Euclidean Rhythms in Figure

Why haven’t I heard of this before? Did I sleep through the class in undergrad that talked about Euclidean rhythms? Mark Wilson asked about this during an interview with Figure’s project manager, Kalle Paulson over at Fastco Design:

Over each bar is a knob to tweak each instrument’s rhythm (which are based on Euclidean patterns, a mainstay in simple beat creation). “Behind the scenes, there are algorithms at work that distribute these pulses as evenly as possible over a number of slots, in this case 16 slots,”

Smarter than Smart Drums, in my opinion.

Wouter Hisschemöller, along with Ruin and Wesen posted a good article on this back in 2008 based on this great research paper by Godfried Toussaint. (McGill!)

The formula is simple really. It’s an algorithm to distribute an amount of notes as evenly as possible over a period of time, where time is divided in equal parts. A very basic example: Say you have one measure of sixteen sixteenth notes and there are four notes to be played, then this is how those four notes would be equally distributed by the algorithm:

x . . . x . . . x . . . x . . .

A basic house or techno kick drum pattern. There’s four notes on sixteen steps, so the division is easy, 16 / 4 = 4. It gives you one note every four steps. But it gets more interesting when the numbers don’t divide so easily. Take five hits on sixteen steps. Then the pattern becomes more irregular:

x . . . x . . x . . x . . x . .

It’s these irregular patterns that create the best rhythms. Especially when several patterns are combined.

I looked into the app to see if the scale knob obeys these same rules, and it indeed prefers even distribution of tones versus conventional scale/chord logic.

Interestingly, when I first opened Figure I thought I was playing a minor scale, but the song settings indicate major. The default setting for scale is “4”.

The four tones it uses are indeed about as evenly split as 7 divided by 4 can be, which, when put into solfege is:
1- Do
2- Mi
3- Sol
4- La

No leading tones here. Let’s say you’re like me and thought that La was 1 and it’s in minor. To those ears, 1-4 is assigned like this:

1- Do
2- Me
3- Sol
4- Te

In other words, a minor chord with a flat leading tone. So the default setting in this app actually can be perceived as major or minor.

Propellerhead really, truly sweated the details on this app.

Published by

Will Kuhn

I teach music technology to high schoolers. I do some other stuff too. @willkuhn on Twitter.

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