How do you spread three beats as evenly as possible across eight steps? The answer, x . . x . . x ., is the Cuban tresillo. Many traditional rhythms from around the world come about this way. The calculator spreads up to 32 beats across up to 32 steps, shows the result as a ring and as a step pattern, rotates it if you like and names it when the pattern is well known.
Spreads beats as evenly as possible across a bar. Many traditional rhythms arise exactly this way – a good template for the step sequencer.
In the generator Step sequencer: number of steps, steps on/off
The ring starts at the top and runs clockwise. The formula: step i gets a beat when (i · beats) mod steps is smaller than the number of beats.
The name comes from Euclid’s algorithm for the greatest common divisor: in 2005 Godfried Toussaint showed that a procedure with the same structure, Bjorklund’s algorithm, generates many traditional rhythms. A shorter formula gives the same patterns, at most rotated by a few steps:
Example 3 beats on 8 steps: i · 3 mod 8 gives the values 0 3 6 1 4 7 2 5 for i = 0 to 7; they are less than 3 at i = 0, 3 and 6, so x . . x . . x .
| Beats | Steps | Pattern | Known as | In the sequencer |
|---|---|---|---|---|
| 2 | 5 | x . . x . | Khafif-e-ramal (Persia) | – |
| 3 | 4 | x . x x | Cumbia (Colombia), Calypso (Trinidad) | 8 steps, 2 times |
| 3 | 7 | x . . x . x . | Ruchenitza (Bulgaria) | – |
| 3 | 8 | x . . x . . x . | Tresillo (Cuba) | 8 steps |
| 4 | 9 | x . . x . x . x . | Aksak (Turkey) | – |
| 5 | 8 | x . x . x x . x | Cinquillo (Cuba) | 8 steps |
| 5 | 12 | x . . x . x . . x . x . | Venda clapping pattern (South Africa) | – |
| 5 | 16 | x . . . x . . x . . x . . x . . | Bossa nova (Brazil) | 16 steps |
| 7 | 12 | x . x . x . x x . x . x | Bembé bell (West Africa) | – |
| 7 | 16 | x . . x . x . x . . x . x . x . | Samba (Brazil) | 16 steps |
x = beat, . = rest. Some patterns sound more familiar rotated; the tile rotates them with “Rotate”.
ModuloOne is a modular synthesizer that runs in your browser: connect modules with cables and hear what comes out. There you choose the number of steps in the step sequencer (8, 16, 32, 64, 128 or 256) and click the beats. If the pattern has fewer steps, it fits in repeatedly when its length divides the step count: four steps four times into 16. Open the generator