Acoustics & Music Theory
why it sounds like that
Concept

Expressive intonation — where it appears

Playing a note deliberately away from its nominal pitch for musical effect — a leading note sharpened toward its goal, a third narrowed to sound pure. It is possible only where a performer controls the pitch continuously, so it exists for voices and strings and not for keyboards.

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

How far each system sits from equal temperament. Deviation from equal temperament, in cents, for each degree of the chromatic scale. Zero is equal temperament by definition; the just major third is about fourteen cents flat of it and the Pythagorean major third about eight cents sharp.

The note that is sharp because of where it goes

Eleven essays here have tuned notes against other notes sounding at the same time. A melodic line makes the opposite demand of the same note. In C major the leading note wants to be 1088 cents if the argument is vertical — a pure third above the dominant — and 1110 if it is horizontal, because a leading note is a note that is about to arrive somewhere and performers narrow the step. The two answers differ by 21.5 cents, which is a syntonic comma exactly, and no keyboard has ever been able to hold both.

tuning · Melody How far equal temperament puts each interval's coincidence out. For each interval, the pair of partials it brings together and how many cents equal temperament mistunes that coincidence by. A fifth's third-against-second is out by 2 cents and a major third's fifth-against-fourth by 14 — so the same temperament that is inaudible on a fifth produces, at 220 hertz, a beat of 8.7 per second between two sections singing a third, with every singer in both of them perfectly in tune.

A section against another section

The choir has been treated as a unison, and no choir sings only unisons. Two sections an interval apart beat between partials rather than between fundamentals — the third brings the fifth partial of one against the fourth of the other — and equal temperament puts that coincidence fourteen cents out. So two sections singing a tempered third beat at nearly nine per second with every singer in both of them perfectly in tune, and the same temperament is inaudible on a fifth.

timbre · The voice

Named alongside it

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

Just intonationBeatingCentsCritical bandwidthDifference limenEqual temperamentIntonationLeading toneMelodic intervalPartialPythagorean tuningRoughness

All concepts