Acoustics & Music Theory
why it sounds like that
Concept

Quantisation — where it appears

The rounding of a continuous quantity to a grid, which is what notation does to timing and what a heat map does to a measurement. What it removes from a performance is the microtiming, which is most of the style.

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

Where the beats actually fall. Measured timing deviations from a strict grid, in milliseconds, for three published profiles. The right-hand column converts each deviation into the note value it would have to be written as, at three tempi — and because a fixed number of milliseconds is a different fraction of the beat at every tempo, no single notated rhythm describes any of these.

The milliseconds that are the groove

A Viennese orchestra plays the second beat of a waltz about fifty milliseconds early, every bar. A jazz soloist sits thirty behind the ride cymbal. Neither deviation can be notated, and not because notation is coarse — because it measures the wrong quantity.

rhythm · Microtiming Redundancy in bits, and why the number needs a length beside it. Left: the LZ78 cost of each scheme divided by the cost of sending the same symbols flat, against how many bars are sent, with each bar coded as its chord and key. Every scheme is above 1 at a single chorus — the coder loses — and every one falls under it as the piece runs. Right: new dictionary phrases per bar at one chorus, which is the statistic that survives at short lengths.

How much of this is new

Repetition can be counted rather than looked at. Feed a piece's bars to a compressor and the bits it needs are a measure of how much of the piece is a repeat of an earlier part of itself. The measurement works, the number is real, and it turns out to be a statement about the description rather than about the music — which is the most useful thing it has to say.

form · Repetition The same steps, counted by the clock. The step distribution of Ode to Joy and Twinkle, twinkle counted two ways: once per interval, which is what every earlier figure did, and once weighted by how long the note it leaves is held. The two disagree because a tune's long notes are not distributed evenly over its interval sizes — in Ode to Joy the 2-semitone step is 55.2 per cent of the moves and 60.0 per cent of the time. Which of the two a claim about melodic motion means has never been stated here, and the answer matters most exactly where a tune slows down, which is at the ends of its phrases.

The note that has a length

Every melodic figure so far reads a table where each note is a pair — a pitch and a duration — and throws the second number away. A step between two minims and a step between two quavers have been one event in every histogram it has drawn. Weighting the same statistics by time moves the step distribution by up to seven points, changes forty-four of a hundred and one contour signs, and turns up an off-by-one in the one figure that did use the durations: it took the length of the note arrived at where the time between two onsets is the length of the note left.

rhythm · Melody

Named alongside it

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

NotationContourDescription lengthDurationExpressive timingGrooveInter-onset intervalMelodic intervalMicrotimingNull modelOstinatoRedundancy

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