Acoustics & Music Theory
why it sounds like that
Concept

Intonation drift — where it appears

The slow movement of an unaccompanied ensemble's pitch, which follows from tuning each chord purely round a progression that does not close. Measured results describe ensembles steady enough to have a beat to tune by, which excludes a choir with vibrato.

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

Where a progression in pure ratios ends up. A short chord sequence taken in exact whole-number ratios, with the running difference from equal temperament measured in cents. The sequence returns to its starting chord and the pitch does not, which is the comma arriving in ordinary music.

The progression that never comes home

Just intonation is usually said to fail because a keyboard has only twelve keys. That is not the reason. Take one of the commonest chord sequences in tonal music, play every chord in exact whole-number ratios, and it arrives back on its starting chord a syntonic comma flat — on any instrument, including a voice.

harmony · Progression The comma is conserved; only the place it is paid is chosen. Every policy available to a continuous-pitch ensemble on one line: drift per circuit along the bottom, worst mistuned interval up the side. The line is straight and its intercepts are fixed, because the 4 moves of the pump have to absorb 21.51 cents between them however they are shared. Spreading it evenly puts 5.377 cents on each interval — the same narrowing quarter-comma meantone applies to every fifth.

Somebody has to pay the comma

A choir has no frets and no keys, so it can tune every chord exactly — and a common progression sung that way arrives a comma flat, every circuit. The freedom a keyboard lacks turns out to be a freedom about where the error goes rather than whether there is one, and the two costs always add to the same number.

harmony · The comma

Named alongside it

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

Comma pumpJust intonationSyntonic commaCentsProgressionTemperamentTuning by ear

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