KUMO – SOUTH AFRICAN EUCLID

Video for the very succinct @kingkoomz.

“One of the many things that Euclid, the 4th century BC Greek mathematician and the Father of Geometry, left us is the first algorithm: a method to compute the greatest common divisor between 2 given integers. The algorithm is used in particle physics and computer science, but in 2005 Canadian mathematician Godfried Toussaint noticed something extraordinary when he applied it to musical rhythm. Using the algorithm to distribute beats and silences as evenly as possible in a bar generates almost all of the most important world music rhythms, from Sub-Saharan African music in particular. For example, if you have a bar with 8 pulses and you want to have 5 beats in that bar, the way the algorithm places the beats gives us the Cuban “Cinquillo” rhythm, which has its roots in West African music.

Available from https://sound-space.bandcamp.com/album/euclidean-patterns (or search Bandcamp for Euclidean Patterns)

Available from the EP: Euclidean Patterns
https://sound-space.bandcamp.com/album/euclidean-patterns

One of the many things that Euclid, the 4th century BC Greek mathematician and the Father of Geometry, left us is the first algorithm: a method to compute the greatest common divisor between 2 given integers. The algorithm is used in particle physics and computer science, but in 2005 Canadian mathematician Godfried Toussaint noticed something extraordinary when he applied it to musical rhythm. Using the algorithm to distribute beats and silences as evenly as possible in a bar generates almost all of the most important world music rhythms, from Sub-Saharan African music in particular. For example, if you have a bar with 8 pulses and you want to have 5 beats in that bar, the way the algorithm places the beats gives us the Cuban “Cinquillo” rhythm, which has its roots in West African music.

The examples are endless: 13 into 24 gives us a whole series of rhythms used by the Aka Pygmies of the upper Sangha. Euclid lived his entire life in Alexandria in Egypt, and Herodotus said that the basis of Greek culture was African. Maybe there’s another strand to that relationship we’ve only just uncovered.

The 3 tracks on this EP use all the Euclidean rhythms in bars of 9, 12, and 13, but going further, as the algorithm is used to generate the harmony too. Chords and modes can all be derived by spacing the notes across the octave, for example, 6 distributed evenly across 12 generates a whole tone scale.

This is no dry mathematical exercise, as each set of rhythms and harmonies have their own strong characters: African, Middle-Eastern, and Balkan; the foot-stomping music of Hamilton Bohannon; atmospheres from the red earth of South Africa, the architecture of Ancient Greece, or sounds from the streets of South London. No single place or time in particular, but delving into the principles behind so much of the world’s culture, and bringing a strange familiarity to the stunningly fresh.

Original Euclidean artwork by Sayako Sugawara All the tracks written, recorded, mixed, and mastered by Kumo under lockdown conditions in South London, May-June 2020. releases August 14, 2020
credits
releases August 14, 2020

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KUMO – SOUTH AFRICAN EUCLID