Acoustics & Music Theory
why it sounds like that
Generator

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.
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.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 7 of its 7 placements carry sound, built from the same numbers as the drawing, offering these buttons: The rhythm, The scale, in turn.

Called by 2 essays

the blast radius of changing it

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 The sizes a chain of a pure fifth will make. Chains of a pure fifth of two to 12 notes, each folded into one octave and drawn on a 1200-cent line. A chain has exactly two step sizes at 2, 3, 5, 7, 12 notes and three or more at every other size in this range. The five-note and seven-note cases are the chain's pentatonic and its diatonic set, and they are neighbours in a series rather than two separate facts.

The only sizes a fifth will make

Stack pure fifths and fold them into an octave, and at almost every number of notes the result has three or more different step sizes. At 2, 3, 5, 7, 12, 17 and 29 it has exactly two — and at no other size below thirty. The pentatonic and the diatonic set are not two discoveries. They are neighbours in one series, and it is the comma's series.

scales · The diatonic set

All figures · What can be heard