It’s not “pseudo-”!
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Have I got this right ?
- Euclidean Rhythms is a term defined in 2005. As defined in the original paper, this is not at all the same thing as Polyrhythm because it’s all about “distributing [k] beats within [n] time steps”.
- More recently than that, some polyrhythm implementations have been mis-described (if you take into account the 2005 definition) as ‘Euclidean’.
If I’m right about the timing of those two things, the Elektron (and Torso) description of Euclidean is more correct (prior claim to the term), and any sequencing algorithm that places notes OFF the equally divided beats in a bar may or may not be polyrhythmic, but certainly is not Euclidean.
Is that fair ?
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Yes, that is correct.
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I came for the philosophy, not the math.
Cheers!
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This sounds exactly like what I’d be into.
k/n. Give me 5 beats into 16 steps.
3.2 steps between beats. 
The whole idea about sticking to integers seems kind of arbitrary to me when we have things like micro-timing, swing, rubato, etc.
Alternatively, I could take this rigid definition of euclidean sequencing and do:
5 beats into 160 steps. 32 steps between beats. But play the tempo 10x as fast.
It seems more a matter of resolution and quantization that’s commonly applied but not a necessary feature of being a euclidean rhythm from where I am standing.
The whole idea about sticking to integers is what qualifies it being called Euclidean. It’s perfectly fine to not stick to integers, but if you do that, you’ve strayed away from Euclidean, according to the definition of the guy who invented the term.
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It’s kind of strange that when someone is telling you they’re going to deliver apples, you expect oranges, and then when they deliver apples, you keep on insisting that they should have delivered oranges 
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I don’t understand why anyone needs the word “Euclidean” to apply to equally-spaced beats when the perfectly good and well-established word “polyrhythm” exists. Did anyone do this before the 2005 paper repeatedly referenced here? No. It’s a misapplication of terminology which, granted, is a bit of a stretch in the first place, but at least with reasonable historical+mathematical foundation.
As for sticking to integers, the Greeks were peculiar this way. Or integer ratios. Euclid did give a proof that the square root of 2 was not an integer ratio, but he was fairly late in the game. There is a myth that someone in the Pythagorean school demonstrated this and was quietly dropped overboard while at sea. Probably untrue, but it was a freaking cult. As are many things these days, including many we talk about here.
And Euclidean rhythms are not a major advance, or a unifying philosophy. They’re an interesting technique. It’s fun to turn a knob and change things to a different complex rhythm. Is it the best one possible? Absolutely not, but it’s not a bad one given how easy it is to move on when you’re tired of it.
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It’s kind of strange that when someone is telling you they’re going to deliver apples, you expect oranges, and then when they deliver apples, you keep on insisting that they should have delivered oranges
There’s not a lot of ambiguity on what an Apple is.
All sides here have expressed there being a sizable amount of confusion on this subject out there. I’m just trying to understand it better by poking at the stated constraints. I don’t think there’s anything wrong there.
If its the integer issue, I don’t understand why my example of 5 beats over 160 (x10 tempo) - isn’t completely within the confines of this.
Am I being argumentative? Sure. But unlike this comment, I am at least attempting to add to the conversation with some effort. If my intentions seem elsewhere, I apologize.
One side seems to be confused, yes, but there should not be any ambiguitiy about what Euclidean in electronic music sequencing is refering to. To name some manufacturers and their products who interpret it (and use the term) the way Elektron has:
- VPME - Euclidean Circles
- Expert Sleepers - Disting
- ALM Busy Circuits - Pamelas Workout
- 2hp - Euclid
- Torso Electronics - T-1
Edit: And how could I forget Squarp and their Pyramid 
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5 beats over 160 is equal spacing, because 160 is divisible by 5. But 160 is pulled out of thin air. Why not 5 beats over 5? You are as likely to find a division of a bar into 5 as one into 160 in a given sequencer.
The original application, for timing components of the control system in a particle accelerator, was for even spacing when the clock rate was already fixed by the system. As in, an Elektron sequencer with a focus on sixteen steps (and 2-4 multiples thereof).
Elektron could have provided basically-near-equal spacing (I admit the possibility of some error due to software constraints) but they, probably rightly, judged that the on-beat timing of the “Euclidean” approximation to equal spacing would be of more interest.
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well the technical terms regarding this simple math are certainly straight forward cause they are called “slot” and “pulse”. Where slots are positions a pulse can be placed on. That is you place pulses on a fixed amount of available slots. For Electron machines the available slots would be 16 per 16 steps with a fine grid of (-24 or +24)th of a step per slot. Which also means there are pulses that do not fit on the grid of slots so the slots are either changed or the pulses adapted to fit. And how that is done can be completely different depending on the application. In example: 5 pulses on 16steps is likely a pulse each (153,6th tick). Programming those is very tedious. The whole things is just a convenience method to place the pulses and what to do if the grid can’t express it directly on its slots or “fine-slots”/microtiming/retrigger-timing.
ps: Where slots are not what Electron OS’es mean when something is called slot.
ps: before we had microtiming we did simply a maximum of 16pulses on 16slots or 16pulses on 32slots with twice the pattern speed and so on…
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Very interesting stuff. I read that paper finally. Thanks for this, and the continued good faith responses.
I’ll end with this:
I’m not trying to be a stick in the mud. For real. I came here not knowing much, with a loosely pre-conceived idea of equal spacing that I got from, idk, the ether maybe.
You can still see the phrase “equal spacing” in the top 10 search results for euclidean sequencing, so its not as clear cut of a concept across the masses as it could be. I’m just defending myself on it not being immediately clear what I was getting with the update (which was free, awesome and still appreciated.)
I can definitely accept that terms are what we make of them, and if the general consensus / initially defined examples are fitting those steps into the nearest reasonable sub division, I can tailor my expectations.
I had a vague idea of polyrhythms before but now I definitely need to explore those concepts more because I’ve gotten pretty excited about the potential for strange and unique groove generation more than rhythmic pattern generation.
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I was really gonna end with my last post but for the sake of clarity and posterity for anyone browsing, the micro-timing “fine-slots” are not used in this current implementation on Rytm.
This is kind of what started the whole thing for me. I thought they would be.
My bad if I misunderstand ya. It sounded like you thought it would snap to the nearest fine time resolution.
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have no access to the modernised OS of the Rythm, cause working still on classic Octatrack but for most “Euclidean” sounds very complicated, it just refers to his discoveries that at in example on a circle some angles in repetitive pattern add up perfectly or with multiple cycles still add up on the same angle it started. That is why “evenly spaced” comes into the wording… despite that is utterly the opposite of Euclid discoveries, it’s nothing to bother. You did use it anyway all the time already but not in all possible combinations of those simple rules.
Microtiming: the term used by Electron for the fine grid of each step applies to one step (pulse) therefore having something that helps you placing pulses outside your classic 4 on the floor is and makes most rhythmic talk very musical (again). Suddenly you can play 5/4 takt or 5/8 on a 4/4 takt and enjoy the polyrhythmic on all repeats(pulses) until all pattern reach their 1st position together again, what we usually call “on One”. In example thinking of african rythms like 12/5th takt (kiki-lambe) which sounds very driving forward.
Edit: maybe one word that fits much better here that is it is all just about “proportional” timing.
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This is what IO Labs Flux does, it’s very cool https://www.iolabs.co.uk/.