How do you count a polyrhythm like 3 against 4?

Press "With the counting grid," then "Both voices," and try tapping along.

Challenge: Find a polyrhythm with a counting grid of 20 pulses or more that only lines up on beat one. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Two patterns line up whenever both have reached a whole number of notes. The first time that happens is the least common multiple:

$$\operatorname{lcm}(a, b) = \frac{a\,b}{\gcd(a, b)}$$

For a polyrhythm, divide the bar into that many pulses. Voice A plays every $\operatorname{lcm}/a$ pulses and voice B every $\operatorname{lcm}/b$. For a polymeter, the loops share a beat and start together again after $\operatorname{lcm}(a, b)$ beats. The shaded columns show where both land together. That happens $\gcd(a, b)$ times per bar in a polyrhythm.

Pick the two numbers and the kind. Press "With the counting grid" and count the pulses, then switch to "Both voices" and try to hear it without the grid.

• Start slow. Change the tempo in "More settings."