I'm bogging down in a couple of very wordy pieces, so a little light fare today— just a page of two-voice polyrhythms written out in the simplest possible form. They are written in the form of a ratio: x:y— meaning, x number of evenly spaced notes played simultaneously with, and in the same space as, y number of evenly spaced notes. I only ever use 3:2 and 4:3 in actual playing, but it's fun to fool with the further-out ones, too. These should be playable by anyone with a basic grasp of 16th note and triplet/compound-meter rhythms:
We've got all non-reduceable combinations between 2 and 8, except 7:5, because, well, it didn't fit on the page, and the shortest way to write it without resorting to quintuplets or septuplets is:
...and without the measure of 5/8, it would take seven measures of 15/8 to resolve to a unison on beat 1. Kind of a nightmare.
Play these first with just the hands (playing different sounds), and then with all other combinations of limbs. You could also add a third limb playing the downbeats, or on every beat, or every two beats. Or on the major subdivision of that exercise— 8th notes, triplets, or 16th notes. Whatever works. I don't believe there's any special need to become very fluent with many of these, or to worry about bringing them into your actual playing, but working through them does improve your understanding of rhythm and meter.
I'll give you the steps for writing your own patterns in a few days.
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