Polyrhythms are cool. We like to deal in absolutes, but they remind us that sometimes Schrödinger’s cat is simultaneously alive and dead. They are both simple and mind boggling, providing the perfect way to create contrasts, and to highlight or suggest underlying rhythms in music or dancing.

Alive or Dead?

Multiple rhythms at the same time

At their core, polyrhythms are two or more rhythms that take up the same amount of time but don’t line up inside that time. The simplest of these is two against three. If we take a two beat rhythm, this breaks up the bar into two equal beats. If we take a three beat rhythm, this breaks up the bar into three equal beats (surprise!). If we play both of these rhythms, we can simultaneously break up the bar into two and three equal parts.

The first part that is cool about this is that there is no ground truth. It is both a three count rhythm, and a two count rhythm. And its own special 2+3 thing.

The second part that is cool about this can be observed if you try to play this rhythm with your hands. Tap the two beat rhythm with your left hand on your knee. Now stop with the left hand and tap the three beat rhythm with your right hand. That was easy right?

Now start the two beat rhythm with your left again. Keep playing that two beat rhythm and start the three beat rhythm with your right. Unless you play percussion or an instrument where you are used to playing different parts with your left and right hand, this should be pretty challenging. You probably found it somewhere between difficult and impossible.

Now instead, just say the two against three rhythm pattern out loud: “Koun tch-ka-ts”1. That’s probably a lot easier. You can probably also beat it out with one hand on one knee quite easily. To beat it out with two hands it goes “both right-left-right”, which I also find quite easy.

If you’re like me, doing the rhythm “together” is not so hard. It’s thinking of it as two layered rhythms that is more challenging. I think this is what makes polyrhythms interesting: there is an underlying simplicity (a 2-beat rhythm played together with a 3-beat rhythm) that our brain simultaneously identifies as simple and complex. And surprisingly to me, it’s the “special 2+3 thing” (that I’ll also call the gestalt view, looking at the 2+3 as a whole) that is actually easy to perform, while the apparently simple thing of doing 2 beats with one body part and 3 with another is difficult.

The third part that is cool is what the two beat rhythm suggests about the three beat rhythm and vice versa. If we count the 2+3 thing as if it had a three beat basis, we get “1 2&3”. This suggests an underlying binary rhythm, “1&2&3&”. If we count the 2+3 thing as if it had a two beat basis, we get “1 a2n”, suggesting an underlying ternary rhythm, “1na2na”.

Both of these break down into an underlying six beat rhythm, with emphasis on different beats2. If we go to a 6 beat interpretation of the rhythm, we can count it in two different ways: “121212” and “123123”. Each count represents the same time value (one sixth of the bar). The first two beats have the same “names” in both ways of counting, and then the two get offset until they meet again after 6 beats. The places where we count “1” are the places that are emphasized in the two against three polyrhythm3. You can also try beating out with both hands on your knees, using a flat hand for the “1”s and the fist for the other two beats.

Two against three in ternary music

While “pure” polyrhythms keep the rhythmic ambiguity of the underlying beat, in many musics, there is a clear beat, with a lot of variation and emphasis being highlighted by polyrhythms 4.

Let’s take some slow blues. Slow blues has a two beat rhythm5. Each of these beats is ternary, which means it has three subdivisions. This creates a context where the underlying six beats we discussed earlier can be found. On top of this two beat rhythm, we can place 3 beats, to create a first polyrhythmic effect, that can be thought of with or without binary subdivisions. In this case, these hypothetical subdivisions of the two rythms line up, but the beats don’t. Alternatively, we could consider the single ternary beat as 3 beats, and place 2 beats on top of that (or a single binary beat). In this case, the beats line up, but the subdivisions don’t (suggesting an underlying subdivision of the beat into 6, and of the two beat rhythm into 12).

(Music credit: (No Need) Pissin’ on a Skunk - Safire - The Uppity Blues Woman)

Both the three beats against two beats and the binary beat against ternary beat patterns can be found in blues music. The first is a very frequent variation, such as in the same song.

The second is slightly rarer and tends to be a more ambiguous move away from pure ternary beats. But in some songs, such as the following, whole sections shift over to binary for a period, before moving back to ternary.

(Music credit: Need a Little More Time - Sugaray Rayford)

Both variations played against each other give the “next” simplest polyrhythm: three against four

Two against three in binary music

A lot of binary blues music comes either directly from latin/carribean music, or indirectly through ragtime-y charleston-y influences. A main motif of this is the tresillo rhythm, also known as 332. You can think of it in several ways. One is that you break 8 counts into 123 456 78. Another is that you take four main beats and place a two over three on the first three beats and leave the 4th intact. This places an emphasis on beat 1, the “and” between beats 2 and 3, and on beat 4. When clapping, it creates a sort of “clap on the one, miss the two, clap on the “and”, miss the three, clap on four”, If you combine tresillo with an accent on the odd beats (1 and 3), you get the familiar habanera rhythm, found in kizomba, milonga, and many other musics.

Another way of thinking of the habanera rhythm is a “displaced” two in a four beat rhythm (in this case delayed). The tresillo can then be thought of as a displaced beat in a rumba rhythm. The rumba goes “slow, quick, quick”. In tresillo, we anticipate the first quick and call it “slow” instead, leading to a sort of “slow, slow, quick” (where the slow takes up 1.5 beats, rather that 2 beats).

This kind of rhythm can be found in a lot latin blues, either as a permanent rhythmic feature of a kind of habanera, or as a variation in which the rumba rhythm is displaced. In turn, habanera can be thought of as rumba+tresillo.

(Music credit: Hello Mrs Brown by Byther Smith)

Going further

Some combination of our brain’s basic faculties and the pop music culture we are familiar with makes playing with 2 and 3, binary and ternary, relatively easy. Everything subdivides into 6, 8 or 12 and if necessary we can pretend that all the subdivisions are there and figure things out from there. When we get into higher orders such as five against four, the subdivision into 20 is no longer as feasible and we get into “real” polyrhythm territory. This is also not helped by current pop culture where 5s and 7s are mostly absent.

A common feature of polyrhythms of any order is their symmetry. You do a thing until halfway and then do it in reverse.

In all cases, thinking of any polyrhythm in its four ways can be useful. For example when dancing a three over two

  • I can think of doing a variation accenting three subdivisions over an underlying two beats.
  • I can think of the music as being an accent of two subdivisions of the three beat rhythm I’m dancing.

And if I’m trying to dance both parts of the polyrhythm

  • I can consider the two beat and the three beat rhythm as being independant and layered on top of each other.
  • I can consider that on each beat that I accent, my body is creating a shape that matches that beat, creating four distinct shapes in my body, that I transition between following the overall rhythm.

Happy polyrhythming! And if you find it harder than it seems like it ought to be, maybe you can take consolation in the fact that after a whole year of practicing off and on I still can’t hit three beats with my chest while dancing two beats with my feet.

  1. I’ll be using ideosyncratic but consistent sounds and throughout.

    Two beats are called “koun” and “ka”. The binary subdivisions are called “ke”. The ternary subdivisions are called “ts” and “tch”. The complete subdivision of 2 beats into 12 would be “koun-ki-ts-ke-tch-ki-ka-ki-ts-ke-tch-ki”.

    I also call mostly call beats by numbers, with binary subdivisions called “&” and ternary subdivisions called “n” and “a” (“n” is short for “and”). This at least eliminates confusion as to whether I’m writing a binary or ternary subdivision (note that there are no subdivisons into 4, so nothing is implied to match “1e&a” that is used in quaternary). 

  2. On paper, it can be quite hard to decide whether a “6 beat” rhythm is actually 6 beats, 2 ternary beats, or 3 binary beats. Given musical context (like a song), one of these interpretations of “the beat” is usually dominant (as the place where we would clap our hands, snap our fingers or pulse our body). Because polyrhythms revel in ambiguity, I’ll sometimes refer to non-dominant interpretations of “the beat”. I mean these as a way of thinking about it on paper, rather than a claim that it is “reality”. 

  3. Technically once we start counting like that, it’s bars or beats of different lengths and it’s a polymeter, not a polyrhythm. But especially with the two against three, it’s also a useful way of looking at it. 

  4. This is especially true of, but not limited to, music that has an African cultural heritage, such as blues and pop music. 

  5. Generally grouped together in bars of 4 beats, but we can ignore that for now.