A polyrhythm is the simultaneous sounding of more than one rhythm. I find polyrhythms endlessly interesting, mainly because they play with our perceptions, especially our sense of what is foreground and what is background. In this way, polyrhythms are the aural equivalent of those optical illusions you may remember from Psychology 101, such as the faces/vase illusion
and the young woman/old woman illusion.
These optical illusions come to life to the degree that you can bend your perception through them. If there is a “trick” to seeing them the “right” way, it’s to allow yourself to perceptually move among multiple viewing perspectives. Similarly, you can learn to hear the aural illusions of polyrhythms with the same perceptual flexibility. So if you hear a so-called “two against three” beat polyrhythm that superimposes a three beat pattern over a two beat pattern, in your mind’s ear you can foreground the two or the three, or even hear both of them–their rhythmic gestalt as it were–at the same time. And the best way to learn how to hear something is to learn to play it.
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To play a two against three beat polyrhythm here’s what you do. Place your hands on a table top or your thighs and play the following six beat rhythm (“T” = hands together; “R” = right hand only; “L” = left hand only; “-” = a silent count or rest):
Hands Play: T – R L R –
Beat: 1 2 3 4 5 6
Another way to think about the rhythm is:
Long (T) – short (R) short (L) long (R) – [repeat]
If it helps you stay in time, you can count the beats out loud as your hands play the gestalt T – R L R – pattern.
Play this rhythm very slowly over and over again until it feels comfortable in your hands. Next, speed it up, but make sure you keep the six beat structure intact by observing the rests (on beats 2 and 6 of the pattern). You’re playing a polyrhythm! It’s a polyrhythm with a three beat pattern in your right hand and a two beat pattern in your left.
Once you’re comfortable playing the pattern continuously, you can start playing with your perception of it. One way to induce a perceptual shift is to change the loudness of your hand tapping. While playing the pattern, try making your right hand’s dynamic very soft. As you do this, you’ll notice that the “three” of your two against three pattern fades to the background while your left hand’s “two” pattern is foregrounded because it’s louder. Now bring the right hand’s dynamic back up and then try diminishing the volume of your left hand. As you do this, you’ll notice that the “two” of your pattern is now background, foregrounding your right hand’s “three” pattern. The tricky part of this is keeping your hands steady while you play with changing their dynamics. It’s tricky because what your ear hears conflicts with what your hands feel.
Polyrhythms!
You can read more about aural illusions in music here.
brettworks 
Reblogged this on mikejandrews and commented:
Very simple but interesting introduction to polyrhythms. For me this is both the most fascinating and most frustrating aspect of composing compelling pieces of music. I find the idea of altering velocity/accents between polyrhythms an effective way to grapple the listener and confuse them with their own perceptions of the foreground and background. The concept of tricking the listener into expecting a certain pattern but receiving another entirely is something I yearn to include in my own compositions.