Concept

Bjorklund's algorithm — where it appears

The algorithm that spaces a number of onsets as evenly as a number of steps allows, published for a neutron accelerator and later found to produce named rhythms. It generates a cyclic pattern with no starting position, which is most of what a timeline is.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Six rhythms, all from the same construction. Euclidean rhythms generated by Bjorklund's algorithm, which spreads a number of onsets as evenly as a number of steps allows. The patterns were not transcribed from recordings; they are what the algorithm produces, and the names beside them are where each one is already in use.

As evenly as possible, which turns out to be a famous rhythm

Ask an algorithm to space five strikes over eight beats as evenly as it can. It produces the cinquillo. Ask for three over eight and it produces the tresillo. Nobody told it about Cuba.

rhythm · Euclidean rhythm

One construction, a scale on one side and a rhythm on the other. Both rings are the same computation: k things placed as evenly as possible in n positions. On the left it is 7 notes in 12 semitones, which is the major scale; on the right 5 strikes in 8 steps, which is the cinquillo. The filled positions come from the J-function and the open marks from Bjorklund's algorithm, and they are the same set of positions turned by 9 and 6.

The same algorithm made a Cuban rhythm

Ask Bjorklund's algorithm for seven onsets in twelve steps and it returns 101101011010, which read as pitch classes is the natural minor scale. That function has been producing the tresillo and the cinquillo here from the beginning, and nobody has said that the scale field's central object comes out of it unchanged.

scales · The diatonic set

Named alongside it

The objects these essays reach for when they reach for this one.

Euclidean rhythm Maximal evenness Cycle Diatonic scale Interval pattern Onset pattern Rotation Tresillo

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