Acoustics & Music Theory
why it sounds like that
Concept

Canon — where it appears

A texture in which one voice is accompanied by a delayed copy of itself, at a stated delay and a stated transposition. Whether a tune works as one is decidable before anybody sings it, by scoring the simultaneities every delay produces.

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

Twelve stages, and the composer chose the rule. Every rotation of a 12-step pattern with 8 onsets against the unrotated original. Each row is one stage of a phase piece: the filled cells are what is heard when the two parts sound together, and the count beside it is how many of the two parts' onsets coincide. The number of stages is the length of the pattern, so the length of the piece is arithmetic.

A process that enumerates its own form

Take a twelve-step pattern, play it against itself, and move one copy along by one step at a time. The piece is over when the copy returns to where it started, so its length is twelve — arithmetic, not a decision. What is heard at each stage is the union of the two parts, and nobody composed any of it.

rhythm · Polyrhythm Every delay, scored — a round and a tune that is not one. Mean Plomp-Levelt roughness of the simultaneities a tune makes against a copy of itself entering a whole number of bars later, for Frere Jacques and Twinkle, twinkle. The two do not overlap: the worst delay of the first is smoother than the best delay of the second. The model sees roughness and nothing else — no voice leading, no parallels, no distinction between a passing dissonance and a structural one.

A melody that can accompany itself

Whether a tune works as a round is decidable before anyone sings it. Score every simultaneity it makes against a delayed copy of itself, at every delay, with the roughness model already in use, and two nursery tunes separate completely — every delay of one is smoother than every delay of the other. What the scan does not do is pick out the entry the tradition uses, and that refusal is the most informative thing in it.

harmony · Voice-leading

Named alongside it

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

CounterpointCycleEuclidean rhythmHarmonic rhythmOnset patternPhase shiftingPlomp–Levelt curvePolyrhythmRepetitionResultant patternRotationRoughness

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