Euclidean rhythms are based on a neat math trick and cosmic coincidence promoted by Godfried Toussaint at McGill University in Canada. In short, you take a pattern length – such as 16 – and a number of beats – such as 6 – and spread those beats out across the pattern using an algorithm based on mathematician Euclid’s Elements (circa 300 B.C.). The results are rhythmic patterns that closely or exactly matched many world music styles – in particular, from Sub-Saharan Africa, and especially if you rotate them in time to change where the downbeat falls.
For example, 6 into 16 (notated “6,16” or “3,8”) creates a pattern like this:
1001001010010010
The pattern above is the same as the Cuban Tresillo, considered “the most fundamental and most prevalent duple-pulse rhythmic cell in Sub-Saharan African music traditions.”
Several modules exist that are based on Euclidean rhythms; since the algorithm is easy to compute, they also appear as an extra feature in other modules including Mutable Instruments’ Grids and Yarns, ALM’s Pamela’s New Workout, as well as the DIY Ornament & Crime.
The most well known of the dedicated Euclidean rhythm modules is vpme.de’s Euclidean Circles. It creates either three or six independent sequences at once, with multi-function controls to set the sequence length, pattern (fill), and start point. It can also save and recall 16 presets. For alternate takes on this theme, check out Rebel Technologies’ full-featured Klasmata and Stoicheia, or the simplified 2hp Euclid and Hikari Instruments Eucrhythm. Pictures of many of these as well as more details appear on pages 301 & 301 of Patch & Tweak.
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