Acoustics & Music Theory
why it sounds like that
Concept

Tresillo — where it appears

A pattern of three onsets in the span of eight equal subdivisions, spaced three, three and two. It is the maximally even three-in-eight rhythm, which is the same object an algorithm for evenly spaced leap seconds produces.

Named by 2 essays across one field — 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 pattern, four metres. The same 12-step onset pattern read under 3 candidate metres, each scored by a preference rule set: 3 for a strong position that carries an onset, -2 for one that does not, -1 for an onset that lands off every strong position. The scores are 3/4 -4, 6/8 12, 2/4 -4, so 6/8 wins. The page prints 3/4, which the model does not prefer — it ranks 6/8 above it. Nothing about the sound differs between these readings; the bar line is supplied by the listener.

The time signature is a claim

A bar line is not a measurement. It is a claim about where the accents are, made before the sound exists, and there is a metre-induction model here that can be handed the same onsets and asked whether it agrees. On a hemiola it does not: the page says three and the model says six, by a margin of twelve against minus four. And on a bar of seven the signature is not even a candidate — what decides the reading is the beaming, which the signature does not contain.

rhythm · Notation

Named alongside it

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

Bjorklund's algorithmDownbeatEuclidean rhythmHemiolaMaximal evennessMetreMetrical weightNotationOnset patternSubdivisionSyncopation

All concepts