Why two steady rhythms can fight and still groove: the hidden grid of 3 against 2

30seconds
Tap a steady beat with one hand and three evenly spaced taps in the same time with the other, and you get a 3:2 polyrhythm: two perfectly regular clocks that only agree on the downbeat.
Why does it feel so strange? To write it down you need a hidden grid of six slots, the smallest number both 2 and 3 divide into. The rhythms share only slot 0, and what you hear is four uneven hits, the "nice cup of tea" pattern.
Play with the rings, change the numbers to 4:3 or 5:4, and watch the grid grow to the least common multiple of the two counts.
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