Polyrhythm is when we have two or more rhythms existing simultaneously. The most commonly used polyrhythms are the “two on three” and “three on two”. Shown below are two examples of polyrhythms.
In figure 1, the left hand is clearly playing the basic pulse of a 3/4 time. The right hand however is playing the pulse of a 6/8 time.
In figure 2, the left hand is again playing the basic pulse of a 3/4 time, also sounding much like a 6/4 time. Whereas the right hand is playing the pulse of a 3/2 time.
Almost every accomplished jazz musician has mastered this technique, and is capable of calling it out anywhere in his or her solo.
A motif may be developed, and repeated as polyrhythms to create an interesting effect. Here is an example.
Notice in figure 3, the original time signature is a 4/4. However the motif has a length of a dotted minim each, giving it a rhythmic structure as shown below in figure 4.
The result is a polyrhythm between a basic 4/4 time and a 3/4 time.
Here is the great youtube jazz pianist Lot2learn demonstrating some use of the “two on three” polyrhythm.