Perfect Rhythm

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A drum machine that writes its beats with mathematics and draws them as they play.

What’s going on

Each bar has 16 steps, arranged around the circle like a clock. Four voices play on it: a kick drum, a snare, a hi-hat and bell-like tones from the A minor pentatonic scale. Where each voice hits is not chosen by hand; it comes from a formula, and the formulas turn out to produce rhythms people have played for centuries.

The four modes

Euclidean: Spreads a number of hits as evenly as possible over the 16 steps, using the same algorithm (Bjorklund’s) that times beams in particle accelerators. Musicologist Godfried Toussaint showed in 2005 that these patterns match traditional rhythms worldwide, from the Cuban tresillo to West African bell patterns. Here: 4 kicks, 2 snares, 9 hats and 5 tones.
Polyrhythm: 3, 5, 7 and 4 hits spread over the same bar, so the voices drift in and out of step with each other before meeting again on the one.
Fibonacci: Kicks land on steps 0, 1, 2, 3, 5, 8 and 13, the Fibonacci numbers, so they crowd together at the start and spread out after, like a ball bouncing to rest.
Pentatonic (golden angle): Hits are placed by turning around the circle by the golden angle, about 137.5°, the same spacing sunflowers use for their seeds, so no two land close together.

How to use it

▶ Play (or tap the circle, or press Space) starts the beat; ■ Stop ends it.
− BPM / + BPM change the tempo from 60 to 220 beats a minute (↓ ↑ on a keyboard).
The mode button cycles through Euclidean, Polyrhythm, Fibonacci and Pentatonic (M).

Sound needs a tap first on phones; check that silent mode is off.

Press the share button (top right). It takes a picture of what's on screen and makes a link preview for it. Add a title if you like, then post it to Facebook, copy the link, or send it another way.

Clips: choose a shape (a 9:16 reel or a square) and a length, then Record a clip. The menu buttons hide while it films; press Stop to end early. You can keep playing with the controls while it records. The clip can go on your share page, be saved, or be posted as a Facebook reel.

Each share gets its own page with the picture, the clip if you made one, and a button that reopens this app with your exact settings.

Clips here carry the drums, so a reel plays the beat along with the picture. Turn on Start from the beginning to start the bar from step one as filming begins.

Credits

Euclidean rhythms: Godfried Toussaint, “The Euclidean Algorithm Generates Traditional Musical Rhythms” (2005), after E. Bjorklund’s timing algorithm for the Spallation Neutron Source. All sounds are synthesized live in your browser.

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Made by Jason Buchheim for odd.place.

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