Thoughts On Polyrhythmic Effects

def. Polyrhythm : literally means multiples rhythmes at the same time (I made up this definition). But because the word doesn't mean anything today (because people use it in every situation) we will use it only to refer to phenomenon related to the very definition above.

Annoying person alert: This is not rigorous music theory, don't get irritated if it's not "correct", we are talking about music after all ;)

Consider my beat as being a quarter note. I can divide my beat into two eighth notes, four sixteenth note, eight 32-th or n n*4-th notes (shit it already got mathy).

I can also divide my beat into three (or any number), obtaining 3 notes, non ambiguously named triplet eight notes (but really twelth notes would have been a better name that all this lower power of two equivalent time occupation non sense).

Now if I divide the same beat (that is to say one fixed physical time duration) in two different ways, one in 3 and the other in 2, playing those two subdivisions against each other produce a 3:2 polyrhyhm (obvious you smartass ?).

This way, on a beat level, I can make any polyrhythm. Just play different beat divisions at the same time. Dividing one beat into four sixteenth notes and five quintuplet sixteenth notes leads to a 5:4 polyrhythm.

Of course your beat reference can be the meter beat, but also longer or shorter units (including tuplet, but why would you do that?). While tuplets are fine to use, nobody really grasp their intricate feel right away (or they brag about it a lot). So for poor humans who do not (still) have the natural ability to divide a second into 7, 9 or even 13 equal parts, let's cheat.

I do not cheat I'm being smart (that's what he said)

We can obtain polyrhyhms without using odd time subdivisions, we just have to use odd time meters (cheating isnt' easy, it's easier). Because odd meters have - duh - odd number of beats in a measure, simply dividing by even numbers the beats yield an ideal playground to derive (interesting) polyrhythms. Fine, show me the recipe !

• Choose an odd number, we don't care. Hey 21, how are you ?
• Find divisors of 21 (hey 7, hey 3, how are you ?)
• Play every 7 notes to make a 3 against 21 polyrhythm. (assuming the beat is played, which is the whole life purpose of a metronome)

• Play every 3 notes to make a 7 against 21 polyrhythm.

Tada. If your polyrhythm isn't to your insert-sarcastic-description-of-overly-enthousiastic-music-theory-folks taste, then just math it.

• Multiply your odd number by any even number, hey 2 do you know 21 ? no ? you are now best friends, hey 42 (totally random number). And yes, no one composes in 21/16 meters, but hey if music has rules find me the guy who wrote them.

• Find again the divisors, hey 2, 3, 6, 7, 14, 21

• Play a note every 2 notes to make a 21 against 42 polyrhythm

• Play a note every 3 notes to make a 14 against 42 polyrhythm

• Play a note every 6 notes to make a 7 against 42 polyrhythm

• Play a note every 7 notes to make a 6 against 42 polyrhythm

• Play a note every 14 notes to make a 3 against 42 polyrhythm (that one is neat, give it a try -- jk don't do that)

You say counting fourteen 32-th notes is harder than learning tuplets ? Come one, just a bit of practice (it's impossible).

I intentionaly iterated through all possibilities for your better understanding. I have to admit that the 21/16 meter was probably not the smartest choice for an initial example, so we'll get back to the 2018 era music scope and focus on a 9/8 meter and do the same thing.

• Choose an odd number : 9, I chose you.
• Find divisors : 3 (those saying there is 9 and 1, stop being so funny)
• play a note every 3 notes to make a 3 against 9 polyrhythm.

Ok this is not to my snobby taste so I will multiply that disgustingly-simple 9 by 2.

• Hey 18 how are you ?
• Find divisors of 18, hey 2, 3, 6 and 9 (and 1 and 18 yes thank you)
• Play a note every 2 notes to make a 9 against 18 polyrhythm
• Play a note every 3 notes to make a 6 against 18 polyrhythm
• Play a note every 6 notes to make a 3 against 18 polyrhythm
• Play a note every 9 notes to make a 2 against 18 polyrhythm

Now we want additional magic, before you could either :

• Play a note every 2 notes to make a 9 against 18 polyrhythm
• Play a note every 3 notes to make a 6 against 18 polyrhythm

But you could do both at the same time : boom 9 against 6 polyrhythm in a 9/8 meter, without even trying to (which would implicitly also be a polyrhythm against 18, the beat).

And yes you could also do a 2 against 3 against 6 against 9 against 18 polyrhythm using only even subdivisions of the meter, that's the hidden power of odd meters.

The same method can be applied to even meters, but what's the point of doing only 2N:2M polyrhythms ? This is what pop music (and 95% of music) is all about (I love pop music btw).

Now I tackle the unending debate of polymeter vs polyrhythm on the internet. And while differences are clear, I only point out here that repeating polymeter can have a polyrhythmic feel. If I repeat a phrase in 4/4 against a phrase in 5/4, the repetition produces a unique pattern that lasts 20 beats, repeating itself every 4 measures.

While it's clear that the two phrase are not polyrhythms against each other, the whole pattern of 20 beats is a polyrhythm. The observation that you can play 4 phrase of 5 beats in the same amount of time that you can play 5 phrases of 4 beats is trivial. If we were to play the first beat of every phrase, we would observe a 5:4 macro polyrhythm (or 4:5 depending on the chosen reference).

That's why, in my opinion, polymeter phrasing has such an interesting effect. It's like a slow polyrhythm, where the unit of pulse in not a simple note, but an entire musical idea.

I hope you saw that the word polyrhythm being such an high-level concept, we can start to see polyrhythms everywhere. In an opposed approach, trying to fit the polyrhythm idea in multiple different context is a playful and joyful creative process.