Polyrhythms have been used by composers, improvisers and within various cultures since we expressed ourselves through music. They are the result of one or more people experiencing time in different ways simultaneously and often occur organically. At other times composers create polyrhythms between different instruments or for one player.
Polyrhythms can be challenging for some individuals, but there are ways that you can improve and even master them.
A good place to start is to make sure that your various subdivisions of pulse are sturdy and consistent. Legendary Drummer, Joe Morello’s book “Master Studies” presents what he calls the “Table of time” in which you practice quarter notes for a measure and then do the same for quarter note triplets, eighth notes, eighth note triplets, sixteenth notes, quintuplets, sextuplets, septuplets, octuplets, nonuplets, decuplets, undecuplets (groups of 11), duodecuplets (groups of 12). After you have mastered these subdivisions (preferably with a metronome), you can advance to polyrhythms.
So how do we understand polyrhythms? One of the first polyrhythms that we encounter in music is the concept of 2 against 3 or 3 against 2. You can have 3 notes that are expressed at the same time as 2 are being expressed or vice versa. There are a couple of ways that you can notate and imagine this polyrhythm. Firstly, using basic math, you multiple the 2 numbers and you’ll get a composite rhythm that will accommodate your polyrhythm. In this example, you multiply 2 x 3 and get 6. Your measure should express 6 equal notes. You can write a measure of 2/4 with eighth triplets on each quarter note or a measure of 6/8. Next you divide your total of 6 by each of the polyrhythm subdivisions, so that you know where you will attack. 6 divided by 2 is 3. Write in an accent on every 3rd note of the 6 and you’ll have 2 groups of 3. There is your 2! Now divide the 6 by 3 and you get 2. Mark an accent on every other note of your 6 and you’ll have 3 groups of 2 (see below). There is your 3!
This same method works with much more complex polyrhythms. a short cut is to make one of the numbers your meter, the other number your subdivision and then make the initial number your accent. Let’s take a simple one first. We want to express 4 against 3. We create a measure of 4/4, subdivide that measure with groups of 3 (eighth more triplets) and then go back to your original number 4 and accent every 4th note of the triplets. The 4/4 is expressing the 4 while the every fourth note of the triplet is expressing the 3 (see below)!
Let’s take on a slightly more challenging polyrhythm of 2 against 5. Start with a measure of 2/4. Subdivide each of your 2 quarter notes by groups of 5 and then accent every 2nd note. You’ll wind up with your 5 (see below).
In a closely related polyrhythm of 4 against 5, you would create a measure of 4/4, subdivide each quarter note with groups of 5 and then accent every 4th note of your 5’s (see below).