The Polyrhythm Page

On this page you'll see definitions, examples, tricks, oddities and other stuff related to Poly-rhythms.

Some terms that I will (occasionally) use:

Sufficient Subdivision

The smallest subdivision of a given pulse that is necessary to contain all notes of a given rhythm. (Example A)

Redundant Subdivision

The subdivision of a given pulse that contains more notes than is necessary to contain a given rhythm. (Example B)

Given rhythm:

Example A - Sufficient Subdivision:

All the notes of the given rhythm are included in the subdivision, but there are no notes smaller than in the given rhythm.

Example B - Redundant Subdivision:
All the notes of the given rhythm are included in the subdivision, but this time the subdivision contains smaller notes that do not contribute to the given rhythm.

What is a poly rhythm?

The prefix poly- means many, and according to this, one of my dictionaries tells me that:

"Poly rhythm is the systematic exploitation of different rhythms performed simultaneously"

But this definition makes all music consisting of two (or more) different rhythmic lines, poly rhythmic.
Thus, the next example is (according to the above definition) poly rhythmic:

Ex. 1

Generally spoken this is not what makes up a real poly rhythm.

Some Definitions of Poly rhythms:

First definition:

To qualify as a poly rhythm, the contributing rhythms should be chosen such that the numbers denoting their rhythmic relation, are relatively prime to each other.

Second definition:

If the sum of two (or more) simultaneously sounding rhythms results in a subdivision of the beat that is not present in either of the constituting rhythms, we call this resultant rhythm poly rhythmic.

Third definition:

Two different rhythmic patterns do not result in a poly rhythm (when played simultaneously), when one of those rhythms can be contained in the subdivision of the beat that is implied by the other rhythm.

This is a poly rhythm:

Ex. 2

One major point to think about is that to qualify as a poly rhythm, the two constituting rhythms should be clearly heard and felt as separate rhythms, each with their own properties!
If I play example 2 on two snare drums with the same pitch and the same loudness, it just sounds like one rhythm, being the sum of the two building parts! But it is no longer a poly rhythm (unless you put the two players far apart).

Be careful with this example:

Ex. 3

It looks like a poly rhythm, but doesn't sound like one (even if the players are far apart and playing on contrasting instruments)!
So, not the way we write down a rhythm, but the way a rhythm sounds through interacting and conflicting subdivisions, makes it poly rhythmic or not.

The next example is a real poly rhythm again:

Ex. 4

And try this one on your drum set:

Ex. 5

Now some complicated examples:

This example is clearly a poly rhythm: the top line has a rhythm based on a group of 4 notes, the bottom line has a rhythm based on a group of 3 notes. 3 and 4 are relatively prime to each other, hence it's a poly rhythm.

Ex. 6

Now I change this rhythm a little bit so that it becomes:

Ex. 7

Is this still a poly rhythm or not?
If we look more closely to the subdivision for this example, we see that the rhythm on the first quarter is based on a group of twelve notes:

Ex. 8

The bottom rhythm didn't change, so we have a group of 12 and a group of 3, which are not relatively prime and hence this is no longer a poly rhythm. As a matter of fact, the rhythm on the first quarter (of example 7) sounds like a 3/8 bar, regularly divided in three groups of 4!

What can we conclude from this?

To be a poly rhythm, two rhythms (at least!) are needed to form this poly rhythm, and these two rhythms:

1. should be based on relatively prime subdivisions
2. should be clearly distinct from one another

Both conditions have to be met at the same time!

Here is another interesting poly rhythmic example:

Ex. 9

To see how close the two rhythms really are, lets set up the minimum subdivision of the beat that includes all notes:

Ex. 10

The accented notes denote the rhythm from example 9. The sixteenth note and the 2nd note of the quarter note triplet, differ only by 1/48 note!
What's that? A 1/48 note? Yes that's another way of giving a name to a 32nd triplet! For the same reason I often call 8th note triplets 12th notes! (And quarter note triplets 1/6 notes).
This gives rise to some very interesting time signature changes! Play four bars of 4/4 time alternated with two bars of 4/6 time. Or try this: two bars each of 4/4 - 4/5 - 4/6 - 4/7 - 4/8.
Henry Cowell (in his book: New Musical Resources) once devised a whole system with appropriate note heads to make writing such changes easier! If you experiment with this a little, you're sure to come up with some interesting material. Give it a try!