Acoustics & Music Theory
why it sounds like that
Concept

Motor delay — where it appears

The variable lag between the instant a movement is scheduled and the instant it produces a sound. It is one of the two noise sources in a model of a timekeeper, and separating it from timing noise is what makes such a model testable.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

Where the two accounts part company. The spread of the error between the hands, in milliseconds, against bar number, averaged over 120 seeded runs of each model at 100 bars a minute. With one timekeeper it is flat at about 9 ms after 24 bars; with two it reaches 106 ms and is still climbing, because a random walk has nothing to return to. Measured players hold 3 against 2 inside about 25 ms indefinitely.

One player is not two clocks

Two accounts of a pianist playing three against two, simulated from the same noise. With a timekeeper in each hand the hands drift apart by a hundred milliseconds inside two dozen bars. With one timekeeper they never drift at all. The measurement everybody cites as evidence for a timekeeper turns out to be the same number under both accounts.

rhythm · Polyrhythm Two kinds of systematic timing, which share a word. Each measured profile split into a constant offset from the grid and a pattern that varies by position in the bar. Viennese waltz, second beat is −10.0 ms of offset and 33.4 ms of pattern; jazz soloist against the ride is 28.8 ms of offset and 1.9 ms of pattern; quantised is 0.0 ms of offset and 0.0 ms of pattern. A motor deviation anywhere in the 8 to 20 ms range published for skilled performers leaves 74–95% of Viennese waltz, second beat's variation systematic, 1–5% of jazz soloist against the ride's variation systematic. The two quantities are independent and no single deviation figure distinguishes them.

The deviations are not noise

Two published timing profiles, split into the quantities they actually carry. A jazz soloist thirty milliseconds behind the ride is almost pure offset and has no pattern at all. A Viennese second beat is almost pure pattern and has no offset. They are different things, they are reported under one word, and no figure of total deviation tells them apart.

rhythm · Microtiming Two players, and the correction that keeps them together. The spread of the asynchrony between two players, in milliseconds, against beat number, for 3 correction gains, averaged over 120 seeded runs each. It reaches 120 ms after 64 beats at a gain of 0, 27 ms after 64 beats at a gain of 0.1, 20 ms after 64 beats at a gain of 0.3. With no correction at all the asynchrony is a random walk and grows without bound; with any correction it settles at a fixed spread within a few beats and stays there. Two people cannot share a timekeeper, so the fact that ensembles do not come apart is itself the evidence that they are correcting.

Two players and no clock

Two people cannot share a timekeeper, and two independent ones drift a hundred and twenty milliseconds apart inside a minute. Ensembles do not, so something is correcting — and the measurement everybody reaches for recovers the pair's total responsiveness exactly and cannot tell which of the two is doing it. Four tenths from one player and two tenths each give the identical number.

instruments · Microtiming Which ensembles have this problem and which do not. The width of the heard-moment spread built into 7 standard instrumentations, before any player does anything. An ensemble drawn from one attack family has a spread of zero — every note is heard the same distance after it is started, so a common onset is a common heard moment, and this is true of a string quartet and of a gamelan for the same reason and in the same amount. A mixed ensemble carries between 11 and 33 milliseconds of it.

The players who have to be early

Ensembles have been measured for fifty years and found to be about forty milliseconds out of alignment, which has always been reported as the limit of human precision. Part of it is not: an ensemble that mixes attack families carries a heard-moment spread of ten to thirty-three milliseconds before anybody plays a note, and an ensemble drawn from one family carries none at all — which is true of a string quartet and of a gamelan for the same reason.

instruments · Perceptual-centre The distribution that can be measured is not the one the player has. A player aiming at a short note of 100 milliseconds with a standard deviation of 15, against a floor at 100. The pale curve is what the player is doing and the heavy one is what can be recorded, because the 50 per cent of the parent below the floor arrives at the floor instead. The measured mean is 112.0 milliseconds rather than 100 and the measured standard deviation is 9.0 rather than 15. At 160 beats per minute that turns an intended swing ratio of 2.75 into a measured 2.35.

A quantity resting against a wall

The short note of a swung pair was found sitting exactly on the fast edge of the tempo window. If that edge is a floor rather than a fitted number, then every swing statistic computed until now was computed on a censored sample — and a censored sample has a mean that is 0.80 standard deviations too high, a spread that is 40 per cent too low, and a correction gain that can come out twice what the players actually have.

rhythm · Microtiming

Named alongside it

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

Timing deviationEntrainmentMicrotimingRandom walkSwingTempoTimekeeperAttack transientCensoringEnsemble asynchronyExpressive timingGroove

All concepts