Updating my old badly formatted page of polyrhythms from 2013, adding some things, and hopefully making it easier for more people to read and use. I've written them in the easiest possible form, expressed as 8th notes, 16th notes, or triplets (or compound 8ths) in common meters. I had to do one of them in quintuplets. And I included a check rhythm, with all the notes of the polyrhythm highlighted, and I wrote in how to count the combined rhythm of both parts together, and any rests that would be helpful to count.
The names of the polyrhythms are expressed as a ratio, e.g. 4:3, which would be spoken as “4 against 3.” The second number is the rhythm native to the time signature, and the first number is the cross rhythm. For example, with the 2:3 example in 3/4 time, there are three beats per measure, and the 2 is the cross rhythm.
Top line is the right hand, bottom line is the left hand, on two different instruments. Or use any two limbs you want. Count the combined rhythm of both parts, then play it. You could run a metronome at the grid speed below the staff if any of them give you problems.
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