A couple weeks ago I wrote, in a general and impersonal way, about playing three-against-two. In this post I revisit that topic, but personally. This is a long email I’d written to Walter Freeman, a neurobiologist at UCal Berkeley, about how I’d learned to play polyrhythms, first two against three, then three against four. Note especially the last section, which is about breathlessness that seems to be induced by a certain kind of rhythmic practice. This email is dated 22 March 2002.
Dear Walter,
I thought I’d offer some informal observations about learning to play polyrhythms. The occasion for these observations is simple: about a week ago I was finally able to play 3 beats in the left hand against 4 in the right. But I’m getting ahead of the story.
The Early Years
The early part of the story takes place in my childhood, of which my memories are poor. I started learning the trumpet in the 4th grade, when I was 10. Somewhere, say within the first two years, I learned to play eight-note triplets, three (more or less) evenly spaced notes within a single beat. I then learned to play quarter-note or “drag” triplets, three notes spaced over two beats. I vaguely remember that as being somewhat more difficult. The problem was that, like lots of kids, I was taught to beat time with my foot. Eight-note triplets occur within the span of a single foot tap, while quarter-note triplets span two foot-tapes. That’s the problem, placing three notes over two foot taps. You are, in effect, playing polyrhythms between the arm-hand-tongue-breath system of trumpeting and the foot system of time-keeping (which also has a verbal component). In any event, I somehow learned that. [My impression is that, in general, children have a more difficult time learning quarter-note triplets than eight-note triplets.]
We move ahead a few years to my early teens when I took piano lessons for about two years (in addition to continuing on trumpet). Somewhere in that period I encountered playing two in the left hand against three in the right. I lost the encounter. I couldn’t get the hang of it.
Two Against Three
We now move ahead about 30 years. I was playing with a group called the New African Music Collective (NAMC). The group varied from one occasion to the next, but had a core personnel of me on trumpet (and some percussion), Ade on percussion, and Druis on percussion and vocals. When we added players to the group, we added percussionists, though we had a bass player for awhile. The central musical premise of the group was to explore African and Afro-Cuban rhythms: polyrhythm central. So I got used to floating my trumpet lines over and against polyrhythms and became proficient at superimposing various groupings on whatever was happening with the percussionists. Thus I could play lines that would have been four-square and dull if they had stood alone; but they bristled with tension and force in a polyrhythmic context.
It is in this context that I began to practice playing an small 8-key balaphone (a marimba-like instrument with gourd resonators) and a tongue drum (a wooden box with eight “tongues” cut into the top surface). Every so often I’d take a wack at playing 2 against 3 (2-3). One day it just clicked. And it became reliable fairly quickly, within one or two days. That is to say, I could sit down at the instrument (whether balaphone or tongue drum) and start playing 2 against 3 without any preparation.
Initially I played only two tones, one for the left hand and one for the right. However, I quickly developed the ability to move one hand or the other over some range of keys while the other hand remained anchored on one key. Then I worked on moving both hands over some range of keys while still maintaining a steady and consistent 2-3. Given that I am right-handed, it has always been easier to play two in the left hand against three in the right. Playing three in the left against two in the right is more difficult, as is switching back and forth between the two regimes, 2/left against 3/right, 3/left against 2/right. As I have had no particular interest in becoming really proficient on these instruments I have never spent a great deal of time practicing 3/left against 2/right. I have no idea how things would change if I were to spend, say, a mere half hour a day for six months working on that regime.
Now, the thing about 2-3 is that it can easily be parsed into 6. You can’t really count it in six at faster tempos, but . . . The trick that made 2-3 work for me was simply to hear the two middle strokes as successive pitches in one single line. Once I could do that I found it easy to do 2-3 at any tempo and even to accelerate and decelerate at will. When the tempo gets fast enough, however, those two middle tones no longer “stream” to the same line. Rather the notes break apart into two lines, one with three notes and the other with two. Actually, when I’m moving both hands from one tone to another it gets more complicated than that.
During this period I’d attempt 3-4 every now and then, but had little or no success. That brings us to the present.
Three Against Four
About a week ago I managed to play three in the left hand against four in the right with some success. By that I mean I could sustain the pattern for 10s of seconds and the playing in each hand was fairly steady. I’ve been able to repeat the performance each day since then, so it’s not a fluke.
But it’s far from being rock steady. It’s only today that I’ve been able to sit down at the tongue drum and play three-against-four (3-4) right off, without any preparation. However, it’s not very steady; it doesn’t feel at all “locked.” And I’m pretty much limited to playing on only one tone with each hand. The minute I attempt to move one hand or the other back and forth between two tones the 3-4 coupling breaks down. I assume that will change with practice, though I have no sense of how much practice will be required.
The most interesting aspect of this process is the fact that I’ve had to work my way into the 3-4 pattern at each playing session. The most successful technique (though not the only one I’ve tried) is to start by playing a four-beat pattern in the right hand (at a comfortable pace) and playing the left hand on the first beat of the pattern. Once that is going nice a even — which is easy to do — I then direct my attention to the left hand and start playing three beats in the appropriate interval. Sometimes it works and sometimes not. Eventually it works and once it does, I can keep it up.
You might observe that, after all, one might achieve 3-4 by starting off with three in the left against two in the right. You then double the number of strokes in the right and you’ve got it. I haven’t found that to work very well. However, I find that, when playing 3-4, I am beginning to be able to “hear” 3-2 “within” the overall pattern. I don’t really know what’s going on here, but how I hear things is crucial.
I also notice that, at times, it seems as though I’m simultaneously counting 3 for the left and 4 for the right. That is to say, one inner voice is counting “1 2 3 1 2 3 . . . .” while another inner voice is counting “1 2 3 4 1 2 3 4 . . . .” I don’t regard this introspection as terribly reliable, but my intention seems to be to get those two counts going simultaneously. But I also believe that rock-steady success requires that I get beyond counting anything with inner voices. Sometimes I’m counting, sometimes not. I also observe that, when fumbling my way to 3-4 I sometimes slip into 3-6 (which, of course, is easy) and 3-5 (which should not be easy). Once I’ve got 3-4 in better shape I may go after 3-5.
Now I want to consider a different aspect of this.
Breathlessness
I’ve spent some time over the last year or so on a single trumpet project, a completely notated set of unaccompanied variations using the form of Thelonius Monk’s “Epistrophy.” The object of this project is rhythm. The variations are arranged into three movements where I used different approaches to rhythm in each movement. Here I’m concerned only with the first and third movements.
This first movement goes through Monk’s form three times (with three additional bars at the end) and, in effect, uses four different meters, though it isn’t notated that way. It is notated in 2/2 time, with the melody line written in quarter notes or eight notes as convenient. Each measure is to have the same duration regardless of how many notes are in it. The phrases written as quarter notes (mostly in the first chorus) are, in fact, quarter-note triplets and many of the eighth-note phrases are, in fact, quintuplets or sextuplets.
Rather than make the score busy by explicitly indicating these triplets, etc. in the standard fashion (or by changing meters often) I’ve simply written quarter notes and eight notes. However, one should feel the piece as being in different meters: 3/X, 4/X, 5/X, and 6/X (where X is the pulse carrying note value). As I’ve indicated, each measure, whether 3/X, 4/X, 5/X, or 6/X has the same duration and each meter lasts for 8 or 16 bars and then we switch to a different meter.
Now, when, say, Stravinsky shifts from one meter to another (say, from 5/16 to 3/16) the duration of the unit carrying the basic moving pulse stays the same. The sixteenth note in 5/16 is the same as a sixteenth note in 3/16 but the duration of a single measure necessarily changes. What I’m doing is different. An eighth note in 4/4 is just a bit longer than an eighth note in (what is in effect) 10/8. The duration of a single measure stays the same, but the pace of notes within the measure changes. Stravinsky’s trick involves “counting” while mine involves the basic “pulse.”
For some reason that is mysterious, I find my practice to be unexpectedly “exhausting.” I mean, no, it’s not really exhausting. But I find myself breathing heavily and sweating while playing this movement. As far as I know nothing I or any other trumpet player does while playing involves the kind of energy expenditures that requires perspiration to dissipate heat. Nonetheless trumpeters (and other musicians) do perspire while playing. It’s not terribly unusual, not for me or for others and I take it as a sign of emotional arousal, though I’m not aware of anyone having studied it.
However, it’s unusual for me to perspire while playing something that I can’t quite pull off. Perspiration normally comes when I’m playing something I know well and am beyond the need to practice it for the purpose of executing the notes properly. It requires mastery of the material. That’s not the case with these variations. I haven’t quite got it down. But I can still work up a sweat.
The same thing happens when I work on the third movement. This movement begins with long strings of eighth notes that are to be played “fluidly, like congas.” The underlying idea was inspired by the sound of congas. Imagine two congas one a bit higher than the other. You play a simple pattern of eighth notes, playing a triple pattern where the first note is playing on one drum and the second two notes are played on the other drum. This determines the interval pattern of the eighth-note lines in this movement. However, those lines are superimposed on Monk’s chord changes, which move by half-notes (e.g. four eighth notes) in the A sections and whole notes in the bridge. So, for most of the piece what have a three-note triple rhythm being played against a four-note harmonic rhythm. That tension is what gives this movement its propulsive force. As is the case with the first movement, practicing this leaves me breathless and sweaty.
In fact, breathlessness is even more likely here than with the first movement. I’ve got plenty of opportunity to breath while playing, but that doesn’t seem to be enough. It would be interesting to monitor my breathing, heart rate, and metabolism while playing these pieces and compare the readings to those taken when I’m playing pieces which make similar technical demands but don’t involve the rhythmic complexity. I’m guessing that the rhythmic complexity of the music brings about a different entrainment with physiology and that’s what’s making me breathless. If that’s the case, then I think that successful performance of these pieces will require a different pattern of coupling between the structure of the music and my underlying physiology.
This makes me wonder about the breathing of Indian musicians in the Carnatic tradition, which involves fierce polyrhythms.
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