] It all varies by institution, curriculum, goals, student body and preparation and the kinds of majors, all those things.
 
0:37:22.3 GR: But I guess maybe a corollary of that would be that if you're not able to have a certain degree of rigor in what you're teaching, maybe teaching fewer subjects with more rigor is better than trying to cover more with less rigor.
 
0:37:37.4 MH: For sure. Like maybe you don't get to seventh chords. Maybe you just do triads and that's fine. Or maybe no alto and tenor clef. I mean, for a non-major fundamentals course, I would never do alto and tenor clef. I just do that because I'm teaching first year music majors. And I know that they're gonna be looking at orchestral scores and music history and stuff like that, and so they need to know those things, but... And I think it's of course good for things like sight-singing, 'cause it tends to put everybody on a level playing field to read a clef that's really not very familiar to almost anyone. But for a non-major fundamentals class, it'd be very different.
 
0:38:19.7 GR: Your third best practice, more assessment opportunities are better than fewer.
 
0:38:24.0 MH: Oh yeah, that's just so that no one assessment activity is like this behemoth, terrifying, do-or-die kind of situation. So as I mentioned, we have graded assignments every week, we have five quizzes, one of which is dropped, so they can have a bad day, or it doesn't have to be this big stressful thing. And then a mid-term and a final. We've tried to make it so they have a lot of chances and that they can improve as the semester goes on. And if something weird happens, we work with a given student, like if they've had a bad run of health or they're in crisis or something like that, of course, we work with them and try to help them find ways to make up some of that work. So we make exceptions, of course, we'll re-give quizzes again or write a new one or whatever.
 
0:39:29.1 GR: And I guess really related, your next best practices, the prompt grading and specific feedback are important for learning.
 
0:39:36.1 MH: Yeah, like I said earlier, just I try to turn things around by the next class period, just so that they have time to get the feedback before the next thing is due, or before our... If we're having a quiz that Friday, before the quiz, so that they have time to... We have supplemental instruction which is offered through our Academic Success Center and it's a couple of sessions taught by an upper level student, and it's for Theory 1 and 2. And so SI is offered on Thursday and Friday, which is perfect. So if I give the homeworks back... They hand them in Tuesday, I turn them around and get them back to the students by Thursday morning, then they can take it to SI and get help with it there, or I can address any questions in class that day, and then they're good to go for the next one that's due the following week. But if you hold on to something like that for a week, that kind of... It doesn't happen in time for them to improve, so.
 
0:40:43.3 GR: Right. I think for me, this is where I often turn to technology as well, because just the ease of students... Am I writing the scale correctly? I don't have to wait two days between when I turn it in and get it back to find out whether I've written that scale correctly.
 
0:40:56.6 MH: Absolutely, of course. And we really need to explore some of those ideas, I think that that would be a good direction for us to take.
 
0:41:05.0 GR: You've already talked a bit about your fifth best practice, involve students and finding examples of various techniques. Anything else to say there?
 
0:41:09.5 MH: Oh yeah. I mean, just that I'm always saying things like, for later in the year, I really need some musical theater examples of ascending five, six sequences, or I don't have enough compound triple minor mode pop music examples. And every now and then, even an upper level student who I haven't had since their first year, will send me an email and be like, "Hey, this video game has... Here's a YouTube video," or this one kid sent me a rap example and was like, "Before you play it in class, make sure you find a clean version." [laughter] He wanted to make sure I didn't just play it without listening more of the way into the track, 'cause I think it's fairly profane. Anyway, I definitely, especially some of them who I know are really into it, I'm like, "Please go find some of these things, or listen for them and send them to me," and it just kinda helps them stay... Keep their theory brain on when they're not in theory.
 
0:42:23.5 DN: I've been doing the same thing in oral skills with... And we've listened to Childish Gambino twice this semester. We're doing metric modulation, and one of his songs does metric modulation.
 
0:42:35.7 MH: Oh cool.
 
0:42:37.3 DN: It's great. And just used the Marvel Studios theme song too this week.
 
0:42:45.2 MH: See? And that's what I rely on students for because my knowledge of film music is not good. I mean I know a few things, but I'm not like they are, and certainly not video game music, other than the Super Mario Brothers from my childhood, which is surprisingly still relevant, I found.
 
[laughter]
 
0:43:04.1 GR: It's amazing.
 
0:43:05.3 MH: It's wonderful.
 
0:43:06.5 GR: That's my favorite [0:43:07.6] ____ is the opening of... [chuckle]
 
0:43:11.2 MH: Or of mode mixture when he dies.
 
[vocalization]
 
0:43:15.7 MH: Oh yeah, totally.
 
0:43:16.4 GR: Yeah, absolutely. Yeah. [laughter]
 
0:43:17.6 MH: It's so great. It's the best example of mode mixture ever.
 
0:43:21.0 GR: Yes.
 
0:43:23.5 MH: Yeah.
 
0:43:23.6 GR: The Water World, The Planning, oh god, don't get me started. [laughter] Well, I guess related to our lecture, your last best practice is have fun, and I think you've given us some ideas of how you create that fun environment in your classes. Anything else to say along those lines?
 
0:43:41.9 MH: Use puns. [laughter] No, I mean I'm kind of joking, but I just find that it depends on how you are in the classroom. Everybody is different. But for me, I tend to be fairly silly. I mainly... I feel like I just want them to see me as approachable. And I think they do, and I want them to see Music Theory as something that is pleasant and interesting and fun. And so especially with the first year students, I tend to be rather silly. Like today, we were talking about, as I said, instrumental transposition, and a couple of the instruments had to be transposed to C to sound in B-flat and I said, "Do you see what I mean? No pun intended." And it's like the stupidest joke ever, but they all laughed even though it's like... I mean talk about a dumb, worst, stupid pun ever, but...
 
0:44:44.1 DN: They don't need to be good to be fun.
 
0:44:45.5 MH: No, they're better if they're bad. [laughter] It's even stupider. But I mean just having fun and adopting a sense of joy and, I don't know, like a sense of wonder or like, "Isn't a half diminished seventh chord the most amazing thing ever?" and then play in a couple of quick examples just on the keyboard, like "Listen to that. Nothing else sounds like that." And just trying to kind of infect them with some of that sense of wonder. And the success varies. Some students are maybe not ever gonna feel like that about Music Theory, but I hope some of them do. [laughter]
 
0:45:35.9 GR: Gosh, well, this has been just a delight. Any last words of advice or wisdom for our listeners?
 
0:45:42.1 MH: I mean, I think I mentioned at the beginning, I think the next hurdle, at least for me, is trying to just find a way to acknowledge that this is like, we're talking about total Western tonal music fundamentals and maybe building in even some like, just little writing assignments here and there. And especially if I were teaching non-majors, I would do it a lot more, I think, if I weren't building toward this later curriculum of comparing and contrasting something like Ragas and minor modes, and a way of acknowledging that there's this whole other part of the world and that we value that and we are curious about it regardless of what our focus happens to be here. So I think finding a way to do that in a way that's meaningful and respectful and fosters a sense of curiosity. I think that's kind of like the next, for me, the next hurdle for me and my curriculum and my students at my school. So that's the next challenge.
 
0:47:00.4 DN: Well, we're so grateful to have you spend this time with us.
 
0:47:02.9 MH: Yeah, it's wonderful to talk to both of you, and I'm definitely going to look up that Bruce Haynes, The History of "A".
 
0:47:09.7 GR: Yeah, it's really fun. The funny thing, of course, is if you type the History of A into Google, you get totally unhelpful results. [laughter] So, I think it's either performance pitch or performing pitch, the story of A. So yeah.
 
0:47:25.6 MH: Okay. I will definitely have to look that up because, I mean I know some things about the history of instruments and stuff like that, but...
 
0:47:35.0 GR: Yeah. And he goes really down into the weeds, so like...
 
0:47:37.8 DN: Yes. The details of why a clarinet is...
 
0:47:40.1 GR: "We measured the C pipe of this organ in this city built in this year, et cetera."
 
0:47:40.2 MH: Very fascinating. And it would be great to have something like that to point students toward so they can just nerd out on their own time.
 
0:47:53.6 GR: Totally.
 
0:47:54.9 DN: That's why we have Bach Magnificat in D, which is later the Bach Magnificat in E. 'Cause it was easier to transpose some of the parts to match...
 
0:48:07.3 MH: Oh.
 
0:48:08.2 GR: To match the local pitch.
 
0:48:09.4 DN: Yeah.
 
0:48:09.9 MH: Huh. I did not know that. Very fascinating.
 
0:48:13.7 GR: We are definitely approaching our time in here, so yeah, Melissa, thank you again so much.
 
0:48:20.3 MH: Yeah, it's wonderful to meet you and to talk to you both.
 
0:48:23.5 GR: Excellent. Thank you again.
 
0:48:24.8 MH: Yes thank you.
 
[music]
 
0:48:30.1 Leah Sheldon: Notes From the Staff is produced by utheory.com.
 
0:48:32.8 GR: UTheory is the most advanced online learning platform for music theory.
 
0:48:36.7 LS: With video lessons, individualized practice and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm and ear training.
 
0:48:47.6 GR: Create your own free teacher account at utheory.com/teach.
 

Season Finale & Coming Features

Leah, David and Greg reflect back on favorite moments of first season of Notes from the Staff, and chat about coming features for uTheory.
Links:
Solfege Sally
uTheory.com
Show notes:
0:00:00 Theme Song
0:00:20 Introductions
0:01:00 How David jumped in and sang a Mozart Requiem with Greg on 5 minutes notice
0:03:45 Reflecting on the 2022 Pedagogy in Practice conference
0:05:30 Favorite moments from season one of Notes from the Staff
0:06:14 Theme 1: Using multiple systems to reach learners in multiple ways
0:08:15 Theme 2: Making learning engaging
0:10:30 Theme 3: Trends in Music Theory Pedagogy today
0:14:10 Solfege Sally -- our silly Simon-like solfege game.
0:17:35 What we've accomplished with uTheory this year: a complete backend and frontend rewrite into modern frameworks, over 120,000 lines of code written (or rewritten)
0:18:20 New features coming to uTheory
0:19:00 The ability to create practice assignments
0:20:15 Consolidating all assignment types into a Learn tab, and allowing assigning of content to entire classes, groups of students or individual students within a class.
0:21:10 Rolling out the new uTheory extended curriculum: a curriculum designed to be used over a two-three year period, especially in a high school or middle school context, to allow a carefully paced introduction with ample time for building fluency.
0:22:05 The lessons and exercises will be customized for the student's primary clef, whether its treble, bass, alto or (for pianists) grand staff.
0:22:48 The curriculum will interweave written music theory, rhythm, ear training and improvisation together.
0:23:20 The curriculum will be a spiral curriculum, so that concepts are introduced at a basic level, and returned to with review and more advanced work frequently throughout the curriculum.
0:23:50 And the curriculum will be much more gamified -- with little touches like confetti, badges, and games like Solfege Sally.
0:24:30 With these changes, configuring lesson and assignment order will become as easy as dragging and dropping -- one of the most frequent feature requests we hear from teachers who are using uTheory.
0:25:40 Practice vs Mastery Assignments
0:30:00 The new curriculum should make it even easier for teachers to use uTheory with their classes and students, because it will do even more of the work of customizing the learning for individual students.
0:31:00 Previewing a new game, "Pitchy Fish" to help teach pitch matching and vocal control.
0:35:30 Previewing some of David's new music theory songs which will make appearances in the new curriculum: Where the Half Steps Live, and Black Notes on Pianos
0:38:50 Chit-chatting and signing off for the summer!
Transcript:
0:00:00.0 [Theme Song]
0:00:21.2 Leah Sheldon: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:34.6 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and Associate Professor of Conducting at the Oberlin Conservatory.
0:00:40.8 LS: I'm Leah Sheldon, head of teacher engagement for uTheory.
0:00:44.6 David Newman: I'm David Newman, and I teach voice and music theory at James Madison University, and I write code and create content for uTheory. A quick thanks to listeners for all your comments and episode suggestions. We love to read them. Send them our way by email at notes@utheory.com. And remember to like us and subscribe wherever you get your podcasts.
0:01:06.3 GR: So it's episode 11, and it's our last episode of the first season. Today, we're gonna look back at some of the highlights from our first ten episodes. We're gonna chit-chat a bit, and we'll share a preview of some of the things that we're working on for uTheory. David, Leah, how are you guys doing? 
0:01:24.3 DN: Good.
0:01:27.4 LS: Great.
0:01:27.5 GR: Leah, I think you know this, 'cause you saw it on Facebook, but David and I had this delightful experience this weekend, where I was conducting a concert at Oberlin and a big alumni and community performance of the Mozart Requiem. And about five minutes before the show started, I walked out into the lobby, and who do I see but David Newman there.
[laughter]
0:01:50.7 LS: Did you know he was coming? 
0:01:53.2 GR: No, I... I knew he was driving through, 'cause David, you were at a conference, right? 
0:01:57.7 DN: Right.
0:01:58.6 GR: So, he was driving through from Virginia to Ann Arbor, Michigan. And I... We'd seen each other when David was on the way there, 'cause he has to drive right by Oberlin, but I didn't know David was gonna stop in on the way back, and... Anyway, so I was like, "Hey, wanna jump in and sing?"
0:02:15.1 DN: And... And I did. I didn't... I didn't know you were gonna have a concert on the way back, and when I saw that I was gonna arrive near Oberlin around 1:30, I thought either it would be shameful for me not to go and sit down and take a break from driving to attend [laughter] a performance of the Mozart Requiem, but instead, I got to sing it, which was great fun. So.
0:02:39.1 GR: And I don't know if you know, but you were actually standing basically right behind my dad, who said he was just delighted to have your voice behind him.
0:02:44.4 DN: [laughter] Ah, I did not make the connection.
0:02:49.2 LS: And for our listeners who don't realize, it's not very often that the three or even two of us are together in person, frequently.
[chuckle]
0:02:58.1 GR: That's right, yeah, we're in three different states.
0:03:01.1 LS: So this is very exciting. [chuckle]
0:03:03.3 GR: Yes. [chuckle] Anyway, David, thanks for jumping in. That was... That was... That was...
0:03:08.3 DN: Well, it was my pleasure, and... And... Yeah, it really was a joy, and what a great thing to be a part of. And... Yes, as anyone who saw my Facebook post knows that... I also think it's cool, because my great-great-grandfather was the pastor of the other congregational church in... In town, where the Oberlin Conservatory now stands.
0:03:34.4 GR: So that was second, yeah. For anyone who knows Oberlin... Oberlin history, that was second church, yeah, and that's... My office is right on top of where the sanctuary was. That's very cool.
0:03:45.1 DN: Anyway, it was a cool family connection thing for me.
0:03:51.5 GR: So, David, you're just... You're just back from a cool conference. You wanna talk about that a bit? 
0:03:56.3 DN: Yeah, I... This was the 2022 Pedagogy into Practice conference. I think we were supposed to do it in 20... The last one was in 2019, and then the... It had been cancelled due to COVID, or altered due to COVID, so this was our first time back together. And it's a great organization and a great conference, at which we are really looking at how to be better theory teachers. And... There are so many presentations, and it's such an incredibly supportive community as well, so I really love that. It doesn't feel like many other academic conferences. It feels like everyone is there to support each other in being better teachers. And all of the talks tend to be on just things that we can do in the classroom to be better teachers, so I'm actually hoping that we can get some of those people on our podcast and let them share their talks more widely with our audience.
0:05:09.3 GR: Yeah, and some of them we've already had on our podcast. You mentioned that you saw Betsy Marvin there? 
0:05:14.1 DN: I did; I got to have lunch with Betsy twice. [laughter]
0:05:17.3 GR: Excellent.
0:05:20.4 DN: And Peter Schubert, and Steve Laitz, and Jenny Snodgrass. I hope we can get any or all of them on. [laughter]
0:05:33.3 GR: Awesome. So yeah, you know, I was... As I was getting ready for this episode, I was going back and listening to our previous episodes of the season. We... It's... We've only been doing this, what, since January? And wow, we've talked to some really, really cool people. Leah, David, what are some of your favorite moments? 
0:05:58.3 LS: Well, I think that I did the same as Greg; I listened back. I've listened all season long, and several times on some of the episodes, and I've got two major themes that kind of stuck out to me, if I could kinda go in that direction.
0:06:12.5 GR: Yeah.
0:06:14.5 LS: And the first being... Since we just mentioned Betsy Marvin, I'll talk about the importance of using systems, whether it's a solfege system or a rhythm system, and not just from her episode, but from multiple episodes. I guess I just... What stuck out to me was that students learn in so many different ways, and we know that, but hearing it back really makes you think about it, and... Have different learning experiences early on that influence the type of learner that they become later. So, having not just one system, like a rhythm system or a solfege system, but having two systems is so beneficial. This helps for sight-singing. So, when we talked about choral sight-singing with Denise Eaton. And sight-reading; we talked about contest sight-reading with Dr. Andrew Machamer. And then for students who learn with perfect pitch, how sometimes, one system can be confusing; you know, fixed... Or movable do might be confusing versus fixed do, and switching to numbers instead. So, as a teacher, having a system for teaching your students, but then having two systems to get at all the different learners that are in front of you.
0:07:28.6 GR: Yeah. Totally, right? And of course, with pitch solfege, then we're typically talking about the system that names the notes, whether that's letters or fixed do, and we're talking about a system that names function, where something is in the scale, and that's typically our scale degrees in movable do. And then yeah, I hadn't thought about it, but yes, totally, that's a great connection to when we were talking about rhythm systems. And we were talking about systems that are kind of analytical, that label the various subdivisions of the beat, or possibly the... Where the beats are in the measure. And mnemonic system systems, where we give kinda fun names to... To rhythms, whether that's lemon yellow, or watermelon, or you know, whatever kinds of things. Yeah. Nice. That's a great theme.
0:08:16.3 DN: Yeah, and there was a... I don't know if I'm jumping in on you, but one of the other big themes was how to make... How to be... How we can make all of these lessons engaging with the students, and Jed Dearybury talking about the value of play, and... This was... There was a... There was a presentation at the conference I was just at about gamifying the aural skills classroom. Or maybe it was music theory; I'm not sure whether it was specific to aural skills, but... And of course, all the Dalcroze games that we played together, Greg. You know, I love them, and I just... I want to use them as much as I can. I want that kind of spirit in my classroom, so I hope that... I hope we were able to share that with other people in a way that they also felt like they wanted to incorporate that spirit.
0:09:18.6 GR: That was such a fun episode for me to record with you, David, the Dalcroze games episode. And, you know, I think also related to that, our episode on your music theory and ear training songs, right? Like, talk about playful spirit and bringing that kind of joy into the classroom. Those are just so wonderful.
0:09:38.7 DN: Well, I'm working on more, so there we go. [chuckle]
0:09:41.3 GR: Excellent. [chuckle]
0:09:43.9 LS: Funny enough, that was my other theme from the season, was the importance of play in teaching, and specifically, those three episodes stood out to me.
0:09:53.2 DN: And I think especially in the wake of COVID too, we're really living through some collective trauma, and I think we need to have reasons for students to be engaged with us, so that they have a sense of... That learning doesn't... Isn't some tedious thing that they have to buckle down and apply to, but that they can... I think if we make it enjoyable, then they will come more joyously and maybe more fully.
0:10:28.4 GR: Totally, yeah.
0:10:30.7 LS: And I would maybe add one more into that; the part of the episode with Megan Long, where we talked about trends in theory pedagogy. And as someone who's not in that world all the time, or at least as much as Greg and David are, it was really interesting to hear from Megan talk about how she's adapting teaching to... So for example, she talked about analyzing music and broadening the tools that we would need to analyze music beyond just harmonic analysis. That was really interesting to me.
0:11:09.5 GR: Yeah. David, were those themes echoed at the Pedagogy and Practice conference? In terms of broadening approaches to analysis of music beyond just, say, Roman numeral, Schenkerian-style analysis? 
0:11:23.5 DN: Were they included? [laughter] Well, Philip Ewell gave the keynote address at the end of the conference, so yes. And yes, you saw that throughout the... There was a lot of presentations about sort of decolonizing or recentering various pedagogies. There's a grad student I'd love to bring on here who talked about using rap to teach rhythm. And that was a really... That was a thought echoed through several different presentations, and one of the things that was a common thread through them was putting up words, so that even students who didn't know notation could align things with where certain words were happening, and talk about what was happening in the music at those words. And there was a lot of talk about ways to talk about musical things without having to use notation, or at least using some kinds of protonotation, which is another theme that we've at least been wanting to talk about.
0:12:40.2 GR: Yeah, I think those had, really, a lot of my... My favorites, I... You know, listening back, there were things I was just... That I came away with as sort of gems of knowledge. I think about, like, Denise Eaton's advice that when you're learning to teach solfege or ear training, find a mentor who's good at it and ask them how they do it. And, you know, this coming from someone who has written a bunch of books on teaching it, that she's right; so much of that is about seeing someone else do it live, and trying out what they do with your own students, and seeing how it goes. I was thinking about our chat with Betsy Marvin. And, you know, I thought I knew so much about what we know about perfect pitch, but it turns out there's a ton I didn't know, and there's so much that we... That I thought we knew, that in fact, we don't know, right? I mean, it was sort of the gospel for about a decade that you couldn't acquire perfect pitch after about age 6, and Betsy really blew my mind when she said, "Well, actually, there may be some research, or there's some research recently that suggests that, in fact, maybe it is possible to acquire perfect pitch later." Yeah, really just fascinating stuff, so I feel really lucky that we get the chance to ask these brilliant people questions and hear what they have to say.
0:14:09.7 DN: Yeah.
0:14:11.7 GR: Great, so shall we... Shall we change gears and maybe talk a little bit about what we have planned for uTheory coming up? 
0:14:18.0 LS: Definitely.
0:14:18.9 DN: Sure. I was excited today when... When... To open up my computer and see that Solfege Sally is now available on uTheory. [chuckle]
0:14:31.2 GR: Yeah, yeah, in our experiment section, yeah. David, you wanna tell us something about Solfege Sally? 
0:14:37.7 DN: Yeah. I mean, it's something that... Well... That I had been thinking about for years, of wanting to create a game like Simon, except with all of the diatonic solfege notes, and then just be able to practice working memory and identification of those diatonic notes in the scale. And then, when we first talked, it turned out you had been thinking about the same thing, so that was exciting, and I was just glad to see it finally come to fruition, and I think it's kind of fun.
0:15:15.1 LS: It's fun.
0:15:15.8 GR: It's totally fun, yeah. [laughter] Absolutely. [laughter] And a friend of mine... A friend of mine posted on Facebook, "I got 305. What's your top score?" Yeah, I know, I have not gotten to 305. I'm like, "Go, Mattie."
0:15:32.4 DN: Well... Of course, the score is... You know, it adds up... As far as you got every time you hit a correct button, so it's not that the melody was 305 notes long, but... But still, that's impressive.
0:15:48.8 GR: Yeah, yeah, I can't quite do the math backwards to figure out how long that melody would have been, but it'd be long.
0:15:54.7 DN: It involves factorials and... [chuckle]
0:15:57.5 GR: Yeah, yeah, it's a little more complex than factorials, because there's the addition of one on each... Oh, I guess it is just factorials, you're right, yeah, yeah.
0:16:04.4 DN: Yeah. Anyway, it doesn't... It... It... And what I forgot was that you can choose your level that you start at in the... If you click the settings button.
0:16:17.7 GR: Oh.
0:16:18.5 DN: But it's not clearly a settings button, but it definitely... If you go on Jedi Master or whatever is the... The highest level, then you can get some big leaps. [laughter]
0:16:31.6 GR: Yeah. I'll have to try that version of it. Yeah, we'll... We should make that more clearly a button before we graduate it out of the experiments section.
0:16:42.3 DN: Yeah, yeah, yeah, yeah, there's a... There's a few... The layout of that is... Is in need of some repair as well, but... Oh well.
0:16:49.0 GR: Yeah. Yeah, and you know, I think... It's fun, though, to... To share, a little bit, some of the things that we're working on in an incomplete format, just so that... Just so that, you know, people can see it.
0:17:00.8 DN: And to get feedback.
0:17:02.3 GR: Yeah.
0:17:03.0 DN: So I had someone, for example, ask, "Hey, could you... Could you do major and minor pentatonic scales?" And I thought, "Yeah, probably with a few lines of code."
0:17:13.1 GR: Mm-hmm, yeah. And... [chuckle] And I had a friend text me, "Is uTheory perpetuating the terrible lie that the fifth degree of the scale is called so and not sol?"
0:17:25.6 DN: Oh. Oh dear.
0:17:26.9 GR: In a very joking way. [laughter] We can probably change that one too with one letter of code. [chuckle]
0:17:35.2 DN: One letter of code. [chuckle]
0:17:38.3 GR: So, you know, it... It's probably not obvious to most users of uTheory, but we have shipped over 120,000 lines of new code this year; a complete backend and frontend rewrite. And, you know, at this point, you can't see that much of anything has changed, because... Because, really, almost none of the functionality has changed. But what we've done is we have gotten the backend framework in a place to where it has become much easier for us to now create new... New ways of structuring and storing data, and the frontend to a framework that makes it much easier to interact with that data. And those are two kind of key... Key building blocks for allowing us to build bigger features. And so now, as we come into summer, we're... We're turning our attention to some... Frankly, some big changes in uTheory. We're internally calling it uTheory 2.0, although we wanna be clear that your existing classes and settings, all those are going to migrate just fine, and if you like uTheory as it is, fear not, you don't have to change. But... Yeah, but some of the things that are coming are things we've been... that teachers in particular have been asking us for for a long time. So, to start with, we're adding the ability for teachers to create practice assignments and to create mastery assignments. Leah, you wanna talk about that a little bit? 
0:19:16.0 LS: Sure. So, on the... I think the biggest change here is that teachers have a greater customization. So, for example, if you wanna create a practice assignment that has a set number of questions, or even a set amount of time, a minimum amount of time for students to practice, you can configure that when you create the assignment. You'll also be able to customize the topics a little bit further; in terms of, for example, say, an exercise in key signatures, being able to specify which key signatures are included. You'll continue to be able to set due dates, and you'll also be able to set an available date, so you can create the assignments in advance, and they'll become available to the students on the date that you choose. And you can assign practice or mastery assignments to just specific groups of students versus just an entire class.
0:20:16.3 DN: Or even individual students, if you want, within a class.
0:20:17.7 LS: Yes.
0:20:18.4 GR: Yeah. And along the lines of that, as we add these new kinds of assignments, in addition to the existing lesson and checkpoint assignments and skill mastery assignments, we're gonna be consolidating content into a Learn tab. The Learn tab's gonna become the central location for students to find what they should be working on, and that'll include lessons, checkpoints, custom tests, practice and mastery assignments... And... So that you as a teacher can arrange that sequentially, so students don't have to go "Okay, wait, now it's time to take a test. Oh, where is that? Oh, that's on the Test tab," versus "Oh wait, where am I supposed to go for this skill practice?" So yeah, so we're bringing that all together into one place to make it easy to find and easy to sequence.
0:21:10.0 GR: And then, related to that, we're going to roll out a new curriculum. I've started calling this the uTheory extended curriculum, and thinking of the one that exists presently as the uTheory accelerated curriculum. So, you know, when we started building uTheory, the idea was, how can we quickly get students who are thinking about doing a music degree ready for college level music theory and ear training? And so, the curriculum as it exists right now is designed to be done in a pretty intense semester of work. But that doesn't fit the needs of a lot of our users, especially at the high school and middle school levels, where... You know, where teachers work with students for multiple years, and similarly in private lesson studios. And their goal is not to cram all this knowledge in, but they'd like to be able to pace it out and build fluency on that.
0:22:05.9 GR: So, the curriculum that we're building is designed exactly for that. And from the beginning, it'll start with the option to configure the clef that a student... Or clefs that a student is learning in. So, whether their primary clef is treble clef, or bass clef, or viola clef, alto clef, or grand staff, for a pianist. And the lessons and skills practice and mastery assignments and checkpoints will all... And videos will all adjust to that, so that the student's work early on is exclusively in that clef, until eventually, we start introducing other clefs as well. The new curriculum is going to be one that integrates rhythm, ear training, and written music theory concepts all together into one single learning sequence, so that the things that you're learning in... As you're learning, for instance, to write intervals, you're also learning to hear intervals. As you're learning to write scales, you're learning to hear your way around scales in stepwise ways. As you're learning to write chords, you're learning to hear different qualities of chords.
0:23:20.5 GR: And it'll be what we call a spiral curriculum, so, that is to say that, you know, when you learn, you learn the basics of a concept early on, but we're gonna keep coming back to it. We're gonna keep reviewing that concept in later assignments, and gradually increasing the level of difficulty with it. As David sort of previewed with Solfege Sally, it's gonna be a gamified curriculum. It's gonna feel a lot more like... Like Duolingo, right? Complete with badges, and confetti, and literal games, and all of that, so. And I think finally, the big thing about it is it's gonna be much more configurable; that as a teacher... Teachers will be able to create their own lessons, assignments, tests, or to edit the existing ones, to rearrange them. We recognize that teachers know better than a computer ever can what their students do and don't know, so, we want to give 'em all the tools that you need to give your students what they need. So... Yeah, that was a lot of talking. Did I miss anything? 
0:24:34.1 LS: I don't think so. I just wanna highlight again the importance of two things that Greg said based on the requests that we've gotten from teachers, so he mentioned arranging in sequential order, so, this means that you can change the order of the lessons. Teachers have asked, you know, "Is it possible to make this lesson appear before this one?" and now it is; just with a simple click and drag, you'll be able to reorder the lessons. And also, the existing uTheory is not going away or going anywhere for the teachers who are using uTheory as is and love it, and we know that there are a lot of you. This does not mean that you have to change what you're doing. You'll still be able to continue to teach as you have.
0:25:19.3 GR: And effectively for... You know, what will happen is, for existing classes, the Lessons tab will turn into the Learn tab, and will look very much like the Lessons tab looks for your current classes. But you'll have the option then, at that point, if you want, to also add additional assignments, mastery or practice assignments, and tests to that as well.
0:25:43.8 LS: Could we maybe talk just a little bit about the difference between practice and mastery assignments? 
0:25:48.7 GR: Yes, absolutely, created, yeah. So, effectively, practice assignments... The... Obviously, a practice assignment... A goal of a practice assignment is to increase the student's mastery of skills. But we're distinguishing between practice and mastery assignments, in that a practice assignment will be an assignment that has a specific number of questions and kinds of questions on it, or a specific time limit for those kinds of questions, whereas a mastery assignment is an assignment where uTheory will generate questions based on a set of skills that you select for that mastery assignment. So for instance, you might create a mastery assignment for the skills of... Intervals between notes with no accidentals on them, white note intervals. Right, and then, that would... That would provide questions and train students until they reach a certain level of mastery on all of the possible questions from that area. And so, as we're doing this, one of the things that's going to change from the teacher perspective is, currently, under Classes and Choose Skills, you have a bunch of checkboxes for sort of the subskills. And what will happen for each of those skills is instead, you're gonna get a more robust configuration panel, so that let's say we're talking about the skill of triads in pitch and harmony. So that's writing triads, identifying triads, etcetera.
0:27:28.1 GR: That skills panel is now going to give you options for things like whether you want to allow triads in various inversions, what qualities of triads you want to allow, how many accidentals and what kinds of accidentals you want to allow within those triads, or if you wanna filter and say "I only want to allow triads within keys, say, up to two flats or two sharps," you'll be able to do things like that. So we're gonna be writing lots of ways to configure the kind of practice that students get when you configure either practice assignments or mastery assignments. Similarly, the ability to configure what clefs are included. And, you know, you'll have the option of choosing a student's primary clefs, secondary clef or both of those and also, you know, any of the... The seven clefs: Treble clef, bass clef, alto clef, tenor clef, soprano clef, mezzo-soprano clef, baritone clef... Did I miss one? I must have. No, I think that's all. Anyway, there's that, right? So, yeah. If you want... If you want your poor students to have to drill on mezzo-soprano clef, you can absolutely give them second line C-clef and make them do everything in second line C-clef.
0:28:52.8 DN: But I love C-clefs. They tell you exactly where C is. It's so useful.
0:28:57.8 GR: Yeah. Absolutely, absolutely. You know, and... Although we don't usually have to read mezzo-soprano clef unless you're a conductor, in which case, if you put it over in a transposing instrument, like, say, in the Mozart Clarinet Concerto, it comes out in concert pitch. And similarly, we don't usually have to read baritone clef, you know, again, unless you're a conductor and you put it over a G-transposing instrument, like alto clef in Holst's The Planets, and out it comes in concert pitch. So, even in any case, practice versus mastery assignments. A mastery assignment is one that the student just continues working on until they reach a certain level of mastery, whereas a practice assignment is one that has a specified time or a number of questions cutoff to it. So it's a lot more like a traditional homework assignment. So, yeah.
0:29:48.6 LS: And even with all of these new configurations and types of assignments, uTheory will still do the question generation for you and will still do all of the grading, so we're not adding any work to the teachers' plates. [chuckle]
0:30:00.3 GR: That's right, that's right, yeah. And we think also that this... This new curriculum is going to take a lot of work off of teachers' plates. Some of the... Some of the... Or the power users of uTheory have kind of created their own curricula that bounce around to the different parts of uTheory to make it work, and have then... You know, either in their learning management system, or even in Google Sheets for individual students, have then listed out all of those things to help students find where to go. We really think this is just gonna make it a lot easier for a student logging into uTheory to go "Okay, here I am, and oh look, there's the very next thing I need to do," 'cause it'll basically appear as one long kind of list. So, with that, we have some... So we're hoping to get the... What we're thinking of as the first, roughly, year or 12-ish units of the extended curriculum out around August 1st. And we have some stretch goals with that, including rolling out sight-singing elements in ear training, which is really exciting. We've been working for a long time on algorithms to do pitch detection in a way that works for singing, which has more vibrato, which has changing vowels, which has consonants, and I think we're pretty close on that. David's got a great game that he's been working on called Pitchy Fish, where you... Tell us about Pitchy Fish, David.
0:31:38.3 DN: It's a little bit like Flappy Bird, except that instead of hitting a button, you control the height of the fish in the water with your voice, so you sing a higher pitch and the fish goes up, and then you sing a lower pitch and the fish goes down. And this idiom, I think, will, A, make it fun, but, B, just give so much feedback to students, especially ones that may have more trouble than others matching pitch, or getting the pitch in their head to be the pitch that's coming out of their mouth, and to know whether they're on target or not. And we can extend it to actual sight-reading exercises easily, but... But this is a great sort of training ground that I think, like most good games, feels fun as you're learning to do it.
0:32:38.6 GR: Yeah, and I think... You know, any of us who've tried to help shy singers gain confidence with their voice know that finding ways to do that that are fun... It's critical. It's... You know. People are understandably very self-conscious. You know, as a singer... We've always remained a bit self-conscious about our voice; it is an instrument that is literally connected to us. Yeah, so, you know, whether you're working with student singers or student instrumentalists, helping them to find their voice is huge and raises so much awareness of pitch and intonation and all of those wonderful things. Yeah. Pitchy Fish; of course, we can extend it to... You know, to sight-singing particular things. Also to exercises of intonation, of really fine-tuning with things, so yeah.
0:33:42.1 DN: All of which depends on a good pitch detection algorithm, and boy, you can see how hard that is by how not good so many of the products out there are. [laughter]
0:33:53.0 GR: It's true, it's true.
0:33:54.2 DN: But we've been working hard, and I say we, and mostly you, have been working really hard on this problem and coming up with great solutions, but we've tried so many things to get the computer to accurately recognize what someone's actually doing.
0:34:09.8 GR: Yeah, and I don't wanna give away too much of what we're doing, but... Only to say that we are using a combination of traditional algorithmic methods for detecting pitch. Also machine learning. I'm pretty happy with where that's headed. Cool. I don't know, what else should we say? 
0:34:33.1 LS: I don't know. Can we give another call for feedback? 
0:34:38.7 DN: You know, yeah. And I recently had... Speaking of comments and suggestions, I got a comment and suggestion from my in-house critic, my wife, who said... [laughter] Not as a criticism, who said, "You know, you should do an episode where you answer questions from your listeners," and I thought, "Well, that's a little bit what we already do, but we don't." We don't say, "So and so said "I have this question," and I answered it." We could... We could... If... You know, if people send us enough questions, we can do a Q&A. Ask Me Anything. Of course, Ask Me Anything can spiral away from music theory very easily, but...
0:35:23.8 LS: Yeah.
0:35:25.3 GR: Yeah. [chuckle]
0:35:27.0 DN: Ask me anything about music theory.
[chuckle]
0:35:30.4 LS: You're gonna get song requests.
0:35:31.9 DN: [laughter] I am down for song requests.
0:35:36.8 GR: So, one of the things that I'm super excited about, as we're talking about gamifying the curriculum, is that, you know, we're working to include, as we mentioned, literally these games, but also, to start including some fun music theory and ear training learning songs. David, do you wanna preview that a little bit for us? 
0:35:54.7 DN: Well, I did write... I mean, I wrote a couple songs on the way up to the theory conference. And I need to get them recorded, but one of them, I'm... I just almost want to write out just the melody in Notation so that people can play it for themselves, because it's just about how to find C on the piano. And... I mean, maybe if you can't find C on the piano, then this is gonna be problematic to play, but it's "Black notes... " Or I should start on the right key. "Black notes on pianos come in twos and threes. Check out these ebonies. To the left of every pair, you'll find the Cs. That'll get you tickling the ivories."
0:36:44.3 GR: [laughter] Nice. For those of us who have a low F-sharp, yeah.
[laughter]
0:36:49.3 DN: But "Black notes on pianos" (sung an octave higher), we can do it up here.
[laughter]
0:36:52.7 GR: Right? 
0:36:54.8 DN: But, you know, if you... If someone decides that they wanna sit down and play it on the piano, then...
[music]
0:37:04.1 DN: Then they're gonna be doing exactly what they... What those words say, and they'll go "Oh wow, I wanna find the Cs. Oh, look at that, that's a C. How useful." [laughter]
0:37:20.2 GR: Nice.
0:37:22.7 DN: I don't know. I was pleased with that, and I've... I've envisaged a nice ragtime accompaniment for it, but I haven't actually written it out yet.
[chuckle]
0:37:34.3 GR: Great. And "Where the... " "Where the half steps are", is that...
0:37:40.6 DN: Do you want a preview? 
0:37:42.4 GR: Sure.
0:37:44.3 DN: How does it... "From... From sev to one and back again, this is where a half-step lives. And from three to four and back again, this is where a half-step lives. In a major scale, the other steps are whole steps. So let's celebrate where the half-steps live. Where the half-steps live. And let them bring us home."
0:38:34.6 LS: Yes.
[applause]
0:38:37.0 GR: Oh, I love it. Yeah, David, if that's done before... In the next three weeks, I am totally using that with my Interlochen students this summer as we dive into writing scales.
0:38:47.6 DN: Okay. Then it will be done in the next three weeks.
0:38:50.4 LS: That's the deadline.
[laughter]
0:38:52.2 GR: Yeah, exactly.
0:38:54.3 DN: I think it probably won't be done while I'm in Illinois, but then as soon as I get back...
0:38:58.9 GR: Mm-hmm. You're off to sing some Bach again? 
0:39:01.9 DN: I am. I'm gonna go sing St Matthew Passion with Andrew Megill and the Illinois Bach Academy, and then I have a week-and-a-half break, and then I... Well, break... [chuckle] Break from singing, and then I'll be in Carmel and doing the St John Passion with Andrew Megill.
0:39:23.6 GR: Oh wow.
0:39:24.7 DN: And we're... Also, we... This is... We're... At Carmel, we are finishing up a search for the new director, which means that we have all three final candidates coming in to direct different programs, which is... They've each chosen these amazing programs, and I can't wait to work with all of them. So we're gonna do Brahms' Requiem and Bach Easter Oratorio. There's so much great music happening this summer, I can't wait.
0:39:58.0 GR: Nice, nice. Excellent. Well, maybe this is a good place to wrap things up. This has been so fun, I have to say... You know, the... I thank Leah for coming up with a crazy brilliant name for this podcast, and David for our delightful theme music, and all the wonderful editing and everything else you do is just... Yeah. This has been a ton of fun, and I will miss our recording sessions over the summer, but I'm so looking forward to our next season of Notes from the Staff together. Yeah. As always, if you... If... Listeners, if you have any feedback, send it to us, notes@utheory.com.
[music]
0:40:47.5 LS: Notes from the Staff is produced by utheory.com.
0:40:50.4 GR: UTheory is the most advanced online learning platform for music theory.
0:40:54.3 LS: With video lessons, individualized practice, and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm, and ear training.
0:41:05.1 GR: Create your own free teacher account at utheory.com/teach.

Music Theory Songs with David Newman

David Newman shares his music theory and aural skills teaching songs, as well as some of the stories behind them, in this laughter-filled episode of Notes from the Staff.
Links:
The Well Trained Ear on BandCamp
David Newman on YouTube
Show notes:
0:00:20 Introductions
0:02:03 How did you begin writing teaching songs?
0:03:48 David's most popular song: The Periodic Table Rap
0:11:00 Greg and Leah's favorite songs of David
0:11:46 The Dominant Seventh Song
0:14:13 Hinting at future topics in songs about more basic topics
0:15:57 Sophie Lay on My Sofa
0:20:00 Collaborators on the songs
0:23:47 Third Away song
0:26:22 Navigating singing Bach professionally, and recording these popular style theory songs
0:30:25 Intervals in Inversions song
0:34:00 David's favorite song: Second Inversions
0:38:45 The Chord Spelling Song
0:42:51 How teaching songs can help students hear and recognize things as they're happening.
0:46:41 Where can listeners find your songs?
0:49:30 The Notes from the Staff theme song
Transcript:
[music]
0:00:20.0 Leah Sheldon: Welcome to Notes From The Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.
0:00:33.9 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and associate professor of conducting at the Oberlin Conservatory.
0:00:40.6 LS: Hi, I'm Leah Sheldon, head of teacher engagement for uTheory.
0:00:44.6 David Newman: Hi, I'm David Newman. I teach at James Madison University and I write code and create content for uTheory. A quick thanks to listeners for all your comments and episode suggestions. We love to read them. Send them our way by email at notes@uTheory.com and remember to like us and subscribe wherever you get your podcasts.
0:01:03.7 GR: In our second to last episode for the season, we're turning the tables one more time. And Leah and I will be interviewing our co-host Baritone David Newman. David teaches aural skills, music theory and voice on the faculty of James Madison University. He's famous for his teaching songs, which have millions of views on YouTube. He released his music theory songs in a 2019 album, The Well Trained Ear. They're widely used by elementary, middle, high school and college teachers. Previously, David taught at the University of California Davis, San Jose State University, University of Virginia and Shenandoah Conservatory. He maintains an active performing career as a classical singer and can be heard on the Philips, Dorian, Analecta, K617, and Nexus Labels. Despite COVID-19 precautions, David continued to make music and inspire others to join in the harmony with his innovative drive and choir concept profiled in both the LA Times and New York Times. David thanks for joining us.
0:02:01.5 DN: I'm so glad to be here.
[chuckle]
0:02:03.6 GR: So, we're gonna talk about your teaching songs which are just utterly delightful. I think this is a lovely follow up to our episode a couple of weeks ago with Jed Dearybury about The Playful Classroom. How did you get started writing teaching songs? 
0:02:16.6 DN: Oh, wow. I mean, I could go really far back and say that I initially went to music school with the thought of that being a backup for my great career as a singer-songwriter, but really it started when my daughter was in third grade and she brought me a study packet for science and asked me if I would help her study for a test. And we looked at the... I looked at the packet and there was a lot of stuff to memorize. And I said, "You know, we could probably turn some of this into a song." And so I wrote a quick little ditty about soil, [chuckle] and its components and recorded it. And I threw it out on YouTube just to share it that night and got such a positive response that I wrote another song the next day. And I wrote four songs in four days and then I completely burnt out.
[laughter]
0:03:25.2 DN: But then I did it again several times, and this was also in the first year that I was teaching aural skills. And so, later in that year, I just thought, "If I can do this for my third grade daughter, why can't I do this for my aural skills students?" And then I wrote a few songs for them and it just kept going from there.
0:03:48.8 GR: What's your most popular song? Is it one of your music theory songs or is it one of your songs for other... [laughter] A uTheory advantage of having YouTube statistics, right? So.
0:04:00.6 DN: You know, I know... And it's... I don't know if I should be embarrassed about this or not, but my... Yeah, my most popular song is me rapping the periodic table of elements. I have over a million views on that song alone.
0:04:15.4 GR: Can we take a listen to that? 
0:04:18.2 DN: Sure. [chuckle] And there's of course... I also wrote that in one afternoon/evening, and I was finally ready to record the female vocal parts at midnight, which meant that I accosted my wife at midnight as she was wanting to go to sleep, and I said, "Please, I just need you to sing these few things." [laughter] Yeah. And then I just think it's funny that my entire career as I view it has been as a classical singer, singing Bach, but I probably have reached more people with my rap stylings.
[laughter]
These are the elements, the periodic table, in orderSo we got hydrogen, helium, lithium, berylium, boron, carbon, nitrogine and oxygen, flourine. Now stop snoring... this isn't boring, and this is stuff you shouldn't be ignoring. Neon ("noble"), sodium, magnesium, aluminum, silicon, phosphorous, sulfur, chlorine. That's under Flourine. Hey, we're up to 17! You've never had it better for remembering the elements.
These are the elements...Then we got argon ("nobel"), potassium, calcium, scandium, titanium, vanadium, chromium. Manganese, iron, cobalt nicketl cpper zinc, gallium, germanium, arsenic, selenium, and bromine. That's under chlorine and flourine. Just keep storing the order for your mortar board.
Krypton, rubidium, strontium, ytrium zirconium niobium molybdenum, technitium (it's radioactive, woah). Ruthenium, rhodium, palladium, silver ("bling"), cadmium and indium. Tin, antimony, tellurium and iodine.
[laughter]
0:06:29.6 DN: I love watching your reactions.
[laughter]
0:06:33.2 DN: Well, that was the... Yeah. I don't know. And I would feel totally guilty writing a rap. Which is not my wheelhouse at all, except that, I know what I like about rap. I'm frustrated by educational music that doesn't honor the musical side of things. And so I did try to make it interesting. And I did try to do things like internal rhyme and the kinds of things that make rap enjoyable for me. And I loved so much, sorry, I loved so much watching your reactions. 'Cause I guess you hadn't seen that before. [laughter] And I do try to work humor into my songs. And I really do love sharing some of them for the first time with people who haven't heard them before, and just seeing them react to things that they get. The little inside jokes. I think sometimes the inside jokes are useful for students, too, because if they don't get them, then they want to get them. They wanna know why everyone else reacted at that moment.
0:08:00.6 LS: Or why that "Noble" was such a moment.
[laughter]
0:08:08.9 DN: Which I did after every noble element.
0:08:10.5 LS: That will help me remember the noble moments.
0:08:14.4 DN: Of course, I wrote this, what, 11 years ago? And... 12 years ago, maybe? And now it's incomplete. [laughter] There have been eight more... No six more named elements since then, so 118 completes are all of the table.
0:08:40.0 GR: I'm sure that people have made the comparison of this to Tom Lehrer's Element song just made me think of his last verse, 'cause like, there may be many others.
[overlapping conversation]
0:08:50.2 DN: These are the only ones of which the news has come to Harvard, and there may be many others, but they haven't been discovered.
[laughter]
0:09:00.3 GR: Yeah. That's right. Yeah.
0:09:01.0 DN: Which is, of course, a Gilbert and Sullivan tune. Yeah, I was aware of that. And Tom Lehrer is, of course, one of my huge influences. But the frustrating thing about the Tom Lehrer version of that song is that it's not in order. It's not only very incomplete by today's standards, but it's also not in order. So it's more just a witty thing that you can do naming a bunch of elements and not particularly useful for learning anything. Or no, you could argue that memorizing the table isn't particularly useful for anything either. But memorizing it in order is something that Virginia students have to do. And so I was writing it specifically in response to a request from my sister who said, "Kids need this." I thought, "Okay, challenge accepted, I will come up with something."
0:10:07.3 GR: And you said, you started writing these teaching songs, right at the same time as you're starting to teach aural skills. And so I presume that's what led to all of your music theory and aural skills songs as well.
0:10:18.5 DN: Yeah. And also, I think there's something... Teaching a new course, especially when it's not something that you've spent a long time thinking about how you were gonna teach, I feel like I grew a million brain neurons [chuckle] that year. I think there's something about learning something new, digging deep into something new that just fosters creativity. And that was an incredibly creative year for me.
0:10:54.1 GR: I know Leah and I have both listened to probably all if not most...
0:10:58.1 LS: I think so.
0:11:00.5 GR: Of... Probably most if not all of your teaching songs. Leah, do you have a favorite? 
0:11:07.4 LS: Well I like a lot of them but I do think that... I'm gonna put Sophie up there.
[laughter]
0:11:20.4 LS: And maybe The Dominant 7th.
0:11:24.8 GR: Yeah, I was... Yeah. For me the... For me... Yeah, I love Dominant 7th would be totally top of my list, partly 'cause it's just so darn useful. You just play this once as students are coming to the classroom and they never forget what the notes are of that Dominant 7th.
0:11:41.3 DN: Right. As long as you're using movable do.
[laughter]
0:11:46.4 GR: As long as you're using movable do, that's right. Yeah. Yeah. Should we listen to it a bit? 
0:11:50.8 DN: Sure.
This is a I chord and a V in first inversion,Then a vi, a passing I 64, then IV.But this song might get boring and you’d prob’ly start ignoring meIf I tried naming every single chord.
But there’s one chord that’s terrific, and its function is specific,And it hangs around in cadences for fun.With solfege we can state it if we just arpeggiate it, andSol-ti-re-fa is a dominant 7, which brings us home to I.
Of course the IV chord (FA-LA-DO) can be pleasant to the ear.Then there’s V7/V (RE-FI-LA-DO)That’s a chord we’re going to learn about more next year!
We’re back to I now, and there’s that V in first inversion,Just repeating what we’d played when we’d begun.And this path that we had charted’s going to finish what we started‘Cause SOL-TI-RE-FA is a dominant 7, which brings us home to…
OH NO! That cadence was deceptive!It went to minor vi instead of I!That sort of trick can be effectiveAt making things last longer when we thought that we were done!
0:13:34.1 GR: I love that deceptive cadence, David.
0:13:35.9 DN: [laughter] I have to give credit to Matt Grisset, one of my students, for that. I was still writing the song... I don't know. It was written over a period of time, and I shared my initial thoughts, maybe the first verse or two with my students that year, and Matt said, "You need to put a deceptive cadence in there," and challenge accepted. [laughter]
0:14:10.2 GR: [chuckle] Nice.
0:14:13.1 DN: But that was great, and the... It was so useful... It is useful in the classroom, if you're teaching in movable do, to be able to say "So ti re fa," and just... Then... People... Yeah, it just gets stuck in their heads, which is the thing that you want to have happen. [laughter]
0:14:34.1 GR: Totally, totally.
0:14:35.6 LS: But you also acknowledged other concepts in there without taking away from the Dominant 7th, but really staying true to what's happening musically.
0:14:45.0 DN: Yeah, and pedagogically, we talk about spiraling, or coming back to the same concepts and seeing them with new eyes, and I... Add into that the... I think it's totally fine, in fact, admirable to introduce... To throw out a concept that they haven't learned yet, so that when they get to it, you can say, "Hey, remember when we listened to that song? Remember when it did "Re fi la do"? Now we're gonna talk about what that is. That's secondary dominant, and it gives them a hook to go, "Oh, this is a thing I already know." And I hope, when we're teaching aural skills, that a lot of it can be, instead of, "Here's a theory thing that you have to know," it's, "Here's a thing that you know and love. And now I'm gonna put a name to it. I'm gonna give you a way to name it and understand that it's happening. You already love it. You already know what it sounds like. It's just here's a context for it."
0:15:57.7 GR: When we were talking with Megan Long a couple of weeks ago about hexachordal solfege, and she started talking about [0:16:07.1] ____ and solfege puns from the Renaissance era. Of course, you know, that brings to mind Leah's favorite song, Sophie Lay on My Sofa, which is just... Can you introduce that for us a little bit, David? 
0:16:24.5 DN: Oh gosh. Well, I had already written one solfege pun song, but that was just a sort of attempt to do Sound of Music, Do-Re-Mi, but, you know, in a different way.
0:16:39.4 GR: Is that the silly solfege song? 
0:16:39.8 LS: The silly solfege? 
0:16:41.5 DN: The silly solfege song.
0:16:42.0 LS: I love that too.
0:16:43.3 DN: Which is fine, although it still bothers me that I had to use bad grammar in order to keep the solfege puns going. I mean, it really, really pains me, [chuckle] but I wanted to see if I could incorporate a solfege pun song with lots of chromatic solfege and... Get, yeah, more of those relationships in there, and then, that became a fun challenge, just to see how to write the story in a way that it would make musical sense. And also, I really, really wanted to get "Fa li" in there, which of course means that the li has to be followed by a ti, so how can I make a story that has "Fa li" followed by the word tea. And the version that I recorded and put on YouTube was just me and a guitar. But the version we recorded for the album turned out to be kind of a really fun, bluesy song. [chuckle]
0:18:04.9 GR: Nice. Well, let's have a listen.
Sophie lay on my sofaEating raw dough, and drinking teaSophie don't lay on my sofa so...Don't tease me so!Let yourself fall for me.Eating raw dough is folly.Tea's not so bad.But Sophie, don't lay on my sofaEating dough.
0:19:27.4 GR: [chuckle] Love it. I love it. Of course, if you're a la bass minor person, that one is going to be very confusing, for us do bass minor people. [laughter]
0:19:38.5 DN: Well, I'd also... I mean, I think it sort of modulates there in the middle, and I don't modulate the syllables at all, but whatever.
0:19:45.7 GR: Yeah.
0:19:46.7 DN: I achieved my pun goal, and that was the important thing, [laughter] right? So I don't know if that one's pedagogically, you know, super useful, but...
0:20:00.6 GR: I mean, I think just the experience of listening and saying "Oh my god, that is actually so. Oh, that's fi." Right? And yeah, it is totally fun and valuable, pedagogically.
0:20:13.9 DN: I also think this is a good place to give a shout out to Jacob Rose Meisel, who was one of my voice students at JMU, who came to me in the middle of his senior year and said, "Hey, I arranged one of your songs, and I want you to see what you think of it," and it was the Non-Dominant 7ths, and he had created this elaborate progressive rock kind of arrangement of it, and I was... I just thought, "Wow, this is amazing. Can you do this with other things?" And he ended up producing and playing instruments, and he was the driving force behind making this album happen out of a bunch of YouTube videos that I, you know, mostly wrote and recorded in the same day. [chuckle]
0:21:18.5 GR: And you said your backing vocals, those are your wife and daughters, is that right? 
0:21:27.1 DN: Depending on the track. Sometimes, it's my wife and daughters. There were a couple songs where I got... I just asked for student volunteers and community... Student and community volunteers, I think. I just had a bunch of people on the album. I got a bunch of people together, and we just recorded all of the backing vocals together, including at the end of the Second Inversions song, Manny Davis did this great, completely ad-libbed riff of Amen [chuckle] at the end of the Second Inversions song, and it's fantastic. I'm just so grateful for all those amazing people who sort of stepped in and helped. Oh my gosh, and... Sorry, if I'm talking about amazing people who stepped in and helped, my friend and colleague Sam Suggs came in and played bass on a bunch of tracks. My friend and colleague, Dave Pope, came in and recorded a sax solo. He came into the recording studio, he did one take, we listened to it, and he said, "Yep, that's good."
[laughter]
0:22:53.2 DN: And I'm sure I'm forgetting someone. Who else came in? Oh, Casey Cangelosi, my friend, colleague, and neighbor, came in. He wrote a whole sort of aleatoric drum thing, percussion thing for the first piece.
0:23:20.3 GR: Nice, nice. I was thinking, you know, one of the ones that I love is... Sometimes, when we're trying to convey an idea to students, like for instance, "If you're having trouble finding a note, don't just blindly leap for it, but use your reference pitches of one and five or Do and So in the scale," you know, that's a big concept to convey to them, and it's hard to make it fun.
[laughter]
0:23:47.3 GR: So, I was just thinking, I love your Third Away song for that idea, because it does... It says so clearly, and in such a fun way, that any note you need is never more than a Third Away from one or five, from Do or So. And, you know, yeah, it makes it joyous to think about it that way. Should we listen to it a little? 
0:24:10.5 DN: Sure.
When you're trying hard to sightread and see a leapto a Fa, La, Ti, Mi, or a Re...Well as long as you can always find So and Do,You're never more than a third away.You can try and sing big intervals that you see,And if you're good at it, well that's okay.But as long as you can always find So and Do,You're never more than a third away.
So if you're leaping to "Mi," you can think "So Mi"And if you're leaping to "La," you can think "So La"And if you're leaping to "Ti," you can think "Do Ti" yeah...as long as you've got So and Do, you'll go far!
So keep working on your intervals big and smallAnd try to practice them every dayBut as long as you can always find So and Do,You're never more than a third away.Yeah, as long as you can always find So and Do, yeah...You're never more than a third away.
0:25:24.0 GR: We really get a sense of your vocal range through these songs from a very low to a very high David.
[laughter]
0:25:30.3 DN: I did sing that high C just 'cause I could.
[laughter]
0:25:31.9 LS: 'Cause you should.
0:25:32.0 GR: What's the low note like on Sophie? Was that a low F? What was that? 
0:25:42.6 DN: I don't know. The Dominant 7th song is a low F. I don't really think about it. Either I can sing it or I can't. I mean, I can probably... Well, if I cheat, I can get close to four octaves now, but that means having to do, [pitched vocal fry] "Ahhhhh," can't get any lower than that today.
0:26:11.3 GR: Okay.
0:26:15.2 DN: But that's a trick. [laughter]
0:26:19.2 LS: And that's a whole 'nother episode.
0:26:22.3 GR: Yeah. Exactly.
0:26:22.4 DN: Right, right. Yeah, yeah, yeah. No... It is funny, I was afraid. When I first started sharing these songs, my biggest fear, and something that almost held me back from sharing them, was I make my living singing Bach. And I thought what if someone hears these and thinks, "Oh, that's not the voice I want." But I decided, and I hope I was right, that someone who hears that I have the flexibility to sing all these different styles will go, "Oh, and he sings Bach well. Okay."
0:27:06.7 GR: Yeah, I have to say, as we've gotten to know each other, I just continue to be blown away by the variety of things that you do and do well, it's...
[laughter]
0:27:22.4 DN: I fear sometimes that I do too many things and don't do any of them well, but I guess that's the life of a musician is having to explore all opportunities. [chuckle]
0:27:40.2 GR: Yeah, there's so much fun wordplay in your songs, have you always been one for puns and wordplay and that sort of thing? 
0:27:49.4 DN: Boy, I haven't thought of that. I do enjoy it. Have I always enjoyed it? I think I've always enjoyed it, but I don't know that... I think it was especially writing educational songs that I felt both the desire and cultivated the ability to engage in wordplay. But thinking about the best educational songs that I knew and grew up with, the best ones were really compelling both musically and lyrically in ways that made me want to hear them again, or that would make them stick in my head, and I think especially the Tom Lehrer-esque wordplay, for me, was something that just went hand in hand with good educational songs.
0:28:49.2 GR: Yeah.
0:28:49.9 LS: And that's so important that holding true to the musical side of things, because there are a lot of creative lyrics out there that are not musical or are just spoken and auto-tuned and they are very hard on the ears even though the information in the lyrics is good.
0:29:13.9 DN: Yeah.
0:29:14.7 LS: Yeah.
0:29:16.3 DN: It looks like I'm gonna be co-presenting for a conference in the fall that is about music and education, but a challenge in educational music is sometimes that it's written by educators or scientists who maybe didn't think about as much about the musical side of things. And there is even a sense in some aspects of that community that it doesn't matter, that it's all about the content and not about the musical side of things, and I think the musical side of things really does matter, and you can... I just would hate to force my students to listen to music that wasn't very good, just to get a point across. Now, that sounds like I have a high flute in opinion of my own music. And I don't love all my own songs, but I do try really hard to make them good.
0:30:25.1 GR: One of the ones I find most musically impressive, frankly, is the Intervals Inversion song that you were able to make all of these inverted intervals work melodically, which can't have been an easy thing to do.
0:30:40.0 DN: You know the irony is that one wrote itself in about 15 minutes, it just...
0:30:45.6 GR: You're kidding. [chuckle]
0:30:46.1 DN: It wasn't a puzzle to be solved. I was actually reading an old theory textbook from, like, 1920 and looking at its explanations of chords and inversions, and I just, sort of, like, that opening line I was just thinking, "Ta-ta-ta-taa. Ta-ta-ta-taah. Oh." And that just makes such a natural thing and the rest just flowed right out of it in 15 minutes. [laughter]
0:31:22.3 GR: We should listen.
A minor third is a major sixth in inversionA major third is a minor sixth in inversionA perfect fourth is a perfect fifth in inversion. Oh.A minor second's a major seventhA major second's a minor seventh, and oh...A perfect unison's an octave in this gameBut what we call a tritone stays the same.
0:32:24.5 GR: I think one of the things I love about that is that totally takes me back to '90s cheesy pop, right? There's something about that that just speaks to the music I loved in my childhood, the music theater, that time period and, yeah.
0:32:43.9 DN: I was listening to that and just remembering, oh yeah, the introduction is all showing different inversions in both hands, and I guess it's not in the left hand, but in the right hand, it's doing inversions deliberately. And I've been asked about the tritone bit because of course, technically a tritone is three whole steps, and so only one of those is a technical tritone. This is though why I said what we call a tritone because in aural skills class when it's out of context, that interval is a tritone.
0:33:24.3 GR: Mm-hmm.
0:33:25.3 DN: At least in my class. Yeah I understand how someone could quibble with that, but I deliberately said what we call a tritone for a reason. [laughter]
0:33:36.5 GR: Yeah.
0:33:37.1 DN: If you wanna listen to... You may not have heard my science song "Erosion", but you'll like that one too. It's got the same era vibe. [laughter]
0:33:47.7 GR: Nice. I'd say the acoustic base on that, I love. When that just comes in, it's so good.
0:33:52.9 DN: Thank you, Sam. Oh my gosh, yeah.
0:33:57.4 GR: Yeah.
0:33:57.8 DN: He's amazing.
[chuckle]
0:34:00.7 GR: David, what's your favorite song? 
0:34:04.0 DN: Oh wow. What is my favorite song? I've been asked this and I... But I like Second Inversions a lot. I like it because it's got a great groove. I feel like it's extremely pedagogically useful, even though some people disagree with me. [chuckle] And I feel like it just works.
[music]Second inversions are chords I adoreI write them down with a 6 and a 4.These chords we encounter in four different ways…You can tell from the context you hear,From the chords that are near,And the movement you hear in the bass.
The first we’ll call pedal (or stationary)‘Cause the bass stays the same.But when bass notes move stepwiseOften passing’s the name.When the bass goes a leaping, arpeggiated’s what we’ll say.And when we come to the end of a section, my friendA cadential 64 can help carry the day….
(IV 64)... well that IV 64 was stationary, oh…(I 64)... a passing I 64! Passing I 64!(vi 64)... ain’t it great when we can arpeggiate!And for the next one I’m just going to savor it‘Cause a cadential 64 is my favorite second inversion….Second inversion…Mmm, Second inversion…
0:36:39.0 GR: And that was the famous "Amen" that you were talking about earlier, yeah? 
[laughter]
0:36:43.2 DN: Yeah. Oh gosh.
0:36:46.3 GR: That's great.
0:36:48.6 DN: I do enjoy this. The criticism that I've gotten for this is that it's not the way some people wanna teach second inversion chords, or they may even say that they don't even believe in second inversion chords. And it's very much the way it was taught in the book that I was using at the time. And of course, people have different names for these things. I've even learned new terminology that I didn't know before through responses to some of these songs.
0:37:20.3 GR: Mm-hmm.
0:37:21.7 DN: In the Dominant 7 song, the deceptive cadence, I got a note from someone in England saying, "Is that what we call an interrupted cadence?" "Oh, apparently it is."
0:37:37.4 GR: See, and now this is gonna take me right back to my Schenkerian training, because an interrupted cadence is... An interruption in Schenkerian terminology is effectively a half cadence, right? 'Cause the phrase is interrupted before it's able to complete its normative motion of three, two, one or five, four, three, two, one.
0:38:00.1 DN: And some people will insist on calling it deceptive motion.
0:38:06.1 GR: Mm-hmm, or deceptive resolution, yeah. Mm-hmm.
0:38:09.0 DN: Right. The funny thing is, when I'm teaching, at least, I just sort of say there's lots of names for things and there are many lenses to view it through and not one of them is correct.
0:38:22.7 GR: And I think probably at the heart of it, it matters less what we call it, and more that we know what it is as a thing.
0:38:30.5 DN: Right, right, or that you recognize... Yeah, yeah, ideally, we would recognize these things happening musically and just sort of know why they work and not in a limited fashion but in a holistic fashion to go, "Oh, this has a lot of aspects to it."
0:38:48.3 GR: Mm-hmm. So the other one that I find just delightful is the Chord Spelling song because Like...
[laughter]
0:38:58.9 GR: Can you tell us about that? 'Cause this one is so clearly to me like this is a pedagogical song, this is a song that I would totally just pull out and use within my classroom. In fact I'm thinking about just transcribing, so that I can do this in singing with my students.
0:39:13.4 DN: It has been transcribed. Mark Boyle has transcribed it, and I will talk to him, but I think maybe we can put up a transcription so that people can use it, he uses it as a warm-up with his choirs.
0:39:29.4 GR: Yeah, can you tell us a bit about the song? 
0:39:31.3 DN: Yeah, I think it was my second year of teaching aural skills and I was heading into school. At that point, I had an hour commute, and I was heading into school, and the topic of the day was going to be spelling all the different chords, and as I was driving into in school, I thought, "I cannot stand the thought of standing in front of a blackboard and spelling out one chord after another, each diatonic chord and singing them, there's gotta be a more interesting way to do this." And I basically wrote the song on my commute, and by the time I got to school, I had the general framework of it written, and I taught it to each of my classes that day, and then we sang it at the end of class and recorded it and put it on YouTube.
[laughter]
0:40:30.5 GR: Nice.
0:40:31.5 DN: So, that was... Yeah that was composed and recorded within a couple of hours.
0:40:39.2 GR: And when we hear that on The Well Trained Ear Album, are those of your students we're hearing singing? 
0:40:46.7 DN: Those are my students although that... And honestly, I think that the recording on YouTube that was recorded within a few hours is probably better than the one on the album.
[laughter]
0:41:02.2 DN: The album was recorded very much on a budget, and that particular song suffered because I recorded it without people singing along, I played the piano part and I played it way too fast, and so it's a little bit too fast on the album for my taste.
0:41:23.2 GR: Well shall we listen to the YouTube version? 
0:41:25.9 DN: Sure. Yeah, let's listen to the YouTube version. I mean, what's cool about the YouTube version anyway, it's just that students really... I taught it to them. That was the end of class.
Do Mi SoFa La DoSo Ti Re Ti So Do Do DoDo Mi SoFa La DoSo Ti Re Ti So DoLa ... La Do MiRe ... Re Fa LaLa ... La Do MiMi Si TiSo Ti Re
Do Mi SoFa La DoSo Ti Re Ti So Do Do DoDo Mi SoFa La DoSo Ti Re Ti So DoDo ... Do Mi SoMi ... Mi So TiLa ... La Do MiRe ... Re Fi La
So DoSo So Re TiSo So DoSo So Fa Re TiSo So DoSo So Fa Re Ti Si MiLa Do MiDo Mi So TeFa La DoSo Ti Re Ti SoDo Ti Do Ti Do Ti Do Ti Do Ti Do!
[laughter]
0:42:45.6 GR: I love it, I love it.
0:42:51.7 DN: And that has more of that cycling, spiraling idea of, but introducing concepts ahead of time. Because at that time you just need to know, here's what I have to sing here, but then later I'm... I could say, well remember when we sang, do re mi so ti, but that's, that's a five, seven, zero, four. And then when they hear that sound they can connect it with the place in the song where they've heard it. And, I mean for me, that seems like a... I just thought why hasn't anyone done this before? , and a little bit the answer is that, people had done it before and I just didn't know. [laughter] And so it's been really cool like to meet Joseph Downing, who has written a bunch of music theory songs, but they're not on YouTube. I probably should... He's sent me the sheet music for his songs, so I should probably record some of them and put them on YouTube. [laughter] But hearing things in context, that's the other tricky thing about aural skills, is that you can't understand any of these things out of context. It's all about hearing them in context. And then, how do you get someone to recognize it in context? So, that's q place, where I think that the songs are useful, because it's just naming things as they happen.
0:44:27.1 GR: Yeah.
0:44:29.0 DN: And to a degree naming things... I was surprised to share my International Chord song with some people and to point out things that were being explicitly named in the, in the song and to discover that some of my colleagues didn't, didn't even recognize what was happening. Didn't recognize, what that those things were being named as they happened, or didn't recognize all the subtleties, I don't know. You know, when I, when I do, sometimes I... Like, sometimes I want to hear some German, sometimes, you know, sometimes I like to hear some French, and then I on the French, you know, I... French is the note that distinguishes him from German.
[laughter]
0:45:27.0 GR: Yeah. Yeah, exactly. That's reality too.
0:45:29.6 DN: But understanding those chords and how they work, It's just helpful to hear them in context.
0:45:37.8 LS: And surely that will help students make the connection to their rap.
0:45:41.9 GR: And also to hear that I think in more popular styles were so often we're teaching these concepts with reference to Western classical music, which frankly, maybe our students aren't listening to that much.
0:45:52.9 DN: You know, I forgot until just now that, you know, I showed you my second inversion song, but that the predecessor to that [chuckle] was the first year I taught, I wrote a chorale. I wrote a chorale that did all four of the second inversions that we were supposed... That I was supposed to teach. And I gave it to them as a dictation. And I wrote little words, you know, about second inversions are chords I adore. I write them down with a six and a four. [laughter] But I didn't... Yeah, the chorale wasn't quite as catchy as the gospel-ly song.
0:46:39.2 GR: The bluesy. Gospel. Yeah.
0:46:40.5 DN: Yeah. [laughter]
0:46:41.1 GR: But this has been really fun to where if people want to hear more of your songs, where can they find them? Where can they find you? 
0:46:49.1 DN: They're scattered all over YouTube. And, of course, I have the album on Bandcamp The Well-Trained Ear. If you google The Well-Trained Ear, you will find it. And, of course, I would be deliriously happy if anyone wanted to buy the album on Bandcamp, but you can also listen to it for free. [chuckle]
0:47:14.3 GR: Awesome. So, yeah, hopefully our listeners will support the creation of these wonderful music theory teaching songs. And, yeah, I certainly... I have the album in my iTunes and...
[laughter]
0:47:27.0 GR: Yeah, yeah, I hope. Hope others will as well. It's always a little funny when like I'll have it on shuffle at a party and then suddenly, you know, up pops David Newman singing the Silly Solfege Song.
0:47:39.9 DN: That could be particularly shocking if it turned out to be The Locrian Song.
[laughter]
0:47:45.9 DN: In what on an any normal album would be shockingly inappropriate. I love that, it goes straight from a poly meter heavy metal song to a swinging jazz tune.
[laughter]
0:48:09.9 LS: And let's not forget about TikTok.
[laughter]
0:48:13.5 LS: One of my favorite little things is David Newman singing his office number for his students to remember, now I have it memorized as well.
0:48:23.1 DN: That's fantastic. Yeah, no, it's great. And you know, I did write it for my students. Although, actually, I wrote it for me, because I got moved into a new office and then COVID hit. And then I wasn't in that office, and I knew where to find it, but I couldn't remember my own office number, so I thought I need to share this, and then of course, when I realized I was in office 213, re do mi. So that is not on the album. I guess I could add it, add it to the album. Yeah, I put it on TikTok. I have a couple of things on TikTok that are not on the album. So yeah, follow me on TikTok. And if people start following me on TikTok, maybe I'll start making more content for it. [chuckle]
0:49:18.1 GR: Well, I wonder should we close out by hearing The Locrian tune, what an unsettling way to end.
[laughter]
0:49:25.1 DN: I'm not sure. That might be something people have to seek out for themselves.
[chuckle]
0:49:30.0 GR: Alright, that's fair, that's fair. You know, our listeners may not know or may not realize it, of course, you wrote the theme song for Notes, Notes From The Staff. So that's...
0:49:41.0 DN: You know, I wanted to talk about that.
0:49:42.4 GR: David's voice in here.
0:49:43.1 DN: Do we have time to talk about that? 
0:49:44.5 GR: Yeah. Sure.
0:49:46.2 DN: As we close up? I mean, obviously. I started with a surprise.
[laughter]
0:49:55.8 GR: In the form of the Surprise Symphony? 
0:49:58.7 DN: And I figured that everyone upon hearing, you know, tun tun tun tun tun tun tun they know what to expect. And then I don't give them what they expect. And the way I think about writing these, I am really inspired also by Bach. And, when I thought about writing this I had already seen the the logo with a treble clef and notes on the staff. So I decided that I was going to make the melody do all of the notes on the staff, on the treble clef staff. So that is the opening line is, these are the Notes From The Staff da da. So I did every single note that is on the staff.
[laughter]
0:50:48.5 DN: You know, I think sometimes maybe it doesn't add anything, but I think sometimes, I think, what we learn as creative people, is that a blank page is scary, and so it's great to give yourself limitations like that, and out of that, springs creativity.
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0:51:13.9 LS: Notes From The Staff is produced by uTheory.com.
0:51:16.0 GR: UTheory is the most advanced online learning platform for music theory.
0:51:30.9 LS: With video lessons, individualized practice, and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm and ear training.
0:51:37.0 GR: Create your own free teacher account at uTheory.com/teach.
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