How to recognise polyrhythm in a piece

Question

I came across a part I found really interesting and quite challenging to my piano level in the piece Arabesque No.1 in E major by Claude Debussy, where both hands seems to not follow the same time pattern. I realized while practicing that it could be an example of polyrhythm, which is a concept I didn't really know, so I started to do some research to prove or not my assumption. I understands the idea of the concept, but I don't feel able to recognize it in a piece.

My question to you would be, is this part an example of polyrhythm, since to me it looks like triplets over dublets in four beats ? If not, is there some clues or tips to quickly recognize a polyrhythm part in a piece ?

Thank you very much !

Answer 1

Yes, you could call this 'two against three' pattern a simple example of Polyrhythm. Not sure why it's so important to label it? More importantly, have you a strategy for PLAYING it?

The count is 1 2-and 3. The 3-group hits 1 2 3. The 2-group hits One and.

Practice it tapping two hands on the table before trying to play it.

Answer 2

A two-against-three is sometimes called a "hemiola." (Next time you see it in a trivia game, you'll know.)

You can always work out polyrhythms by taking the least common multiple of the two voices, and working out where the notes hit. So, with two against three, the LCM is six. Count in sixes. Both voices hit on one, the three hits on 3 and 5, and the two hits on 4. So, the two hits right between the second and third three. You can tap it out like this (keep saying "pa" under your breath as you go) BOTH pa R L R pa BOTH pa R L R pa. Then you can try reversing your hands.

For three against four, you do the same thing with 12. The four hits every third 12th, and the three hits every fourth 12th. You can tap it out like this: BOTH pa pa L R pa L pa R L pa pa.

Chopin's Fantasie Impromptu is a well-known piece with three against four through most of the piece:

And here's a part of Debussy's L'Île Joyeuse that has some tougher polyrhythms: five against threes with a few five against sixes on the last beat, and some five against twos. I'll leave the arithmetic to you if you're interested. :)