Euclidean sequencers in modular distribute a set number of triggers evenly across a pattern length to generate rhythmic patterns quickly

A Euclidean sequencer is a trigger generator where the operator specifies a length (number of steps) and a density (number of trigger events). The sequencer distributes the triggers as evenly as possible across the steps using the Euclidean algorithm — the same process that produces well-known world rhythms. Length and density can be prime numbers, producing non-repeating cross-rhythmic patterns. An offset parameter shifts where in the cycle the triggers begin. In Eurorack, Euclidean sequencers provide a fast way to generate dance-floor-ready rhythms without programming individual steps. They complement clock dividers and can be layered to create polyrhythmic patches.

Examples

Length=8, Density=3 produces E(3,8)=[x..x..x.] — the tresillo. Length=16, Density=5 produces a cinquillo-derived kick pattern. Offset by 1 shifts the pattern by one step.

Assessment

Set up a Euclidean sequencer with length 16, density 5, and describe the resulting pattern. Then change density to 7 — predict whether the pattern repeats or creates a longer cycle.