Acoustics & Music Theory
why it sounds like that
Concept

Mistuned partial — where it appears

A component of a complex tone that is not a whole multiple of the fundamental. About one per cent off is enough for it to be heard as a separate sound rather than as part of the note, which turns inharmonicity from a fact about a spectrum into a count of how many partials fuse.

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

Partial 3, mistuned by 3%. A 10-partial tone on 220 Hz with one partial treated differently from the rest. Mistuning it moves it off the harmonic grid by 3.0 per cent, which is 19.8 Hz — slow enough to be heard as a beat rather than as a separate pitch, and enough for the partial to be heard out of the note as a whistle of its own. An onset difference does the same to a partial that is exactly in tune.

What makes two partials one note

A note is a stack of ten or twenty simultaneous tones and is heard as one thing. The obvious explanation is that they are whole-number multiples of a fundamental — and the obvious explanation is not sufficient. Mistune one partial by three per cent and it leaves the note; give a perfectly harmonic partial a thirty-millisecond head start and it leaves too. Shared behaviour beats arithmetic.

timbre · Auditory scene How much of each spectrum a listener can assemble into one note. Each partial of each spectrum at the harmonic number it is nearest, against the whole-number series that fuses the most of them, with anything more than 1 per cent out marked as heard separately. an ideal string keeps 10 of 10; a piano string keeps 9 of 10; a bell keeps 7 of 8; a bar keeps 2 of 6; a kettledrum keeps 3 of 5. The fundamental is capped at a tenth of the top partial, and the cap is load-bearing rather than tidy: a bell's ratios are all whole multiples of a tenth, so an unconstrained search finds a fundamental twenty-five harmonics down, calls every partial exact, and reports that a bell fuses perfectly. Nothing that high is resolved and the low harmonics of it are not there.

The spectrum that will not fuse

A partial about one per cent off its harmonic is heard as a sound of its own rather than as part of a note. Apply that criterion to a whole spectrum instead of to one mistuned component and it becomes a count: a piano string keeps nine of its ten partials, a bell keeps seven of eight, a bar keeps two of six. The physics of inharmonicity has had an essay here for a long time. This is what it sounds like.

perception · Auditory scene

Named alongside it

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

FusionTimbreAuditory scene analysisBellCommon fateHarmonicityHearing outInharmonicityPartialSimultaneitySpectrum

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