Acoustics & Music Theory
why it sounds like that
Concept

Modal practice — where it appears

Writing or improvising with a scale's own internal hierarchy rather than with the chord functions of tonal harmony. What makes a mode a mode is which degree is home and how the others behave toward it, not which notes are in it.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Maqam Rast, Arabic theory. Maqam Rast, Arabic theory: its degrees in cents above the tonic, drawn against the twelve equal steps of a keyboard. the third and the seventh sit halfway between major and minor — by convention, exactly halfway. Source: the quarter-tone convention fixed at the Cairo congress of 1932.

A scale is not a set of pitches

Two ragas can have identical pitch sets and be different ragas. Two national theories of one maqam put its third degree thirty-five cents apart. Both facts are fatal to the idea that a mode is a collection of notes, and both are ordinary in the traditions concerned.

scales · Beyond twelve Where one interval stops being itself. Identification as a function of interval size: the probability that a listener names each category, modelled as a logistic with the boundary positions and sharpness a study reports. One category's share falls from three-quarters to one-quarter over 24 cents, against the 100 that separate adjacent categories — so the change of mind happens in 24% of the gap and the rest of it is not in doubt at all. That is what makes a mistuned third a third that is out, rather than a different interval.

The ear sorts into boxes, and the boxes are the theory

Slide one note slowly upward against another and the interval between them changes continuously. What a listener reports does not. It stays a minor third, stays a minor third, and then in the space of about twenty cents becomes a major third — and nothing in the sound corresponds to the moment of the change.

intervals · Categorical-hearing Which traditions make the requirements that produce a comma. Four requirements and five tuning traditions. A comma is what is left over when a scale is generated by fifths, the octave is kept pure, and the chain has to close so that any degree can be a tonic — so a tradition that declines any one of them has no comma to hide. The best fifth each system actually contains is printed beside it, because declining a requirement has its own price.

Where the chain was never closed

Eleven earlier essays treat the comma as a fact about music. It is a fact about three requirements — that the scale is built from fifths, that the octave stays pure, and that the chain closes so any degree can be a tonic — and most of the world's tuning traditions decline at least one of them. What they pay instead is computable, and it is paid somewhere else entirely.

scales · The comma

Named alongside it

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

CentsMaqamMicrotonalityCategorical perceptionChain of fifthsEqual divisionIntervalJust-noticeable differenceRagaTemperament

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