Naturally, players of single-line instruments never have to worry about poly-rhythms, as long as they can play their own line and not be thrown off by a hearing a different rhythm in other instruments playing alongside. But pianists have to learn to master this challenge since poly-rhythms will need to be played between the two hands.
Over the years I have heard and read a great deal of advice from teachers regarding how to learn to master poly-rhythms. Most of it involves what I would call the "cheater" approach: find the common denominator, go slowly, and just make sure each hand's part comes out mathematically where it should. For example, two against three would mean you divide in 6 "beats" and play one hand on the 1st and 4th, the other hand on the 1st, 3rd and 5th. In this example you'd be hearing notes on beats 1,3,4 and 5, which could also sound exactly like a quarter, two-eighths, quarter. It's metrically correct but doesn't sound the way the poly-rhythm is meant to sound. Many people can eventually learn to do it this way. However, you are not really training yourself to hear the two lines of music independently; you are hearing them combined together. This is a problem if you have to play one line very softly and one louder: if you only can really hear them combined together you can't play them at different dynamic levels. It's also a problem because you can't do any rubato (nuances of time) which is essential in music, especially the kind of music where you are most likely to find these rhythms (again, Chopin and Debussy are two great examples). The "cheater" approach would be next to impossible in unusual rhythms such as two against five (which I am encountering now in learning Debussy's L'isle Joyeuse). The "cheater" method will not result in beautiful, fluid, melodic lines.
Instead, you have to take the path that may take a bit longer initially but will have more musical, and long-lasting, results, which is learning to "hear in stereo," as I like to call it. When you can truly hear the rhythms independently, your brain will essentially get re-wired to be able to play them and you'll never lose the ability. Here's the process:
Start out by tapping with your hands on a table or the closed lid of the piano. Tap what I will call the "unit," which is essentially a beat, in both hands (they are doing identical rhythms at this point). Then divide one hand, let's say the left hand, into normal eighth notes, so it is dividing the beat into two, while the right hand continues with just the beat. Then return to the unit/beat for a few times, and then have the right hand divide in three (triplets) while the left hand continues with just the beat. Keep alternating which hand divides, and returning to the unit/beat in between often to keep reinforcing the unit, which helps you hear how to divide it. Keep alternating, back and forth, until it starts to become easy. At first you may even have trouble doing this step, as one hand will unconsciously want to imitate or fit in with the other hand. Don't try to use a metronome or "cheat" in any way. Just keep doing the process using your own listening skills. It's like the proverbial rubbing your stomach while patting your head (which I have my students do!). At first you can't but eventually the brain figures out how to do it. It's really all about what is happening in the brain.
When you can alternate successfully, then you just let the hands try it together. The process could be like this:
- the unit (hands together)
- RH divides (LH does unit)
- LH divides (RH does unit)
- RH divides (now you're skipping the step of reinforcing the unit)
- LH divides
- RH and LH together, each in their own rhythm
When this begins to work for you, switch hands (do threes in the hand that did twos before and vice-versa).
After tapping becomes easier you can try it on some notes. For example, if the RH is doing triplets, playing the notes C-D-E-F will give you a triplet, ending on the next new beat (which will be F). You must always end on the next beat, so you have a full unit to divide. The LH, doing eighth notes, will do C-D-E, giving you one beat, ending on the next new beat (which will be E). Do the same process you did with tapping, letting the hands alternate as to which one divides, and put them together in the end. The notes themselves may have some dissonance but just listen for the rhythm and don't worry about the notes. Then reverse the hands, as you did with the tapping.
Chopin wrote several Etudes for the purpose of mastering this technique. The Opus Posthumous Etude in A-flat is a great one. But I must emphasize the importance of mastering poly-rhythms with the tapping or with simple notes before you attempt a whole composition. If you play this etude, or any similar piece, with the "cheater" method, it will sound very stiff and ungainly.
If the concept of dividing the beat is unclear to you, read my post entitled "Rhythm"(October 2010) and see how I approach learning rhythm.
I believe that if the brain and ear (the auditory cortex) can "hear" it, the hands can play it. Skip the cheater method and try this elegant approach.