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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