EXAMPLE 1
Tresillo
E(3,8)
x..x..x.
Three accents across eight steps produce a familiar syncopated cell that works for kicks, bass and hand percussion.
Rhythm generator
Euclidean Rhythm Generator
Distribute a chosen number of hits as evenly as possible across a sequence, rotate the result and audition patterns before programming them in your DAW.
FreeNo loginWorks offlineWeb and desktop
Core formula
E(k,n): k hits distributed across n steps
hit(i) = ((i × k) mod n) < k
rotated(i) = base((i - rotation) mod n)
step (ms) = (60,000 / BPM) × (4 / note denominator)
Amanita uses x for a hit and . for a rest. Different generators may display the same rhythm with a different rotation.
What is a Euclidean rhythm?
A Euclidean rhythm places k pulses across n steps with the most even spacing available. The notation E(k,n) means k hits distributed over n positions; rotation changes the starting point without changing the spacing structure.
These patterns appear naturally in many musical traditions and are useful for percussion, arpeggios, modulation and layered polymeters. Amanita lets you hear the result at the BPM shared with the Tempo tool.
Worked examples
Concrete values you can verify in the calculator and transfer directly to a production session.
EXAMPLE 2
Five over sixteen
E(5,16)
x...x..x..x..x..
A spacious five-hit pattern that can sit over a conventional four-beat loop without repeating too quickly.
EXAMPLE 3
Dense eight-step groove
E(5,8)
x.x.xx.x
Five hits create alternating gaps and a compact rhythm suited to hats, claps or melodic triggers.
| Pattern | Sequence | Density | Typical use |
|---|---|---|---|
| E(3,8) | x..x..x. | 37.5% | Tresillo / kick layer |
| E(4,9) | x..x.x.x. | 44.4% | Asymmetric percussion |
| E(5,16) | x...x..x..x..x.. | 31.3% | Sparse long cycle |
| E(7,12) | x.x.x.xx.x.x | 58.3% | Dense 12-step phrase |
Use it in a session
The calculator is deliberately direct: set the musical context, inspect the result and copy it where you need it.
- Set the number of stepsChoose a cycle length from 1 to 16 positions.
- Choose hits and rotationIncrease the pulse count, then rotate the sequence until the downbeat feels right.
- Select the step valueAudition the pattern as eighths, sixteenths or another subdivision at the current BPM.
Where it helps
Percussion
Build balanced kick, clap, rim and hand-percussion layers.
Polymeter
Place a 9- or 12-step pattern against a conventional 16-step loop.
Modular sequencing
Use hits as triggers for envelopes, samples or clocked modulation.
Arrangement variation
Rotate one pattern between sections while keeping its internal spacing.
Studio note: When layering patterns, leave different amounts of space in each one. Two dense Euclidean sequences can mask each other even when their mathematics is elegant.
Calculate it in Amanita
Open the exact tool with your saved tempo and tuning values intact. Nothing to install, no account and no ads.