00:05:35 Mutation -- linking hexachords together to melodies beyond a range of a hexachord
00:06:30 Singing a scale with hexachordal solmisation
00:08:15 Relationship between mutation and points of imitation in Rennaisance music
00:10:00 Solmisation in Renaissance musical pedagogy, and the connection to improvisation
00:11:05 The Gamut
00:12:00 Renaissance names of notes, like "C sol fa ut"
00:15:40 The relationship of letter names and hexachordal solfege, and the question of octave equivalence
00:16:30 The Guidonian Hand
00:18:53 The "Do a Deer" of the Renaissance
00:20:40 The interconnectedness of the history of solfege and of staff notation
00:21:30 How do we get the other accidentals, besides B-flat, that aren't in the gamut?
00:24:50 What is musica ficta?
00:28:25 How does thinking in hexachordal solmisation change how you hear Renaissance music?
00:30:15 Puns and jokes in hexachordal solmisation
00:35:30 The intersection of movable and fixed solfege in hexachordal solmisation
00:37:00 Teaching and learning hexachordal solmisation
00:41:50 If we want to learn the basics of hexachordal solmisation, where should we start?
00:42:45 How is the field of music theory adapting to the changing world of music, and a desire to broaden the music that students are able to understand and analyze?
00:46:45 Oberlin's reframing of the music theory curriculum: Rhythm, timbre, melody, harmony and bass.
00:51:15 How might we refocus the music theory teaching we're doing at the high school level?
00:53:17 Do we have to sacrifice part writing for this?
00:55:53 Transforming the first-year theory curriculum from being a weed-out course, to become an entry point and gateway into learning music.
00:57:30 Wrapping up -- plus several conferences to be aware of
0:00:03.9 Theme Song: These 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're hope you're learning something new, 'cause the path to mastering theory begins with you.
0:00:21.1 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.
0:00:35.3 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and Associate Professor of Conducting at the Oberlin Conservatory of Music.
0:00:42.2 DN: And I'm David Newman, I teach at James Madison University and I write code and create content for uTheory. We have two topics for today, hexachordal solmization and recent trends in music theory pedagogy and with us to talk about both is Dr. Megan Kaes Long.
0:01:00.1 GR: Dr. Long is Associate Professor of Music Theory at the Oberlin Conservatory of Music and a scholar of vocal music in the 16th and 17th centuries. She's the recipient of the 2021 Wallace Berry Award from the Society for Music Theory, the top award for music theory book for her work Hearing Homophony: Tonal Expectations at the Turn of the 17th Century. Her writing has appeared in the Journal of Music Theory and Music Theory Spectrum among others, and she's the editor of SMTV, the Society for Music Theory's video journal, we've put a link in the show notes. She's received numerous grants and fellowships including awards from the National Endowment for the Humanities and the American Council of Learned Societies. Megan, thanks so much for joining us.
0:01:42.3 ML: Thanks so much for having me. It's a delight to be here.
0:01:45.9 GR: I'm really excited for both of our topics today, hexachordal solmization is something I've heard a lot about over the years but not really done, we thought it'd be fun to chat about because it's this solfège pedagogy system that has a really rich history, but that is I think not something I know. David, have you done much hexachordal solmization?
0:02:07.9 DN: I've done almost none, but I have been super interested in historical pedagogical styles and part a mentee, and when I read about the book The Solfeggio Tradition, I ordered a copy and I started to read it, and so, I've found it incredibly interesting.
0:02:26.1 ML: Yeah, one of the things I really love about hexachordal solmization is that it sounds really scary, the word sounds really scary, hexachordal solmization, and when you read about it, it sounds impossible, how would you possibly do it? But it's actually pretty simple to learn and to put together, and it was invented to teach little children how to sing, just the same reasons that we use solfège today. And it's just as accessible and just as logical and approachable as any of the other kinds of solfège systems that we already use and we already teach, and especially if like me, you're immersed in music of the Middle Ages and the Renaissance, it is so illuminating and it really... The way they say, when you learn a new language, you start to think in a different way, I feel very much that way about singing Renaissance music using hexachordal solmization, I just hear the music differently, I make different musical connections. I feel like I have a much better understanding of how the composers and the musicians that they were writing for understood what they were doing, and that I find extremely exciting, it's like unlocking a door into the world of the Renaissance, which can be a hard place to access.
0:03:38.2 GR: So, what is hexachordal solmization? I think the only time I heard the word hexachordal, in my music theory training...
0:03:43.9 GR: Was poly-hexachordal combinatoriality, literally like...
0:03:46.8 DN: Oh, my gosh.
0:03:47.0 GR: Crazy 20th century set theory work. We're not talking about 6-Z7 hexachords, are we? What is this?
0:03:55.2 ML: Absolutely not, it is the opposite of that in every way. So hexachordal solmization is the original kind of solfège and it dates from the Middle Ages, and it was used all the way through the Renaissance, and a hexachord just means a six-note collection, hexa, six, six notes. And so the pattern of the hexachord is ut, re, mi, fa, so, la. So just like our modern do-re-mi-fa-so-la, except we use ut instead of do, and the idea in the Middle Ages was that the notes that were available to sing, the scale, the gamut, you could make that six-note pattern in three different places, so you could make it on F, using a B-flat, ut, re, mi, fa, so, la and you could make it on C with no B, ut, re, mi, fa, so, la. And then you could make it on G, I'm not in the right key, ut, re, mi, fa, so, la with a B natural. And so you have this one pattern and it can only be replicated at three places in the gamut, and those three places are important and distinct because the middle of our hexachord is our half step between mi and fa. And so the hexachord is always helping us orient to where the half step is. And so just like modern solmization helps us figure out where our half steps are, just exactly the same principle is supporting hexachords, just a little more flexible than modern solmization because the way the scale is constructed in the Renaissance is a little bit different and a little more flexible than the modern scale.
0:05:35.2 ML: The other thing that's important to understand about hexachords is that obviously most melodies have more than six notes in them.
0:05:41.7 ML: Right? So the way it works is that you do what's called mutation, you mutate from one hexachord to another hexachord when you're extending beyond the range of your single hexachord, and it's by linking these hexachords together that you can fill out and sing a whole tune.
0:06:03.2 GR: So if we wanted to just sing what we think of now as a major scale, how could we do that since we don't have ti?
0:06:11.3 ML: Yeah, I think... Actually, I think the minor scales are a better way of demonstrating what's interesting about hexachords. Do you have a D? Could I get a D for the here?
0:06:19.3 DN: Yup.
0:06:20.2 ML: Okay, so say we wanted to sing a D Dorian scale, so all the white notes on the piano starting on D, so D, we're gonna start in the C hexachord. So D is gonna be re in the C hexachord, so I'm singing, re, mi, fa, so, la. And when we get to la, we're out of notes, so we need to mutate and since we're headed to B natural, we need the G hexachord 'cause that's the one with B natural in it. So we'll sing re, mi, fa, so, re, mi, fa, so.
0:06:52.5 ML: And that takes us right up our scale, notice that the low "Di-Re" and the high "Di-So" are actually different syllables, so we don't necessarily have octave equivalents in the syllables that we use, but the mutation from the C-hexachord to the G-hexachord makes sure that our half-step is in the right place. Now, say we wanted to sing a D-Aeolian scale, so we're gonna use a B-flat instead of a B-natural, then we need to mutate to the F-hexachord, instead of the G-hexachord, and that's gonna put our half-step in a different place, so we would sing... What would we sing? "Re-Mi-Fa-Re-Mi-Fa-So-La... Re-Mi-Fa-Re-Mi-Fa-So-La... " so we mutate just a teeny, tiny, bit earlier from the C-hexachord into the F-hexachord, and then that ensures that our half-step is between A and B flat, and we get our D Aeolian scale instead of our D Dorian scale. And this is useful because tunes built on D in the Renaissance will use both B natural and B flat, so once you get up to G A, you can kind of go either direction, depending on what your tune is doing.
0:08:02.3 DN: I noticed in both of those, that the text, as it were, of the scale kind of repeated itself. You started, when you mutated, it began with Re-Mi-Fa-So each time. Is that significant in terms of like... We think everyone starts music off having these points of imitation at different pitch levels, is that significant in the solfege system, that you sort of hear where those possible places of repetition are when you solfege?
0:08:29.8 ML: Absolutely. And this is one of the most fun things about singing Renaissance music on solmization. It doesn't work every time, but often when you have a motive and then it's imitated at the fourth or the fifth above or below, the motive will have the same solmization in every hexachord. So we might sing "Re-La-So-Fa-Mi-Re" and then another voice will sing "Re-La-So-Fa-Mi-Re" [laughter] so then you can hear these connections and then eventually, often, another voice will come in at a new pitch level and we'll introduce a new accidental. Then we get, "Re-La-So-Fa-Mi-Re" so the motivation for the introduction of, say, a B flat or something will come from the solmization, and this desire to maintain the solmization, and Renaissance music theorists even had a special name for imitation where the solmization stayed exactly the same. They called imitation that was diatonic, so where the half-steps might move around, they called that imitazione, and then imitation where the half-steps were exact and the solmization was exactly the same, they called fuga, the precursor to our word fuga. Yeah, and they're very insistent about this, and the treatises is like "No, no, no, no, no."
0:09:50.2 ML: "People said that This was fuga, but the syllables change, and fuga the syllables have to stay the same." So there's this real emphasis on how you're solmising, how you're singing the syllables, what their names are, that shapes what kind of imitation is happening.
0:10:06.4 GR: And obviously this was meant to teach singers, but I gather that it's also meant to teach other kinds of musicians, so that musicians were taught through singing. Is that fair to say?
0:10:18.9 ML: Absolutely, and it's important to remember that before anyone does any composing in the Renaissance, what they're doing is improvising. And so little children are taught to improvise pretty complex polyphonic music, and when a composer is notating music, is writing music out, what they're really doing is writing out a complex improvisation, and so having these patterns that repeat themselves in predictable ways is a really helpful strategy for successfully improvising and then successfully composing complex polyphony because you don't have to memorize as many combinations when you know that those combinations can be transposed by fifth without changing anything about the way your counterpoint is structured.
0:11:01.4 DN: If I'm tracking this right, you have access to B flat and B natural in this system, but what about all of my other black notes?
0:11:12.2 ML: This is a great question, and it's a way in which the background scale of Renaissance music is pretty different from the background scale of contemporary music. Renaissance music is built on what's called the gamut, and if you've heard like, "Oh, we're gonna run the gamut," that comes from solmization. And gamut is a kind of portmanteau of gamma-ut. Gamma being the lowest note of the scale, and ut being the solmization syllable for that note. So the Renaissance gamut, it's the set of notes that are considered diatonic in the Renaissance, so more like a major scale or something than all of the keys on the piano, and it starts from the G at the bottom of the bass clef staff, and it goes up to the E at the top of the treble clef staff, and you hear theorists will say something like, "Well, the reason that's the end of the gamut is because anything below that will sound like a low grumbling, and anything above that will sound like a kind of constrained shrieking." So our gamut is constrained in range and register, and the gamut includes what we think of as all the white notes on the piano and also B flat.
0:12:21.0 ML: So like in the example of the Dorian versus C Aeolian scale, B natural and B flat are both available pretty much all of the time. And if you've seen the complicated names for notes like "A-La-Mi-Re" or "C-Sol-Fa-Ut," what those names are, that's how Renaissance musicians named the notes, they're just the letter name for the note, and then all the possible solmization syllables that that note could have.
0:12:54.5 GR: So, I wish... I'm sorry... [laughter]
0:12:54.9 ML: Greg is making a face like he's in awe right now. [laughter]
0:12:56.1 DN: I'm just thinking of there's that Shakespeare, fa me Bianca. There's these places where you hear this in Shakespeare, and I just thought it was a bunch of notes, but it's like one note?
0:13:06.8 ML: Yes, if we find that passage, I'd be happy to parse it for you, to construe it for you, which is the language he uses. Yeah, so if you wanna dig that up, that might be fun to look at.
0:13:15.8 DN: I think it's maybe "Be me Bianca," what is the line from?
0:13:20.5 ML: She's also conjugating Latin verbs or something.
0:13:23.2 GR: There was also a composer who used the pseudonym Alamire, remember that correctly.
0:13:28.8 ML: Yes, and so Alamire is like A-la-mi-re, so the note A is la in the C hexachord, mi in the F hexachord and re in the G hexachord and this composer Alamire famously would sign his name by just drawing a base clef and the note A.
0:13:47.5 ML: Because if you saw that, you would say A-la-mi-re, that was the name of the note.
0:13:51.6 GR: Awesome, so that was not a pseudonym? It was a real name or was it a pseudonym?
0:13:55.6 ML: I think that was his real name, I don't know for sure, but that's just the sort of... There's a lot of puns that are possible using solmization, and that's... It's I think really indicative of the way musicians in the Middle Ages and the Renaissance thought. Just like we see the note E-flat and we say that's an E-flat, and sometimes students will say, "That's an E," and we're like, "No, no, no, no, the name of the note is E-flat, and that's important." The note A was A-la-mi-re, there was no just A in the Renaissance, it was important that you used all of that note name and all of the syllables and that was one of the ways you learned to navigate through the gamut as a choir boy. Maybe I should kind of restate what I said before about the gamut and talk a little bit about the Guidonian Hand.
0:14:43.9 DN: Oh, yeah.
0:14:44.5 GR: Sure.
0:14:45.5 ML: 'Cause I know Greg's now hunting for Bianca talking about...
0:14:48.6 DN: Yeah, yeah, yeah, yeah. Be my Bianca right, is the... I found it's Act 3, Scene 1 of Shrew but...
0:14:58.6 ML: Oh, here we go. Gamut, I am the ground of all accord, A re, to plead Hortensio's passion. B mi, Bianca, take him for thy Lord. C fa ut, that loves with all affection. D sol re, One clef, two notes have I. E la mi, Show pity or I die. Call you this gamut? Tut, I like it not. Old fashions please me best; I am not so nice to change true rules for old inventions. So what she is doing is learning the gamut the same way a child would learn it, which is you say Gam-ut, A-re, B-mi, C-fa-ut, D-sol-re, E-la-mi. And so she's just learning the first six notes of the gamut and just simply saying their full names in that passage.
0:15:44.9 DN: Wow, so letter names also were a thing.
0:15:49.7 ML: Yes, absolutely, and one of the interesting things that comes up a lot in terms of hexachordal solmization, is there such a thing as octave equivalence in this system. Since you remember when I sang my scales from D to D, D at the bottom was re and D at the top was sol or la, depending on which scale I was in, but they are both D-la-sol-re. So there is that octave equivalence built into the way the notes are named in the gamut, even while they might be solmised in different ways depending on what octaves you're singing in, or sometimes if you're singing in an ensemble, you'll be singing octave Ds say, and we'll be singing different syllables on the same note but somebody will be singing an A that harmonises with it, and that will be the same syllable as something that we're hearing in another voice.
0:16:38.6 GR: So, was this the first version of solfeggian western music?
0:16:41.9 ML: Yeah, so it was and it's the predecessor obviously to our modern solfège. Ut has changed into do, and we have ti now, which is really useful, but it was invented for the same reasons that we use modern solmization. So we don't exactly know the origins of the solmization system, but it's been attributed to Guido of Arezzo who was a monk, and he was active in the early 11th century, he died in the year 1033, and he had... One of his responsibilities as a monk was teaching chant to choir boys, and if you're a monk in the Middle Ages, you sing chant all day and you sing the entire Liber Usualis every year, so you sing thousands and thousands and thousands of chants, and you learn them all by ear and you remember them all because you're in a culture that's steeped in memory. And Guido got frustrated with how time-consuming it was to teach all of this repertory to choir boys and so he came up with this system to make it more efficient to teach them new chant.
0:17:51.6 ML: And so the idea was I will teach these children this pattern ut-re-mi-fa-sol-la, and then I will point to those different notes and then they'll be able to sing those notes back to me, and the way he pointed to them was he drew all of the notes or he would imagine all of the notes in a spiral on the palm of your hand. So you've probably seen these diagrams where you see a hand and a million little letters and note names and things and clefs and all sorts of things written on hand, and the idea was that you would hold up your hand for the choir boys and you would point to whichever joint represented the specific note they were supposed to sing, and then they would sing that note back to you. And the way Guido taught them how the relationships between the notes were, where the half steps and whole steps were, was the same way we teach children now, which is he used a song like doe a deer, a female deer.
0:18:51.0 ML: His song was a chant that he composed called Ut queant laxis but it was the same idea, Ut queant laxīs, Resonāre fibrīs, Mīra gestōrum, so exactly the same idea, ut, re, mi, fa, so, la, each line was one of the notes. And so he used that as a reference and then was able to extrapolate outwards from that with his students to teach them chants, and it's very similar to using solfège hand signs today like we often do in the classroom. It's not a...
0:19:26.1 DN: And... Oop, go ahead.
0:19:26.9 ML: Oh yeah, go ahead, sorry, Greg.
0:19:27.9 DN: As you said, so Ut queant if I remember, 'cause when I took Renaissance Counterpoint in grad school, assignment number one was to memorise Ut queant and to sing it back.
0:19:38.4 DN: And if I recall, it doesn't ever leave those first six notes, that first hexachord, is that right? There are no mutations in it?
0:19:45.7 ML: That's right, and this is how you teach solmization to children, and this is how I teach solmization to my college students too, is you start with tunes that live in one hexachord and you get comfortable, and then you add a single mutation. So you add tunes that start in your main hexachord and then just occasionally mutate upwards by one hexachord. And then you add B-flats and B naturals to introduce a little more complication. And then maybe you add something that will also mutate down below, so you kind of gradually add complexity and add mutations as you go, until each mutation becomes kind of second nature. 'cause you can't... When you're singing on hexachords, it's not like you have access to every possible syllable, every possible moment. There're fixed locations where you might mutate from one hexachord to another, and so it's all about kind of practicing and getting familiar with those exact locations. One more thing I wanted to say about the Guidonian hand and Ut queant laxis is that, it's not a coincidence that the history of staff notation coincides pretty much exactly with the history of solmization.
0:20:55.5 ML: 'cause what's happening in the 11th century is a shift from an entirely oral tradition, where music notation is just a mnemonic device to help remind you, "Wait, which chant was this?" So you've probably seen neumes, unheightened neumes and heightened neumes, which are just kind of squiggles that tell you the contour of your chant. This is the period when, all of a sudden, we have the invention of the five-line staff or the four-line staff and the clef, and these more precise ways for notating the exact locations of half and whole steps. So we have to, if we're gonna have a notation that's exact like that, we also have to have a system for understanding how to read that notation, and hexachordal solmization goes hand-in-hand with staff notation for that reason.
0:21:44.2 DN: I am fascinated by this, I have to say. I'm getting a little caught up on this, but I'm wondering about the... Still, how do I get to the other black notes?
0:21:51.7 ML: Oh, I'm sorry, I forgot to answer your question. So there's this idea that like, "Oh well, Renaissance music, it's in the modes, it's very pure, it just doesn't use accidentals." And that's not true at all. And "Oh, the Gamut, it only has B-flat in it, so what about C-sharp? Surely there are C-sharps." So sharps and flats are different in this period. So sharps are kind of ornamental and you use them to make your cadences lovely. So say, I'm cadencing on D, I might sing, re, ut, re, and I'm gonna be singing a C-sharp there. So the rule, which is not entirely agreed upon by all Renaissance music theorists, but is more or less shared by a critical mass of them, is that when you're singing a sharp, because that's a kind of decorative ornamental thing, you don't change your solmization.
0:22:48.7 ML: So, so, fa, so, no problem, you just kinda sharp your fa, you don't say anything different. Flats though will always change your solmization. So a flat will always be fa, no matter what. So if we're hanging out in a world where we have no B-flats and all of a sudden we have a B-flat, we're gonna call that fa, and that will constitute a mutation into the F hexachord. And if we get an E-flat, same idea, we're gonna imagine what we call a fictive hexachord on B-flat. So imagine that ut is B-flat, and then that E-flat is going to be fa in our B-flat hexachord, so just basically transposing our F hexachord down by a fifth and transposing our whole Gamut down by a fifth to make that happen.
0:23:39.4 DN: Very cool. And that's where people may have heard, was it fa supra la and is that where you just put a B-flat on top of an A briefly?
0:23:51.6 ML: Yeah, more or less. So there's this principle, Una nota supra la. Semper est canenda fa, which is bad Latin for, "If you've only got one note above a la, you're gonna call it fa." And so the idea is if you're singing ut, re, mi, fa, so, la, fa, la, so, la, fa, la, so, fa, mi, you don't have to mutate all the way into your next hexachord, you're just gonna go ahead and sing that one as a fa. And that rule mostly exists to avoid a tritone from fa up to mi, 'cause what we don't want is, fa, so, la, mi, la, so, fa, so, fa, so, la, fa, la, so, fa, kind of helps us prevent that indecorum. It doesn't work every time, and it's not a hard and fast rule, but it's a good rule of thumb, it's a kind of shortcut for a mutation that accommodates really common melodic patterns in Renaissance music.
0:24:49.2 DN: And that starts to get into something that we hadn't even talked about, which is this idea of Musica ficta, in other words, we might be looking at a piece of Renaissance music and there might not be an accidental written, but we might have to sing one?
0:25:00.9 ML: Yes. And the tune Greensleeves is a really good example of this. If we see notated versions, it looks like re, fa, so, la, mi, la, so, mi, ut, something like that. And a lot of people will flatten that B at the top, re, fa, so, la, fa, la, so, mi, ut, that's using the fa supra la principle as a way of approaching that. It's not actually obvious that one or the other of those solutions is the right one or the best one, and it may be that that's a tune that could be sung both ways, because yeah, these Musica ficta accidentals, they're are non-notated accidentals that performers would have known to sing, that composers would have implied, but there's a gap between what composers might have implied and what performers might have chosen to do in practice.
0:25:57.6 GR: And there are some required ones too, like at cadences, like you were saying.
0:26:02.2 ML: Yes. Musica ficta is a whole other situation. It gets into a lot of really messy things that I don't think that your listeners are gonna wanna hear all about in excruciating detail. We tested Musica ficta in my class this week, and I think the students left with a lot more questions than they came in with, because the basic takeaway was, all of your answers are probably right and they're also probably all wrong, and we kinda lived in that space.
0:26:35.4 DN: I also feel like as a choral conductor, as a singer, every rehearsal I've been in where musica ficta ever comes up, we all leave with more questions than answers, like, "What note should I sing in measure 23?"
0:26:46.0 ML: The interesting thing about musica ficta from the perspective of modern performance is we're so used to a score giving us all the information that we need. And in the Renaissance, that wasn't necessarily the case, and it's not because this notation was deficient in some way, it's really like a feature not a bug of the notation that there's stuff left up to the performers and stuff that's left unnotated, and it's hard for us to reconstruct that now because it's been hundreds of years and a lot of that tradition has been lost. But this idea that there's only one right set of notes to sing is a very modern idea. And in the Renaissance, there are stories about people getting into fights about musica ficta in rehearsals, like, "Oh, I think this should be flat, and I don't think this should be flat," and the composer's in the room and nobody asks the composer, that's just not relevant, because there's flexibility. The same way that we wouldn't expect somebody to write out today all the rubato that you would take in a performance. That would be so unmusical to put quarter note equals 60, quarter note equals 58, quarter note equals 54, quarter note equals 62. That kind of...
0:28:00.3 GR: Although I've seen some scores like that. [chuckle]
0:28:02.2 ML: Well, and we've all sung Carmina Burana, where every note has an accent and a tenuto and a staccato mark. So I think, in the Renaissance, it's just like, why would you notate all of that stuff? Why are you trying to control something that should be up to the performer?
0:28:20.4 GR: Very cool.
0:28:22.8 DN: So you mentioned early on, you said that singing this way affects how you hear and understand this music. Could you talk a bit more about that?
0:28:32.1 ML: Oh, that's such a big question. There's almost nothing about Renaissance music that I don't experience differently now that I think more in terms of hexachordal solmization. I think for me, the biggest revelation is that B-flat and B natural are both equal partners in the Renaissance style. There's not one of them is default and the other one is a deviation from the norm, but rather that they're both opportunities that are available to a composer over the course of, say, a motet, and that composer may or may not choose to take advantage of that B-flat that's just right there waiting for him. But it's there if he wants it, and that's a really different way of thinking about what it means to be diatonic than we're used to where we're like, "There's diatonic notes, and then there's chromatic notes."
0:29:29.5 ML: So there's a kind of flexibility that goes all the way back to how I sang those two D-scales. Where once we get to Ray-Mi-Fa-So-La, we have a choice to make, we can go either way. That is everywhere once you start looking for it in Renaissance music. The other thing that I've really notice is imitation; noticing where imitative patterns are repeated with the same solmization syllables at different pitch levels. And when I sing with my students, if you're the second voice to enter and you've already heard your line and it's already been beautifully solmized for you, just 'cause you're entering a fifth above you just copy paste what just happened.
0:30:11.1 ML: So that's a really great opportunity that solmization provides. Renaissance musicians also embedded all kinds of puns and jokes involving solmization into their music all the time, and those are really fun to uncover and really revealing about how people were thinking about solmization all the time, even if they were singing music on words or were just singing "la la la la la." Would you like to hear some more about some of those sorts of things?
0:30:41.6 DN: Absolutely. Please. [chuckle]
0:30:42.9 GR: Are you able to tell these jokes, explain these jokes, in a way that doesn't ruin them for us? [laughter]
0:30:48.5 ML: Absolutely. Absolutely. So there's two kinds of solmization tricks that I really like. The first one is what's called the soggetto cavato, which is the idea of a subject that's carved from the words. And so a famous example is the text Lascia fare mi, which means leave me alone, but if you notice, La-scia-Fa-Re-Mi sounds like the solmization syllables, La-So-Fa-Re-Mi. So, the composer sets it, "Lascia fare mi," and every time it comes back at every pitch level, you can solmize it so that the syllables of the... The solmization syllables match up with the sounds of the words, and there are lots and lots and lots of examples of tunes like this, where the composer took somebody's name, or took their own name or anything like that and turned it into a tune, a kind of precursor to Bach's BACH motif. Same idea.
0:31:51.0 GR: That's the kicker, I don't know anybody who likes solfege puns. [chuckle] I've never heard any solfege puns in my life. [laughter]
0:31:58.0 ML: I'm looking at two of those people. They're everywhere. And sometimes you'll find them just in the middle of a motet or something, all of a sudden, it's just for the Altos and as an alto I'm like, "Alright, this is just for me," [laughter] "Nobody's going to appreciate this but me, but I'm loving it at this moment." The other technique that composers use is a technique called inganni which means deceptions, and the idea of inganni is you take a melody that's solmised in one way, and then you mutate somewhere unexpected and you keep your solmization syllables the same, but you change the melodic contour of the tune. And so it's a deception because you think you're looking at two totally different melodies, but actually the solmization is the same for both of those melodies, which is a neat trick. If you give me a second, I can find an example. Just pulling my copy of Zarlino's Art of Counterpoint off the shelf.
0:33:06.9 DN: As one does.
0:33:06.9 ML: I'm serious, I literally pulled my copy of Zarlino's Art of Counterpoint off the shelf. Okay, so here are Zarlino's examples of this concept that's called Inganni, so deceptions. He gives us a tune, ut, re, mi, fa, la, so, fa, mi, re. And then he gives us the same tune, but different, ut, re, mi, fa, la, so, fa, mi, re. And then he gives it a different way, ut, re, mi, fa, la, so, fa, mi, re.
0:33:48.6 GR: Gotcha.
0:33:49.7 ML: And so there's a mutation between the first four notes, ut, re, mi, fa, and then the last four notes, last what? Five notes, la, so, fa, mi, re. And he changes what that mutation looks like each time, and so that gives us three different versions of the same tune, that if you're looking at a score, you might not notice, you might not find a relationship between them, but if you're singing in solmization, you can't miss them. And there's lots of really great ways to use this trick. It's really common in the ricercar, which is an instrumental type of composition where you showcase like your most learned counterpoint. And there's this question of, okay, well, ricercar means to... Ricercare means to seek out or to search for something.
0:34:38.7 ML: And one theory of what's being searched for, when you're playing, usually on the organ, when you're playing a ricercar, is what you're searching for is the subject, and what the composer is doing is finding as many ways to hide or bury that subject in the counterpoint as possible, and you, as the performer, have to figure out, using these inganni, these deceptions, where is the subject? Where is it now? What's happened to it? And these get extremely complicated, to the point that some early 17th century musicians, like Trabaci, make these really complicated chromatic ones, and they just label them, they're like, "Inganno, inganno, inganno, inganno." 'cause otherwise people can't find them because the tune is so disguised that they're like, "Wait, but I did something really clever, let me show you."
0:35:29.8 DN: Oh, that's great, that's great. I keep thinking with this that, there's an interesting intersection between movable solfège and fixed solfège, and this kinda seems to live somewhere in between the two of them.
0:35:41.8 ML: Absolutely. That's kind of... I grew up on movable do solfège, and now I teach fixed do solfège, which was a challenge, and now I mostly think in terms of hexachordal solfège. So keeping three systems in mind is a real challenge all the time, but one of the things I find interesting is that hexachordal solfège is both a movable solfège and a fixed solfège at the same time. And in some ways, you get a little bit of the best of both worlds when you're using the system, because you get this kind of sense of, here are the actual notes I'm singing, here's where I'm actually living in musical space, relative to the notes I'm reading on the page, but also, here are where the half steps are, here are musical relationships that are being replicated throughout this piece, and I can feel that they're the same, even though they're happening in different places in the scale. One of the reason this works is because there's not that many keys in the Renaissance. So you can't do hexachordal solmization on something in A-flat major or B major or keys with a lot of accidentals, because this is not a system that's designed to accommodate that, but when you live in a world where there's only two key signatures, there's what we call cantus durus, which is no key signature, the hard B, and cantus mollis, soft B, where there's a B-flat signature, it's a lot easier to navigate that whole musical system using this kind of fixed, movable hexachord system.
0:37:18.0 GR: So pedagogically, when you're teaching hexachordal solfège, does that help with fixed do or movable do, or does it hinder? Do people have trouble moving back and forth?
0:37:30.0 ML: That's a great question. So I only teach hexachordal solmization to my juniors and seniors who are taking my Renaissance class. I would not foist it on my freshmen, who are learning fixed do for the first time, but I do like...
0:37:47.3 DN: And they're also learning scale degrees, right?
0:37:48.8 ML: Yeah, and a lot of them came in with movable do, so we do a lot of group therapy in Aural Skills One here.
0:37:57.2 ML: So I reserve hexachordal solmization for my seniors, where I tell them, "You thought you didn't like fixed do, just wait." But I think it really helps you to understand the Renaissance in a new way and helps get you in this mindset that this music is just different in some important ways from music today. And they pick it up pretty fast. And all of a sudden, we're in class, and was like, "Well, isn't that a fa supra la? And isn't this a re tonality and how will that be impacted by the sol cadence here?" And it's really exciting to hear them using this vocabulary that's native to music, and you just can't understand this music without having some of those tools. It's a lot harder to find, for instance, exact imitations versus diatonic imitations, if you don't have access to solmization. It's almost impossible to learn how to do Musica ficta, if you don't have access to the tools of hexachordal solmization. So navigating Renaissance music, specifically, is really useful. When I teach hexachordal solmization, I like to use these duos written by Orlando di Lasso, in this collection from... It's called Novae aliquot something, something, something, something, has this long name, from 1577, and he has 12 texted duos and then 12 untexted duos. And this is a tool I learned from Anne Smith, who is a musicologist and historical performance practice person in the UK.
0:39:33.7 ML: But what she found was that the second set of these duos, the untexted Lasso duos, are they clearly designed to teach you one new solmization challenge per duo, and they're really smartly designed, they're kind of really well-designed rhythms in the Hall Rhythm Book. Which is that they start out in slow notes, with not a lot of mutations, and then each one gets a little faster and then introduces more mutations and then introduces some syncopations and they get harder and harder and harder as they go. And then each duo is designed to work a specific mutation point. So I like to start with those in my class and the students kind of build up their solmization skills as they go. It's a great pedagogical tool, and you can imagine these Renaissance musicians teaching music to choir voice in just exactly the same way.
0:40:29.1 DN: This raises so many interesting thoughts for me, but I think back to episode one, where we were talking about different solfege systems, and even Do-minor versus La-minor, and how, depending on the music that you work with, one may be more suitable than the other. It's so interesting to hear this carried over to hexachordal solfège, and here's a system perfectly matched to this kind of music, and also this balance of thinking in fixed versus movable space, that keeping track of where you are on the staff and also where you are in your scale or hexachord. It's such cool stuff.
0:41:08.6 GR: And at the risk of... I don't wanna prematurely move us on, except that what I think is cool talking about the hexachordal system and how that was developed, and then looking at these... Hearing about these Lasso pieces is that these are people, active musicians, thinking about how to teach about pedagogy. "How am I gonna teach music?" And this was something we wanted to talk about. [laughter] Am I premature in moving us onward?
0:41:43.2 DN: No, no, I think that's good. I feel like... I guess the only other question I would ask, Megan, is if someone wanted to learn, obviously, you have really been spending a lot of time in hexachordal solmization with your own study. If someone wanted to learn the basics of this where should they go?
0:42:00.7 ML: I would recommend two resources that are a great place to start. The first is, there's a YouTube series called Early Music Sources, done by Elam Rotem, that is terrific. And he has a great video on hexachordal solmization that is a great place to start. The other place I would look is Ann Smith who has a book called The Performance of 16th Century Music, and there's a chapter in there that teaches how to mutate between hexachords, and she's written out the solmization for a bunch of tunes and explained the thinking behind it and shows original sources and justifies all of that, and so that's a great place to learn these basic techniques. So those are two places I would start.
0:42:46.8 DN: Those are great, we'll put both of those in the show notes. And the other thing I wanted to chat about, is music theory has been changing a lot in recent years, and I think maybe more than even other fields in academia as we sort of confront the biases, and biases in the way that we've been teaching these things, you've been really involved with a lot of work on that, at Oberlin in particular, and I wonder if you might just talk with us a bit about that. You're so plugged into the broader music theory community, how is the world of music theory evolving?
0:43:24.5 ML: This is something music theorists are thinking really hard about, because the way we teach music theory hasn't changed very much since the 19th century. But the things that we're training musicians to do has changed quite a lot since the 19th century. At a music conservatory like Oberlin, obviously we're training a lot of our students to go play in major orchestras or sing in major operas, in opera companies, but a lot of our students are not doing that. A lot of our students are playing a lot of new music, are doing a lot of innovative work with technology, are thinking about outreach and bringing music to the broader public. And we're seeing a lot more musical hybridization, we're seeing a lot more cultural appreciation in what we think of as the realm of classical music performance.
0:44:15.5 ML: One of the things that we're grappling with as a discipline of pedagogues and a discipline of scholars is how do we prepare all of these musicians for their lives as musicians? One way that we've framed it here at Oberlin is that in the traditional conservatory music theory curriculum, we are really great at teaching our students to say extremely interesting things about music by Beethoven and Brahms, and that's great, that's a really worthwhile thing to do. But it's a little disheartening when you have a junior come to your office with a piece by Ravel and say, "I don't have anything to say about this," that's a real failure of our pedagogy, and Ravel is not out there particularly.
0:45:01.4 ML: Ravel is pretty mainstream canonical composer. So then what do you do when you have a student come in and they wanna talk about hip-hop? Or they wanna talk about music videos? Or they wanna talk about something that Roomful of Teeth is doing? Or they wanna talk about any number of new things happening in the musical world? So different... We're working collectively as a community of music theorists to think about how to approach this problem, and our solutions are emerging and are widely varied. Ranging from... On the one hand, just re-discovering the work of a lot of composers who are Black, composers who are women, composers from South America and Latin America, composers who have been excluded from the canon. I'm hesitant to use the word rediscovery because scholars of color have known about these composers, and have been writing about these composers and teaching about these composers for a long time, but White scholars especially and White pedagogues have not been aware of this music.
0:46:10.7 ML: When we add more of this music into our curriculum, it changes the questions we think to ask and that changes the tools that we need to develop to answer those questions, so that's kind of one way that we're working on revamping the music theory curriculum. Another way is just really thinking much more broadly about what does it mean to think about, talk about and write about music when music isn't just western concert music mostly written between the years 1785 and 1914, what if we wanna build tools to talk about a lot more music, so what we've tried to do at Oberlin is reframe our curriculum in terms of musical parameters that are not specific to any one kind of repertory.
0:47:00.1 ML: So our new freshman curriculum is about teaching about rhythm and meter, and that includes all sorts of things from timelines and the idea of groove, and it creates opportunities for us to talk about really complex metrical structures in 20th century art music but also African drumming and that sort of thing. We're talking about timbre, sound production, the different ways that acoustics work and how timbre might be used as a kind of analytical tool. We're talking about melody, so not just... It used to be that we would teach species counterpoint, we would teach out of the Fux book, which is ostensibly teaching the Palestrina style, we'd say, "Well, Palestrina would write melodies that have no leaps larger than a fourth, and when you leap up by a fourth, you must descend, and that's how you write a good melody." Well, so now in my class, we start with film scores, we start with Princess Leia's theme from the Star Wars soundtrack and come up with why is this a good melody? What are its characteristics? What kinds of tools might we use to analyse the melody and you don't have to use music in this kind of western concert tradition to do that, what are the values of melody in a pop music context? What are the melodic values in the context of the gamelan? We're talking about harmony and different kinds of ways of combining different melodies at the same time.
0:48:38.6 ML: That is where we spend most of our time pretty steeped in western music, but there's lots of other ways to think about and talk about harmony. And we're talking about bass, which is not something that I had ever really thought all that much about but becomes very interesting when you start to think about what are all of the different ways that bass and bass lines work and how is that specific to different repertories, different cultures? I really enjoyed spending some time with my students listening to Herbie Hancock's Chameleon and thinking about the bass riff at the opening of that and how it establishes groove and... So we're trying to think about ways to frame the central questions of the curriculum that aren't necessarily specific to a single repertory.
0:49:26.5 GR: I love that.
0:49:27.8 DN: It sounds like... How are the students responding to it?
0:49:31.1 ML: They love it. I've never had my students be more engaged and more excited. And what my hope is for my class is that every student is gonna see some kind of music that is important to them, and every student is gonna see some kind of music that is totally unfamiliar to them, and I want all of those experiences to be valued, I want my students who come in reading only guitar tablature to feel like their musicianship and musicality is meaningful and relevant. I want students who have only really looked at lead sheets before to feel that that's a kind of music notation that is valuable and that that is as important for classical students to learn as it is for jazz students to learn how to read piano staves. I want students whose primary experience is working with Dos to have something to contribute to the class that nobody else has been able to contribute before. I want students whose background is in traditions that aren't the western tradition, to hear music that they grew up with or music that they like to perform, to hear that represented in the classroom, so we have a long way to go.
0:50:41.2 ML: Obviously, we all have a lot to learn to be able to teach musics that we're not trained in in a way that's ethical and in a way that is accurate and respectful, but it's been a really amazing experience to just start to sit down and learn about some new repertories, and to meet brilliant people around the world who are working on this music and learn from them, and to figure out how we can bring that experience into the classroom.
0:51:12.5 DN: So if I'm working say with high school students to help prepare for this broader approach to music theory, what kinds of things should we be stressing at that level, do you think?
0:51:27.3 ML: I think it's really important to teach students how to ask interesting questions, and to learn that a piece of music or a repertory will tell you what sorts of questions to ask of it if you don't come in with too many preconceived ideas about it. So one way I like to start my theory classes is to play some top 40 song that has a lot of cool production techniques involved in it, and to say if we were to build a music theory just to describe this piece of music, what sorts of things would we need to talk about here? And students hear so much, they're steeped in this music, they hear so much that I don't hear, and they're talking to me about filter sweeps and reverb and like oh, it sounds like she's underwater and like oh, it sounds like she's far away, and all of a sudden we're developing all of these schemas, all these categories, we're talking about what's happening, oh, the size of the space she's in, it feels like it's changing, how does that go with the text?
0:52:31.4 ML: And oh, we're hearing a lot of audible breath, and why is that important? And that's stuff that doesn't come up on the AP Music Theory test, but is very much a part of being a professional musician, a working musician today and having interesting things to say about music, it's training your ears to listen for what's there and build around to that. I think the more we can empower our students to identify what's interesting about something and find their own way of talking about it, the better prepared they're gonna be to embrace a new repertory, a new style that they're unfamiliar with and be game to see how it works and to get to know it.
0:53:14.0 DN: That's very cool. That's very cool. The sort of devil's advocate question, but what about part writing? Can they still part write?
0:53:21.6 ML: We're still teaching chords, we still do a lot of that. And if you actually look at what's being taught in music theory classrooms around the country, as much as we're making space for new repertoires, we're still spending a lot of time on Mozart and Beethoven. These people aren't going away. I feel for my class, if I'm gonna teach Mozart arias, I love teaching Mozart arias, I should pick two instead of nine. So I'm trying to think about how can I focus on the most important of these or the ones that I feel like I get the most pedagogical benefit from, and what opportunities come from making room for other things? If I teach a Coleridge Taylor song instead of a Mozart aria on Thursday, what opportunities are gonna be there and what sorts of questions are my students gonna raise? And I've found that to be really rewarding. Another question to play devil's advocate right back.
0:54:28.5 ML: Is what has part writing done for you lately, Greg?
0:54:31.3 GR: Yeah, that's fair.
0:54:34.8 ML: I don't know that resolving the seventh of a seventh chord down every time is that hard of a thing to learn, but I also don't know that it's that useful of a thing in the real world. I think that we have expanded our part writing curriculum to fill the four semesters that we're given, and it is really useful to a small number of students in some very specific contexts. And so what we're trying to do here is find ways to reach those students in those contexts and give them the tools they need to be successful without making a bunch of students who are never gonna use part writing in their lives and who aren't gonna get that much out of it, spend four semesters on that in lieu of learning about any number of other things that they are gonna encounter every single day.
0:55:22.0 DN: Yeah and you know I have talked about this a lot, and that I had that very classical, I can analyse Mozart through Brahms beautifully kind of music theory training, but part writing didn't click for me until I had figure-based training and was actually having to do real-time part writing improvization at the keyboard, and suddenly I thought, oh, doing this all on paper maybe didn't make the most sense for me originally, even so. So I'm with you on that despite my devil's advocate question.
0:55:52.7 ML: One way I think about this problem is traditionally the freshman theory curriculum at the college level is a weed-out course. These are courses that are really hard and that you have to have really strong fundamentals, and you have to just do a lot of part writing, and a lot of students get through that kind of by counting, by writing in note names and by doing the algorithm and doing the math. I'd rather see the freshman curriculum being an opportunity, being an open door, being an entry point, a gateway into studying music, and then giving the students the opportunity to drill down on those really very specialized skills a little later on.
0:56:31.1 ML: So one of the things we're doing here is offering a portmanteau class for sophomores. And so that's where students who are interested to learn really detailed nuances of 18th century style, they learn to improvise in the 18th century style, they learn to compose in the 18th century style. In a way that's really much more robust than what we do in a traditional part writing curriculum. And jazz students probably won't take that class, and probably a lot of voice majors won't take that class either unless they want to, but organ majors probably will take that class, and will get the very specific skills that they need and that will support the repertoires that they're gonna be performing for the rest of their careers. In a way that's actually a lot more interesting and a lot more historically accurate than the way we teach part writing in the traditional music theory curriculum.
0:57:20.4 DN: Yeah, I think it's really lovely and I am jealous of these students getting this broad approach to music theory, and I just can't wait to see what that means for our next generation of young musicians.
0:57:38.9 ML: We can't wait either, and we're all learning and growing together and we're... I'm sure we're gonna make some mistakes and hopefully be supportive of each other as we all find our way through this new landscape because the thing that's clear is that we can't do nothing, we can't just keep doing things the way they've always been done. And so you have to start somewhere.
0:58:00.8 DN: Awesome. Well, I think that's probably a good place to wrap things up, I don't know, do you think, Megan, David, anything we missed we should talk about?
0:58:09.3 GR: I can just say thank you so much for visiting us and talking with us about this stuff, and actually both of these things and actually if I dare with all this pedagogy stuff, there are some conferences coming up that are going to talk about these issues that are focused on these issues, and one of them I can't go to, but I am definitely going to be at the music theory pedagogy conference in Michigan in early June. I don't know if anyone is planning to be there.
0:58:41.9 ML: I will be this June at a conference at Case Western Reserve University about analysing music by Black composers. Really exciting conference that's hopefully gonna be really inspiring for helping music theorists think more about a much wider swath of repertory and how we can ethically bring that repertory to our students.
0:59:04.6 GR: Yeah, and that one's June 16th, am I right about that?
0:59:09.0 ML: That sounds right.
0:59:09.8 GR: I think that's why I can't go. [laughter]
0:59:12.8 ML: Yeah, June 16 through 18. Theorising African-American music.
0:59:18.9 DN: Meghan, thanks so much for joining us for talking about these two huge topics, I feel like I've learned just an enormous amount in this short time from you, and I'm looking forward to diving into these topics a little more.
0:59:31.1 ML: Absolutely. I am always happy to talk hexachordal solmization, it's my very favorite thing.
0:59:36.8 GR: Thank you so much. Excellent.
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