{"id":6377,"date":"2019-06-13T13:39:00","date_gmt":"2019-06-13T17:39:00","guid":{"rendered":"https:\/\/splice.com\/blog\/?p=6377"},"modified":"2019-08-13T15:41:37","modified_gmt":"2019-08-13T19:41:37","slug":"euclidean-rhythms","status":"publish","type":"post","link":"https:\/\/splice.com\/blog\/euclidean-rhythms\/","title":{"rendered":"What are Euclidean rhythms?"},"content":{"rendered":"

Have you ever felt like math and music are interconnected?<\/h1>\n

If you have, you\u2019re absolutely right – from frequencies to intervals, music is full of values and patterns that can be expressed and analyzed numerically. Euclidean rhythms<\/strong> are one of these many ideas that tie math and music closely together, drawing connections between an ancient algorithm and popular grooves from across the globe. In this article, let\u2019s define Euclidean rhythms, explore their history, and hear them in action.<\/p>\n

Euclid\u2019s algorithm<\/h2>\n

Euclidean rhythms were formally discovered in 2004 by computer scientist Godried Toussaint, but their roots go way back to ~300 BC. Around this time, Greek mathematician Euclid described an algorithm in his text Elements<\/em> that was absolutely revolutionary – it unlocked a systematic method for efficiently finding the greatest common divisor (GCF) of two integers (follow a step-by-step walkthrough of its application here<\/a>).<\/p>\n

What are Euclidean rhythms?<\/h2>\n

Toussaint found that Euclid\u2019s algorithm could be translated to rhythms by using a GCF to distribute a determined number of onsets as evenly as possible across a determined number of steps.<\/strong> If you\u2019re interested in digging even deeper into the details of Euclid\u2019s algorithm and how it relates to music, Toussaint\u2019s paper<\/a> is an excellent resource. If your brain\u2019s feeling a little fried at this point, a picture is worth a thousand words – let\u2019s use some visuals to demonstrate what we\u2019re talking about.<\/p>\n

Softube\u2019s Parallels<\/strong><\/a> is a synth that\u2019s going to come in handy here, since it has a Euclidean sequence generator that allows us to design, hear, and see Euclidean rhythms via an intuitive circular visualization. As we mentioned earlier, a Euclidean rhythm needs a number of onsets<\/strong> that are evenly distributed across a number of steps<\/strong> (per measure). Let\u2019s start with something simple – using the Euclidean sequence generator, we can distribute 4 onsets across 16 steps:<\/p>\n

\"what-are-euclidean-rhythms-gif-01\"<\/p>\n

We can hear how this rhythm sounds by mapping the Euclidean sequence generator to a synth\u2019s filter in Parallels:<\/p>\n

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