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Comment by dwringer | Hacker News Reader

A tangent but to anyone reading who isn't familiar, that would be a type of what's known as a Euclidean sequencer (after [0]), and a mechanical one would be awesome but there are some great electronic and software options. Lately I've been messing around with HY-RPE2[1] which I like for the most part; although I would like a bit more flexibility it's still powerful (and limitations breed creativity, as they say).

[0] http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf

[1] https://hy-plugins.com/product/hy-rpewin-mac/

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I also recommend checking out an app called Fugue Machine. It isn’t laid out in a circle but functionally is in this same vicinity. Simple, approachable, and fun (and does MIDI).

Two repeating drum beats running at different speeds isn't quite the same as a Euclidean sequence. (The latter is probably more musically useful.)

That's a good point, I was just kind of assuming the related periodicity which is not a valid assumption to make. But the parent of the post to which I had replied specified whole number ratios between the periods.

Euclidean sequencers can be useful though in that they model a variety of common rhythms, and with tempo synchronized delay they can give forth a whole lot more common rhythms. Though nothing that can't be achieved a million other ways like anything else with music.

Whole number ratios isn't enough to make it a Euclidean sequence; the main thing is that the timing is quantized and events are sped up or slowed down to fit the quantization. So maybe you have 16 beats in the sequence, and some rhythm that happens seven times per sequence. 16 doesn't evently divide by 7, so you get a pattern that's slightly irregular.

Suppose this device had different speed orbitals and implemented some more sophisticated logic like, "if you see a green dot then don't trigger the beat then but hold it back until you see a red dot" then I think you could get behavior that's more like, but not quite the same as, a Euclidean sequencer.

Thanks for taking the time to explain! I got a bit mentally off track I guess, as the additional complexity for all this comes in when the user places tokens in the circular tracks to program rhythms. A euclidean sequencer forces them to be at that quantized equidistant approximation and slightly irregular pattern, which serves as the basis of so much music. But IMHO I haven't really found a way to turn that "theoretical purity" into something practically useful, and I always find myself wishing I could make non-euclidean sequences with it and abuse some of the same abstractions for other purposes.

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