Following a question on a Facebook page about coping with polyrhythms, I decided to republish this post from 2012. I hope it helps!

I want to suggest some ways of solving a polyrhythm where one hand is playing in divisions of four while the other in divisions of three. I am going to leave out 2 against 3, as this is relatively straightforward – as long as the second note of the duplet comes precisely between the second and third note of the triplet, then bingo!

I’ve decided to go with a common example that trips people up, the 4 against 3 in the second movement of Beethoven’s “Pathétique” Sonata (last beat of the second bar):

Fitting together the two hands slowly here relies first of all on knowing precisely where each note goes in one hand in relation to the other. In a 4 against 3 group, the only place where the hands coincide is the first note of the group. To work the placements out mathematically, on a piece of graph paper draw two lines and divide the top one in 4 and the lower one in 3. You will see that the second LH triplet comes between the second and third demisemiquaver of the RH but not half way (it actually comes a third of the way between). The third LH triplet comes just before the last demisemiquaver.

Do this first by tapping your hands on your knees, using the words “What Atrocious Weather” or “Pass the Goddamn Butter” to help. If you repeat this enough times, you’ll get better and better at it, and you can transfer the activity from patella to keyboard. The main thing is to feel the rhythm in your whole body, not just in your head (imagine you are a drummer).

Practising this slowly is only somewhat useful – do it occasionally, but you’ll need to do it mostly at speed. It is not always easy to make the transition from slow to fast, however, so let me show you a great way to practise using a metronome (a device that makes appearances in my studio only rarely).

Set the metronome to pulse in quavers at whatever performance tempo you choose. Play each hand by itself in alternation, just the last quaver beat of the bar and stopping on the next downbeat (over the barline). This means play the RH once, then the LH, RH again, LH again, and so on. Do this without stopping, literally without skipping a beat (on one beat the RH plays, on the next beat the LH, etc.).

After several repetitions, without thinking too much, attempt to play the hands together (it is important not to stop beforehand – keep with the metronome!). The chances are you will be unsuccessful on your first attempt, but start the process again with the separate-hand alternations and when you feel ready try again hands together.

Eventually, after many attempts, you will coordinate and you will be able to play the polyrhythm successfully. This may not happen the first day, but persist and eventually, I promise, you will be able to do it without thinking. It’s a bit like learning to ride a bicycle.

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