Rings, steps and hits
Each ring is one bar. Steps divides it into equal slots, hits says how many of them sound, and the generator spreads the hits as evenly as it can. That's the Euclidean rule, written E(hits, steps). The polygon inside each ring connects its hits, so an even pattern looks like a regular shape and a syncopated one looks lopsided.
All rings take the same time to go round, however many steps they have. A 3-step ring therefore plays triplets against a 4-step ring's quarter notes, and that is all a polyrhythm is: different equal divisions of the same span, sounding together.
Patterns to try
- E(3,8) tresillo, the habanera and reggaeton rhythm
- E(5,8) cinquillo, Cuban and Brazilian
- E(5,16) shifted close to the bossa nova clave
- E(7,12) the West African bell pattern
- E(4,4) + E(3,3) 4 against 3
Questions
What is a Euclidean rhythm?
A Euclidean rhythm spreads a number of hits as evenly as possible over a number of steps. E(3,8), three hits over eight steps, gives x..x..x., the tresillo. E(5,8) is the cinquillo, E(4,16) four on the floor. Godfried Toussaint showed in 2005 that this one rule produces a large share of the traditional rhythms of the world, from Cuban clave to West African bell patterns.
How do I make a polyrhythm?
Give two rings different step counts and fill every step: 3 steps with 3 hits against 2 steps with 2 hits is the hemiola, 3 against 2. Both rings take the same time to go round, so they meet on the downbeat and drift apart in between. The ratio in the middle of the circle shows what you have.
How do I play it on my drum machine or in my DAW?
Press Connect MIDI and choose your drum machine or a virtual port (IAC Driver on Mac, loopMIDI on Windows). The hits go out on channel 10 with General MIDI drum notes: kick 36, low tom 45, woodblock and rim 37, clap 39, closed hi-hat 42. To keep the pattern, press Download .mid and drag the file onto a drum track.
What does Shift do?
It rotates the pattern by one step, so the same hits start somewhere else in the bar. Rotating the hi-hat by one step turns on-beats into off-beats; rotating a clave pattern turns a 3-2 son clave into a different-sounding but related rhythm.
Does it keep time with my DAW?
Not yet: it runs on its own tempo and does not follow MIDI clock. For a locked groove, download the .mid file at your project tempo and use it in the DAW.