Acoustics & Music Theory
why it sounds like that
Concept

Hemiola — where it appears

A passage in which the notes group in a ratio of three to two against the printed metre, most often two bars of triple time played as three of duple. It is the clearest case of a bar line making a claim about accent that the onsets contradict.

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

3 against 2. Two evenly spaced pulses over the same span, one in 3 and one in 2. They agree only where both grids land together, and the gap between agreements is the least common multiple — which is what makes one polyrhythm sound like a shape and another like two unrelated things.

Two clocks at once, and where they agree

Three against two repeats every six subdivisions and feels like a figure. Seven against five repeats every thirty-five and feels like weather. The difference is one number.

rhythm · Polyrhythm 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.

Cross-rhythmDownbeatEntrainmentLeast common multipleMetreMetrical weightNotationPolyrhythmSubdivisionSyncopationTresillo

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