Episode Overview

In this in-depth episode of the Piano Pedagogy Podcast, hosts Jacqueline Beckoff and Arianne Lakra tackle the nuanced topic of rhythm and polyrhythms in music education.
From the foundational concepts of counting techniques to the sophisticated challenges of teaching polyrhythms, the discussion is both deep and wide-ranging, offering valuable perspectives for music educators and students alike.

Throughout the episode, Jacqueline and Arianne share personal experiences and teaching strategies, highlighting the challenges and rewards of mastering rhythmical complexities. Join them as they explore effective teaching methods, the importance of a tailored approach to individual student needs, and the transformative power of overcoming musical challenges. 

Watch it on Spotify, YouTube, or your favorite podcasting app.

Episode Notes

Foundational Rhythm and Counting Techniques

• The Role of Counting in Music Education: Jacqueline introduces the topic by sharing her strict approach to counting, which does not allow for mixing detailed (subdivided) and beat counting (big beat). This method aims to strengthen students' understanding of rhythm and prevent reliance on subdividing, which can alter the intended feel of music. 
• Arianne's Perspective on Syncopation and Basic Rhythms: Arianne contrasts by discussing the teaching of syncopation and simpler rhythms, emphasizing the need for students to recognize weak and strong beats intuitively.

Advanced Rhythmic Concepts: Teaching Polyrhythms

• Challenges and Strategies: The hosts discuss the difficulties of teaching polyrhythms, a topic that both find challenging yet essential for advanced musical training. They explore various teaching methods, including using visual aids, kinesthetic activities, and auditory examples to help students grasp complex rhythmic patterns. 
• Practical Applications in Lessons: Jacqueline recounts her methods for introducing polyrhythms through familiar pieces like the Chopin E minor prelude, and Arianne suggests using the "Carol of the Bells" to illustrate 3 against 2 polyrhythms. 

Philosophical Approaches to Musical Rhythms

• Memory and Learning: Both hosts discuss the deeper implications of how students memorize and internalize rhythms, reflecting on their own experiences as students and teachers.
• Adapting Teaching to Student Needs: They emphasize the importance of adapting teaching methods to fit individual student needs, recognizing that each student may require different approaches to fully understand and apply rhythmic concepts.

Episode Recap

This episode of the Piano Pedagogy Podcast is a treasure trove of insights for music teachers, providing both foundational knowledge and advanced strategies for teaching rhythm. Jacqueline and Arianne's thoughtful dialogue offers listeners a chance to reflect on their own teaching methods and the potential to deepen their students' musical understanding through the effective teaching of rhythm and counting.

Join Jacqueline and Arianne next week for more enriching discussions and expert insights into the world of music teaching. If you have your own experiences or thoughts on the mnemonic debate or other teaching strategies, feel free to share them on the Defined Music Teacher Facebook page.

Show Transcript Jacqueline: Hi and welcome back to another episode of the Piano Pedagogy Podcast. My name is Jacqueline Beckoff, and with me, as always, is Arianne Lakra. We both own successful music studios in Southern California, and I also own Defined Music Teacher. How are things for you this week, Arianne?

Arianne: Hey! Things are good. How are you?

Jacqueline: I'm doing okay. I just enjoyed a week off after my studio recital, and I celebrated my birthday. I also successfully completed my graduate audition, and I have been invited to join the program at California State University at Fullerton.

Arianne: Yay! Oh, my gosh! Are you planning for the year ahead?

Jacqueline: I'm planning to start in the fall semester, which is 4-5 months away.

Arianne: So you have some time.

Jacqueline: Yes, time to enjoy life as a free woman before I'm in the bondage of music school.

Arianne: It's going to be an adjustment with your schedule and everything, but I think it's going to be totally worth it.

Jacqueline: I'm excited for it. It's going to be a crucible. Nothing like music school to shape an artist and just develop like crazy in a relatively short amount of time. I learned more in three years of my undergrad than I did in the preceding 17 years of piano lessons.

Arianne: Wow.

Jacqueline: Yeah. I applied to the school I was waiting for the audition to see if I was going to actually apply to the school itself, but I did go ahead and actually apply. So it's official. We'll see, but our topic this week, for those of you who heard us last time, I had a particularly spicy opinion about counting. We're going to talk about rhythm and counting and all of that nitty-gritty details. For those of you who haven't listened to the previous episode, my spicy opinion is that I don't allow my students to subdivide eighth notes, and the more in-depth is that my students learn two forms of counting: detailed counting, which is subdividing every beat, and beat counting, which has no subdivision of any kind, and I don't allow students to mix the two. They would either have to count "one and two and three and four and" or "one, two, three, four."

Arianne: And what are the reasons for this approach for you?

Jacqueline: Rhythm in general was one of my weakest points coming into my undergrad and just throughout my piano lessons as a child and a young adult. Rhythm has always been my weakest point, and I strive for the things that were weaknesses for me as a student to be strengths for my students. I have a big focus on memorization because memorization was terrifying to me as a child, and I felt like I was just awful at it. The reason behind my approach has to do with the fact that when a student becomes over-reliant on subdivision, they are essentially changing the time signature of their piece. If a student is in 4/4 and there are eighth notes, and they are just having the hardest time with their eighth notes, oftentimes the whole note will go twice as fast. Does that happen to you?

Arianne: Okay, well, let me counter with this. In cases except cases of syncopation, which you know, if the student is just learning eighth notes, I'm not sure why they would already be on syncopation. So let's just assume there's no syncopation. Wouldn't it just suffice to teach a student who's doing "one and two and three and four" that "and" is generally seen as a weaker beat than the number?

Jacqueline: Yeah, the numbers, of course, are the stronger beats. But I feel like if a student is so lost that they have defaulted back to subdividing everything, and I recall when I was a kid, I would have a bunch of eighth notes leading into a long note, and then I would just subdivide that long note to make sure that I didn't rush the long note. The solution that my teacher gave me was to keep track of your eighth notes because you have to. You already know how the eighth notes feel. So let's just extend that to the whole note, but the flip side of that is the problem isn't in the home note. The problem is that you lose the big beats, you lose the big beat in the eighth notes that you stop feeling in your body. They don't know where the strong beats are. If they knew where the strong beats are, they wouldn't be losing the beats for the whole note.

Arianne: Okay. So between the two things you outlined, which are either saying "one and two and three and four" all the time or just going with the numbers but still clapping out the correct rhythm in both cases, do you have a preference?

Jacqueline: Detailed counting, subdividing, and beat counting with no subdivision. The preference and the counting that my students overwhelmingly use is beat counting. Most of my students do not need to subdivide the beat to understand their eighth note rhythms. They can sight-read music that has eighth notes in it without having to use "ands," and without losing the big beats on whole notes. So my preference is overwhelmingly for beat counting. I just started preparing a student for eighth notes yesterday, actually, and I taught her about beat counting because she was a transfer student returning to music as an adult after not playing for about 40 years. She's aware of eighth notes and vaguely knows the concept of "ands." I explained that "ands" are a practice tool to help us understand our rhythms, not a long-term solution. If you're struggling to understand a rhythm, we can pull out detailed counting. We can tap it, we can clap it, and then, before you go back to whatever you were doing before you started using that detailed counting, get that section back to beat counting before you move on. Don't leave a section on detailed counting, because that's just going to breed a lack of big beat awareness. It's a process rather than results-focused, because subdividing gets you to the right answer—they're going to hold the whole note for the right number of beats—but the way they get there doesn't really resolve the problem.

Arianne: Got it. Okay. Well, when it comes to more complex rhythms, what would you do if you're teaching a 2 against 3 polyrhythm?

Jacqueline: Polyrhythms are not something I have a great deal of experience teaching; I've only taught polyrhythms a handful of times. They tend to feel very mechanical when someone is relying on that kind of method to understand where to put the notes. Polyrhythms are at their best when it feels like you have two different people playing—one person's playing a triplet, and one person's playing an eighth note, and they are completely independent of one another. That's when a polyrhythm really feels good when the student isn't focused on where to place this triplet compared to this eighth note, but just feeling it fluently. Would you agree with that?

Arianne: Yeah, I mean, okay, I'm going to go off on a small tangent here, but it's totally related, I promise. Do you know about the Yanni and Laurel thing? There was this viral sound clip where depending on the listener, you could hear either Yanni or Laurel.

Jacqueline: Yeah.

Arianne: That's how it feels when it comes to learning about polyrhythms for me. Sometimes it really helps to hear the streamlined version as if it were one voice hitting all of those precise marks that both the eighth notes and the triplets hit at once. And then from there, it helps me to separate them out mentally or physically with two different hands.

Jacqueline: So you're saying that you can focus on the triplet and hear the triplet or focus on the eighth note and hear the eighth note?

Arianne: No, what I'm trying to say is that I can focus on the rhythm as if it were all the same instrument doing it, and then from there, mentally, I can separate it out. But in my experience with students, it doesn't always work that way. So I usually resort to some kind of partner activity, where they tap eighth notes with a metronome, and then I come in with triplets. Once they get that in their ear, and they hear the two different voices, then I'll allow them to take over my part after some time and see if they can replicate the sounds that both of us were making independently just on their own.

Jacqueline: Do they come back the next week with it correct, in your experience? The first week after you introduce a polyrhythm to a student, do they bring it back correctly?

Arianne: Sometimes it really just depends on the student. But it's not easy teaching polyrhythms a lot of the time, and it's not easy learning them, either. So, I guess if they understand the theory behind it and they get the approach, and you lay it out visually, and maybe if they've done fractions in math class, that makes it a lot easier.

Jacqueline: You could split it up into like, for 3 against 2, you could split it up into 12 parts, and then chart it on graph paper. And instead of counting, you count "1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6." Have you done that?

Arianne: No, actually, I haven't. Can you say more about that?

Jacqueline: So you would split like 3 against 2. It has to be 12. So you'd have an eighth note on one and seven, and then one for triplets at 1, 4, and 9. Then you would be able to understand. But that approach, do you understand what I'm saying?

Arianne: Yeah. Totally.

Jacqueline: That approach is so micro; it is difficult for me to speed that up to the point where you're fitting everything. You're subdividing a beat into 12 parts to understand everything, and obviously, that's not sustainable. You have to get back to beat counting and understand how all five notes for 3 versus 2 fit together into one beat. I suppose that approach aligns with how I approach eighth notes and triplets by themselves, understanding on a focused scale how the rhythm fits together and then bringing it back to just understanding the beats. But polyrhythms are something I have not had great success with, partly because I've only had one student reach the point where we're doing polyrhythms. I have another student gearing up to try a polyrhythm for the first time because she brought in some music for band. Her band teacher doesn't play the piano, so sometimes he gives her this stuff without realizing the difficulty of what he's just given her, including 5 against 4 and 3 against 2 and 3 against 4, and we've never done any polyrhythms together. So, the Chopin E minor prelude, are you familiar with it? It has 3 against 2 just once in the whole piece, and it took weeks for her to bring it back perfect. I will not sugarcoat that I feel like this is one of my weakest areas, not only as a performer with polyrhythms. If I went over to the piano, I wouldn't be able to do a 3 against 4 or a 5 against 4 on my first try. Are you fluent in polyrhythms? Would you be able to pull out a 3 versus 4 scale?

Arianne: I've tried it, and 3 against 4 is tough. But I was thinking about a memory trick involving the words "I am a piano god."

Jacqueline: I am a piano guy.

Arianne: Yes, "I am a piano god." It's like "I am a pian, no God." Piano is a triplet, "I am."

Jacqueline: That just sounds like coordinates to me.

Arianne: Think of the two-syllable pronunciation of piano. Listen to my fingers snapping.

Jacqueline: Zoom is filtering that out for us.

Arianne: Let me try to visually do it. Whenever I join my fingers, that's the other voice doing the beat. "I am a pian, no God!"

Jacqueline: Polyrhythms are relatively rare, so we struggle even as college-educated performers to reach the generalization stage with polyrhythms, where we can just see them and be fluent in them. I wonder what it would take for us to teach our students to be completely comfortable with polyrhythms.

Arianne: I find that whenever there's a difficult rhythm situation, I like to lean heavily on all three modes of learning: tactile, kinesthetic, visual, and auditory, to make sure that I have hit all three, so it's totally foolproof. Whatever category someone fits into when it comes to learning their rhythms, they're more or less covered. I always like to draw rectangles on a piece of paper that are sectioned off accordingly for visual cues. I allow them to go on YouTube and play as many recordings as they need to, of the repertoire they're learning. Then I always do tapping exercises on the closed keyboard lid with both hands, kind of what I described before in the form of a partner exercise, just guided learning about the theoretical side of it, and then putting it into practice. I find that if I just model the repertoire enough in the section that contains the polyrhythm, usually kids catch on. I also have a very auditory-based curriculum in general.

Jacqueline: It's definitely good. I focus primarily on the auditory aspect and getting my students to tap it, but visually understanding, perhaps subdividing it into 12 parts, or another visual activity would be beneficial for the student, perhaps learning it outside of their repertoire with a scale. For example, if you do a five-finger scale in the left hand and a full octave scale in the right hand, they'll end up back on tonic if one hand does triplets and one does eighth notes. It might need to be a two-octave scale versus a five-finger scale, but we're back to 3 against 2 in this scenario.

Arianne: Yes, you're right.

Jacqueline: Yeah, so that's...

Arianne: Reach the octave that the next C higher. Let's say you're doing a C scale in your right hand. Then you'll be on the G in your left hand.

Jacqueline: Also, you can do a 3 octave scale in your right hand with triplets and a 2 octave scale in your left hand with eighth notes, and that should also line up because it's 3 octaves versus 2 octaves. It should end up back on tonic. I would be really interested to learn how other people teach polyrhythms because I've only ever done it once. I've only ever had one student advanced enough to that point. She's an adult student. But I have some younger students in the wings where I feel like they're going to be at polyrhythms in the near future. And I've only really taught it the way I was taught it, which is modeling it, tapping it. The rhythmic sayings, like "not very hard" or "not difficult," and then one of the other ones that I do is have them shadow play—playing one hand so softly that it doesn't make a sound—shadow play one hand and then play the other hand so that you can hear that triplet while still getting the experience of in your other hand playing the opposing rhythm.

Jacqueline: I feel like when I have more opportunities to teach it, I will be better at it. But I wonder if polyrhythms are perhaps one of the most difficult things to teach for us as pianists. It's also exclusive to pianists and other keyboard instruments. Would that be an accurate statement?

Arianne: Oh, yeah, I think it's right up there for me. Personally, in my experience, it's right up there with teaching staff notation and note identification on the staff in terms of difficulty. And I find that with a lot of students, at first they either get it or they don't. It clicks for some of them immediately, and others we have to work a little bit harder on it, or just pivot to something else entirely. I've definitely given up a couple of times trying to teach polyrhythms to my more intermediate students and just changed the repertoire entirely.

Jacqueline: Avoid the polyrhythm.

Arianne: Yeah. And I'm not proud of that, because I believe everyone can learn it somehow. But I find, one of the easiest approaches, at least going back to 3 against 2, there's the "not difficult" right? And if they're not getting that, which is kind of more verbal-linguistic, I just have them tap both hands at once on the keyboard lid. I'm having a hard time getting my phone into position for this. But like this... So both one, one, one, you know. Both right, left, right.

Jacqueline: So breaking it down into two parts.

Arianne: Yes, because everyone can do right, left, right, assuming they're kindergarteners enough, and everyone can do both at once. So it's just a matter of putting them together. So that's usually my last resort, is just breaking it down. And I find that even not just with rhythm, but with other things too, the kinesthetic approach seems to be the catch-all approach to teaching any difficult concept. If the other two have failed, it's like my last resort, Hail Mary, but also so effective with all these concepts, not even just rhythm.

Jacqueline: I've spoken about how much I believe in preparation stage learning. I used to struggle with my students learning eighth notes, because that was back before I did the preparation stage learning. I would just turn the page, do a brief explanation, demonstrate it, then I asked them to do it, and they'd bring it back in a week, and it'd be awful. But now I have a multi-week preparation lesson plan that I do, and by the time they get to them in their book, they are fluent, and they don't struggle with it. They're not even aware that it's something that students often struggle with. I wonder if there is a way to devise a preparation stage lesson plan for polyrhythms. There's got to be. How do we break down the polyrhythm into preparation stages? The first thing you're supposed to do with preparation stage is that they're supposed to hear it, then they need to do it, and then they see it. Hearing it is easy; you can demonstrate it. Doing would be as simple as them clapping back the same thing that you just did. You could take it a step further and separate it out into the two hands with tapping it before finally showing it to them. I don't want to say exclude, but I almost put polyrhythms in its own category, like, 'Well, this is just too hard.' But I don't think that's true.

Arianne: Yeah, they're definitely different than your average rhythms. We can teach syncopation easily because it's easy to explain the theory behind it—you place more emphasis on the weak beats. It's also easy to teach different time signatures and rhythms made up of discrete note values. The thing with polyrhythms is that occasionally we have playing that's not necessarily stronger, but it occurs on an "and," and we have to calculate that to a certain extent, which makes teaching polyrhythms somewhat layered. As far as application goes, it's easier for a student to apply a polyrhythm using muscle memory than necessarily evaluate a polyrhythm. So in the stages of learning, the Bloom's taxonomy, I am kind of satisfied if my students who want to do a relatively complex piece for a recital are still kind of in the bottom half of that learning pyramid, as long as they know how to reproduce the sound on the keyboard for the purposes of performing. That's fine for me. If they don't know how to explain it mathematically or come up with a new polyrhythm on their own based on what they know about polyrhythms, like can they extrapolate 3 against 4 using their knowledge of 3 against 2 by doubling one hand, I'm not asking them to do that, and so I think that makes it a little bit easier. But what do you think?

Jacqueline: I agree, polyrhythms are so esoteric and advanced that they require a level of independence between the hands that is just technical ability. You as a student might be able to tap or clap it, but having a student play it on the piano is another matter entirely. Because it's so far into piano lessons that they're even broached, there's a big lack of experience with them which makes me nervous to even attempt to go over it with a student. And I tell my students that when there's something that's hard and that we don't understand, we don't run from it, we run towards it; we have to figure it out and understand it. I wonder if I could try to get over my anxiety about teaching polyrhythms if I try to introduce it at an earlier stage, so that I can become more experienced with teaching it, but I think it might be of limited usefulness if they're not going to see it expressed in their repertoire.

Arianne: It surfaces in late intermediate and early advanced repertoire, to my knowledge. And it works out for students who reach that point in their piano journey, which is ideally most of our students. It's useful and fascinating to me personally, which is why I like to share it, though not all my students have that same view, and I understand. But using scales, and I just want to correct myself, if you do a left-hand 5-finger scale and a right-hand octave scale, it's not going to line up perfectly. Actually, when you hit G in your left hand, you'd hit B in your right. So it doesn't really line up perfectly. I think that if you practice polyrhythms right off the bat using scales, it's going to be a nightmare. So I like to just pick one key per hand to repetitively flunk on.

Jacqueline: That's basically a step up from tapping it.

Arianne: It's basically tapping.

Jacqueline: An interesting thought experiment, like eighth notes are taught in method books, and they have cued activities attached to them, and triplets are taught in method books, and they have theory pages that go along with them. What would a theory page targeted at an 11-year-old explaining a polyrhythm look like? What activities would be attached to a theory book explaining a polyrhythm to an 11-year-old instead of an older child?

Arianne: Well, if we look at Faber, this kind of goes back to your counting. Faber likes to do that mixed approach to counting where, if it's a quarter beat like a quarter note, they'll just put the number. But then, if we're in eighth note mode, they'll put the number in.

Jacqueline: My hand.

Arianne: I would just say, pick a color for one voice and a color for another voice. So let's go red and blue, because they're easily distinguishable, unless you're color blind, I don't know. They would probably line up the numbers 1, 2, and 3 in that sort of space proportional way that they do where they give an entire beat a little extra room on the page, and then 2 and get fit in that same amount of space, and then they have 3, 1, 2, and 3, and they put that in red. Then the other one is in blue, 1, 2, and 3 just below it. So they're right on top of each other, stacked. What you could do is circle when each hand plays so the both ones would be circled in a big oval. You know, in the first part, and then for the red one that's counting triplets above, you'd circle the number 2. Then you'd circle the number 3.

Jacqueline: Are you familiar with the Kodály method? Tata Tadita, that rhythmic method.

Arianne: Yeah.

Jacqueline: I wonder if an approach like that would be useful. Teach three different syllables, one for the unison of both hands, and then one for right hand and one for left hand.

Arianne: Yeah, I think the Kodály method, it would just be "ta, ti-ti." And so, yeah, you could circle whatever was relevant in each row. And you could use the notes even if you wanted to. You could use note values instead of numbers, just whatever works. And then they could read it out. I think that could be a decent activity where you don't have to really address fractions. Anyway, 11-year-olds know about fractions as it is. That's one way to do it. Another one could be coloring in a sectioned-off rectangle or drawing the dividing lines in the proper place, to cut one rectangle perfectly in half and another into perfect thirds. These are just some ideas.

Jacqueline: That's interesting. No, I think all of these activities would be useful for students of all ages. This is all about them manipulating the information that they know. If I present a rectangle and then ask them to roughly or precisely give them a graph, or whatever, to draw lines indicating when each note goes where, I think that would force even my adult student that I'm working through the C-sharp minor nocturne with, and I chose that because it would force us both to address her threes versus twos, as well as 3 against 4, and all of the craziness at the end. But I think having her manipulate the knowledge of polyrhythms in that way, I don't know if she could, and that's a failing on my part.

Arianne: Well, okay, that's basically a foundational exercise. Once you get to the level where you're effectively playing Chopin nocturnes and things like that, I think it's important that our listeners know that as piano teachers, we have an obligation to let our students know that after a certain point, the composers are not necessarily wanting you to be a stickler about technically being right on the dot.

Jacqueline: Right.

Arianne: So you can use a little bit of rubato when it comes to polyrhythms in Chopin and other composers, especially the ones from the eighteenth through the twenty-first century.

Jacqueline: Sorry, go ahead.

Arianne: What's the earliest point where polyrhythms make an appearance in keyboard literature?

Jacqueline: I've never come across polyrhythms in Baroque music. Maybe late classical, certainly romantic. When I was talking about fluency with polyrhythms, it is towards that advanced literature where they're really just looking for something that sounds like a triplet in the right hand and a pair of eighth notes in the left hand. There's wiggle room there. It needs to be rubato, not robotic. It needs to have freedom to it.

Arianne: Fantastic.

Jacqueline: Roboto, not robotic. When you know that a student has really got it, it stops being difficult and instead feels like there are triplets in the right hand and eighth notes in the left hand, with the voicing really nice, so that the melody is coming through. It's not sounding like you have two voices; you have left hand harmony, right hand melody, and then polyrhythm, one mono voice, and then you go back to having two voices. Do you know what I mean?

Arianne: At that point, I don't know if I would want to put the cart before the horse. I wouldn't want to teach someone a complex piece of repertoire that requires more analytic backstory and background knowledge about the nature of polyrhythm performance before the student knows how to do a perfect polyrhythm on the keyboard that is precise.

Jacqueline: I need to, with my student, in addition to the Chopin, perhaps do one of those scale exercises. They've experienced polyrhythms and gotten them correct, but they don't have the muscle memory behind it. I think doing a simple scale, E Major, 3 octaves right hand, or whatever the ratios work out to be, would be a valuable exercise. Teachers hate talking about our weaknesses outside of an educational setting. Once we're in the professional world, we don't like to seem ignorant. Revealing something like, "This is really difficult to teach," or "I really don't trust myself to teach polyrhythms," feels vulnerable. It's a moment of, "Thank God! Finally, I've been banging my head against this for weeks now I finally got it." That's my success with polyrhythms.

Arianne: A lot of it has to come from the student and their own motivation to learn whatever it is they need to learn, including polyrhythms. If I'm teaching a student "Clair de Lune," and their heart is not in it, they're never going to get that passage, the E major part. It has to come from within. I feel like the student really has to want to understand polyrhythms to get it.

Jacqueline: A highly motivating piece like the C-sharp minor nocturne can be a very effective motivator.

Arianne: I mean, students push themselves when they are motivated and when they want to know the piece and understand it. If they've heard it and they think it's beautiful, and they really want to dive into it, miracles can happen. This goes for any concept. If you really want to teach something that you feel you're not the strongest in, you can't go wrong having the student select a piece that they absolutely love already, and then just going off that momentum they already have.

Jacqueline: I think it's often tempting to try to remove a concept entirely from the context of a piece of music because it's so much simpler to just tap a polyrhythm, right? If you have them tap a polyrhythm long enough, they'll eventually figure it out, and then you can move on to a piece that uses it. There's a place for that kind of preparatory learning, but I also think that trying to remove the concepts entirely from the context of a piece is a mistake. There is a place for a difficult concept, essentially in a piece where you have polyrhythms in just a handful of places. That's really all they needed, because they have it in about half a dozen measures in the C-sharp minor nocturne, if you don't count the shenanigans at the end with 35 against 4, which is just an entirely different matter. Giving them a highly motivating piece of music is useful, some students are motivated by fast, flashy stuff, and if they need to get better at their scales, then that is an opportunity for them to realize there's a point to it. And the same thing for something like polyrhythms, introducing the concept and then giving a piece that has that concept in it, a famous and beautiful piece of music that people have heard before, and trying to tie the two together.

Arianne: Absolutely. What else is there to talk about rhythm?

Jacqueline: I feel like we almost just turned this into a polyrhythm episode. We talked about polyrhythms for the last 45 minutes. We talked briefly about subdivision and about my approach to subdivision.

Arianne: No, I don't think it's crazy. Actually, I had a very hard time myself growing up learning rhythm until my teacher used your approach, so personally, it really worked out for me when I was learning it. And yet, for some reason, I don't apply that to my own students. Maybe I should.

Jacqueline: It's difficult. There is a lot less room for error. If a student does not use the method and they just do beat counting and don't have the self-awareness or the critical thinking to question if the rhythm is right, it's much safer for us to just say, okay, just subdivide the whole thing. If they don't have the critical thinking or the drive to question, is this right or not? It's much more foolproof for them, and it is foolproof. You can absolutely subdivide an entire piece of music, and you will get to the right answer.

Arianne: Totally.

Jacqueline: It's results-focused, and I try to stay process-focused because I want them to know the why and the how. If they come across an eighth note rhythm, I want them to be able to use their detailed counting to understand it and then move on once they've understood it. Subdividing the entire thing almost feels like admitting defeat, like saying, I really don't know how to do this, so I'm just going to put this on easy mode, and it's not going to sound as good as a result. It's going to be clunky, but I don't know how to hold this whole note long enough any other way.

Arianne: You know what, that goes back to what you first introduced as preparation stage learning. On social media, I've been seeing this viral method in the piano teaching community where you put four plates down on the floor, put an apple on one of the plates, and tap your hand on the ground for each plate until you reach the plate with the apple, then you clap for the apple. It's like tap, tap, clap, ground because the clap is the one with the apple. Then you put two apples in the plate, and it's tap, tap, clap, clap, ground. Does that make sense?

Jacqueline: Yeah, absolutely.

Arianne: Some people even put oranges, and for the orange, they do something else that's not a clap. So, the apple could be the right hand, and the orange the left hand, and you can put different amounts of apples and oranges in these plates. The student just kind of intuitively gets it, even if they don't know a word of English or any other language. It's across the language barrier because it's just you modeling it, and then they repeat it kinesthetically, and it's visual. It's hard for the teacher because you have to swap out the fruits super fast to get to your next round, and the music is going pretty fast. I've tried it, and I totally sucked at it at first, but it took a lot of practice. But that's a decent preparation stage thing to address the complexities of subdividing without having to use language like 'and' or whatever.

Arianne: The plate contains the fruit. And so, that's your window of your beat. However many fruits are right there, and we're not thinking about it in terms of stronger or weaker, which has its pros and cons, right? It goes back to what we were saying about 1, 2, 3, 4 typically being stronger than their respective 'ands', but again, that's just a generalization that we have when we're teaching music. It doesn't allow us to open up our minds as students and think about things like syncopation where that simply wouldn't be true.

Jacqueline: But the fruit works. You just said 1, 2, 3, 4, and that reminded me of—it sounds silly—a thumb war. '1, 2, 3, 4, I declare a thumb war.' There are eighth notes in there.

Arianne: Yeah.

Jacqueline: That reminded me one of the favorite approaches is words, right? Their first piece. Actually, it's famous people, Abraham Lincoln, Harriet Tubman. Right? The work.

Arianne: I wish they put Harriet Tubman in there.

Jacqueline: They do, they rewrote the piece. They did it in a cultural awareness update, and they took out Christopher Columbus and replaced him with Harriet Tubman.

Arianne: Oh, thank goodness!

Jacqueline: I know they updated the piece. I don't know for a fact if it's Harriet Tubman, but I know that they chose better people. And I think there's the taxonomy, being able to replicate it, being able to just parrot it back, or read a word and know the rhythm of the word, relating it to something that they already know. It's a separate level of understanding compared to being able to, for example, explain it to another student, right?

Arianne: Yeah.

Jacqueline: Can you explain if it's not a student? Could you explain polyrhythm to another student? And we need to ask ourselves what we're content with, and polyrhythms don't need to have the deepest level of understanding the first, second, or even the third time that they've been exposed to that rhythm, right? A preparation stage for eighth notes could be doing some of those words, or the thumb war, '1, 2, 3, 4, I declare a thumb war' and trying to figure out where those syllables go. And the reason why the thumb war thing is so good is because it forces them to count in the beginning, feel those big beats, and literally say the numbers in the rhyme. Like all the other concepts we talk about here, preparing your students for it is crucial because they can have that 'Aha!' moment when it all comes together. I wonder if that's possible.

Arianne: I think so. I mean, yeah, preparation stage is so important. I love being able to be like, you know, do preparation stage learning where you do an activity that's seemingly completely unrelated to the actual concept at hand. And then magically the next week, they just know what to do when you introduce the actual concept.

Jacqueline: Absolutely.

Arianne: Such a good feeling. You feel like a magician. You're sneaking it in. They get it conceptually without even knowing that they get it. But I was going to say, I know someone who, if they're listening to this, they're going to laugh out loud. But I have really bad memories of this one Christmas song, 'Carol of the Bells'. Not for any personal reason, except that I find it too repetitive and annoying, and Christmas is supposed to be a happy time. But it feels like it's in too minor of a key, you know, and so I really don't like 'Carol of the Bells', but anytime I ever think about 3 against 2 polyrhythms, 'Carol of the Bells' is always the first thing I think of, and then you can separate it out into the respective voices after the fact. I think that would be one of my strategies for explaining polyrhythms too.

Jacqueline: How is "Carol of the Bells" a polyrhythm? It can't be, can it?

Arianne: Totally. 1, 2, and 3, I mean.

Jacqueline: Isn't that just a dotted 1, 2, 2, 1, 2, 3! Are they? Just quarter 1, 2, 3! Isn't that just quarter notes?

Arianne: But if you separate it out, it works.

Jacqueline: Suppose that's tweaking the rhythm ever so slightly.

Arianne: Yeah, because technically, one third of 100 is 33.33 recurring.

Jacqueline: I think that you're moving through the end of that rhythm a little bit too fast when it's a polyrhythm. Can that work?

Jacqueline: I mean, it makes sense. I hear it, but I'm trying to understand how it makes mathematical sense for the simple rhythm of the bell carol to turn into a polyrhythm of 3 against 2.

Arianne: If you think about it with tapping your right and left hand, it's both right, left, right. Now just separate out the right hand to be both right, right. So, right right, that's a triplet. And then now left, both left, both left, both the lefta. So left, left, left, left. It's totally even, so "Carol of the Bells" works perfectly for the 3 against 2.

Jacqueline: I feel like we're blowing this whole thing wide open. How has this not been talked about? So you just teach someone "Carol of the Bells," and then you teach them the polyrhythm.

Arianne: Yeah, I mean, I've always done that. It works pretty well.

Jacqueline: Fascinating. I wonder if it is mathematically perfect.

Arianne: You can test it out. Or maybe there's a forum online that goes into that. But I mean, I'm just hearing it in my mind, and it feels perfect. I don't know if that's good enough for our purposes. But think about it. If you're dividing a hundred percent of something into 3 equal parts, and you're in 3, 4 time, let's say you have 3 quarter notes that are all just quarter notes in a measure. That's tah, ta! And then in your left hand, you have 2 like dotted quarter notes. That's tah-dit, tah-dit. So, it totally works out.

Jacqueline: That is fascinating.

Arianne: Yeah. And it's ironic because it's my least favorite piece of music ever. And I still use it to teach this concept. It's perfect for that purpose. So even though I resent the piece for separate reasons, I do use it a lot. Sometimes you have to occasionally dive into the things you don't enjoy to effectively teach something.

Jacqueline: I suppose? I think it's interesting because it's just another verbal thing, right? It's essentially the same thing as "not difficult."

Arianne: Oh, yeah, totally. The thing is, you can say the phrase "not difficult" different ways. So if someone's just reading about it, they might not know when to start saying the word "difficult." Some people might read it and think "not difficult," so it's not foolproof. But you have to be told "not difficult," you know, or you have to have it highlighted or accented at certain points in time. "Carol of the Bells" is auditory and so it's just different. But it takes all kinds of methods to reinforce an idea. So there's no wrong way to go about it unless it's technically wrong.

Jacqueline: Well, yeah, absolutely, whatever works. I feel like we just throw...

Arianne: But yeah.

Jacqueline: Think that polyrhythms, right? So did we have...

Arianne: We have.

Jacqueline: This book of things that might work with this particular student. And whatever works, works.

Arianne: Honestly, that should be our motto as piano teachers. Whatever works, works.

Jacqueline: Yeah, no, that is fascinating. But other than polyrhythms and subdividing, anything else about rhythm?

Arianne: I guess.

Jacqueline: Call this episode "Polyrhythms and Subdividing" or "Rhythm"?

Arianne: I don't know. That's a good question. If you wanted to be more generalized, so that more people stumble upon the video, that's one thing. And if you wanted to be more specific to truly highlight what we talked about, that's another. So your guess is as good as mine on what we should title it. But I think another last thing I wanted to quickly say is, if you're a new piano teacher, and you don't have too much experience. And this goes with pitch, also. Do not assume that a student who doesn't figure it out for a long time is a hopeless case. If you've tried everything you can with a certain student regarding rhythm, I think it just means that they need to dance more, and they need to be coached more in their kinesthetic experience of rhythm. And when it comes to pitch, if you feel like a student is tone-deaf, there are cases of students being totally tone-deaf. But there are methods you can use to train someone out of what can be misinterpreted as tone deafness. So don't give up on students who are taking longer than you took to understand things like rhythm. Maybe they just need a little bit more time to process it, or they need a different activity to gradually understand it.

Jacqueline: Yeah, I think learning something over time is not a bad thing. Some students struggle more with one concept versus another. And I think we should allow our students grace and make sure that we don't just throw up our hands and say, "Oh well, that's it. They don't need to know that." Those concepts that are the hardest are the ones that are so important for us to stick with them about. I had some teachers when I was a kid who would just let me use my music during recitals because I struggled so much to memorize my music. That's absolutely the wrong approach. In community college, before I got my undergrad, I was allowed to use my music for juries because I was so bad at memorization. Then, I got to university where I had my audition from memory, and that was a nightmare. I was expected to memorize my music before I could even perform them in workshop, but for the first time, I was really taught all the different ways of doing memorization and figured out a system that worked for me. So don't give up on your students when they struggle with something.

Jacqueline: Don't let your students subdivide forever. Don't let them subdivide all the time because it will give the results, but they will have deficiencies elsewhere because of that method. Take the time, do preparation stage and make sure that your students get to the point where they truly understand what it is that they're doing. Any last thoughts?

Arianne: Mine is that I was hopeless at certain things. It's funny because I leaned too much on memorization to compensate for my terrible sight-reading skills. Whenever I transferred to a new piano teacher in high school or college, they would always wonder how I learned a piece when I was struggling to read a passage we were working on. I hate reading.

Jacqueline: Brute force, so.

Arianne: Every student is different. Every student is going to feel hopeless at some point in some concept that they're doing. Don't let that get you down as a teacher. You already know from experience that if someone really wants to get it, they'll eventually get it.

Jacqueline: Absolutely. Well, I think that about wraps up our discussion of rhythm. Thanks for listening, and we will see you next time.

Arianne: Bye.