Euclidean rhythms distribute a fixed number of pulses as evenly as possible across a fixed number of steps. Many traditional patterns (clave families, West African bells, Middle Eastern rhythms) can be expressed this way.
Concept
- E(k, n): place k hits in n slots with near‑equal spacing (alternating floor(n/k) and ceil(n/k) gaps).
- Examples: E(3, 8) ≈ a tresillo‑like 3 in 8; E(5, 16) is a staple techno groove; E(7, 12) resembles common bell timelines.
- Rotation: shifting the start point yields new feels while preserving evenness.
Bjorklund algorithm (intuition)
- Repeatedly group longer and shorter gaps to approach equal spacing.
- Result is the “maximally even” arrangement for the given k and n.
In the DAW
- Many sequencers provide Euclidean generators; otherwise, program by counting consistent gap sizes.
- Use rotation to find the best pocket for your groove (e.g., move the first hit by a step or two).
- Combine with polymeters: different E(k, n) loops of unequal lengths create evolving textures.
- Morph parameters: automate k from 3→5→7 while holding n constant to sweep the density musically.
Sound design and feel
- Short, percussive voices show the evenness clearly; longer notes blur into hypnotic textures.
- Add swing or tiny micro‑delays to avoid mechanical stiffness—Euclidean does not have to be rigid.
- Delay tricks: dotted or triplet delays against a straight Euclidean line produce lush polymetric echoes.
Examples (16-step)
- Use the sequencer below to dial in any E(k, n) pattern. The grid selector swaps between 8/12/16-step canvases, the pulse slider changes k (density), and the rotation slider offsets the start point without changing the evenness.