Everybody seems to be talking about Euclidean rhythms, but here’s a short explanations on this blog anyway.

The Euclidean algorithm computes the greatest common divisor of two given integers. This is used to distribute numbers as evenly as possible, not only in music, but in applications in many fields of scientific research, e.g. string theory and particle acceleration.

Euclidean rhythms are derived from two values: one that represents the length of the pattern in steps, and the other that defines the hits or notes to be distributed evenly across that pattern. Any remainders are also to be distributed.

Here’s two examples. First: E(2,8), this means a sequence of eight beats and two hits [11000000], where 1 is a hit and 0 represents a rest. Spread out evenly across, it should look something like this [10001000].

A second example: E(5,8), with five hits, [11111000] via [10101011] looks like this after the remainders are distributed as evenly as possible [10110110].

Any two numbers can be combined to generate a semi-repetitive pattern. It’s possible to offset the rotation of the sequence by a certain number of steps. And by playing several patterns with differents lengths and offsets, complex polyrhythms can occur. For example, try playing E(2,8), described as above, together with E(5,16) like this [0010010010010010].