Harmonics, partials and overtones
Pitched sounds are built from sinusoidal components. The strengths of these components decide the timbre, and the words used for them are often confused.
Three words
- Partial: any sinusoidal component of a sound.
- Harmonic: a partial whose frequency is a whole-number multiple of the fundamental.
- Overtone: any partial above the lowest one. The first overtone is the second partial.
For a note with fundamental f, the harmonics are f, 2f, 3f and so on. For an ideal vibrating string or an open pipe, all partials are harmonics. For bars, bells and drums they are not, and the sound is less clearly pitched.
The harmonic series
| Harmonic | Frequency (fundamental 110 Hz) | Interval above the fundamental |
|---|---|---|
| 1 | 110 Hz | fundamental |
| 2 | 220 Hz | octave |
| 3 | 330 Hz | octave plus fifth |
| 4 | 440 Hz | two octaves |
| 5 | 550 Hz | two octaves plus major third |
| 6 | 660 Hz | two octaves plus fifth |
| 7 | 770 Hz | about two octaves plus a flat minor seventh |
| 8 | 880 Hz | three octaves |
The intervals narrow as one goes up: harmonics 8 to 16 span one octave. As a result, there are many more harmonics per octave at high frequencies, which is why the upper part of a sound is dense.
Not quite equal temperament
Harmonics follow exact whole-number ratios, which differ slightly from the tempered scale. The 3rd harmonic is 2 cents sharper than the tempered fifth; the 5th is 14 cents flatter than the tempered major third; the 7th is 31 cents flatter than the tempered minor seventh. See the harmonics tool for the full series with cents.
Inharmonicity
Real stiff strings, as in a piano, have partials that are slightly sharp of the exact multiples, increasingly so for the high partials. Piano tuners stretch the tuning, making the octaves slightly wider than 2:1, to match them. Bells and drums have partials that are not related to the fundamental by simple ratios, and so are perceived as less clearly pitched.
The missing fundamental
The ear can hear the pitch of a harmonic series even when the fundamental is absent, because the spacing between harmonics equals the fundamental frequency. This is why small loudspeakers that cannot reproduce 60 Hz can still convey a bass line: the harmonics at 120, 180 and 240 Hz suggest the pitch.
Pitch and level
For pure tones, pitch can shift slightly with level, low tones going lower and high tones higher as the level rises. The effect is small for musical sounds and mostly of interest in perception research.
Timbre
The relative strengths of the harmonics, together with how they change in time, make an instrument recognisable. A clarinet has mainly odd harmonics at low register; a sawtooth wave has all of them. See Formants, vowels and timbre.
Draft: written by an AI assistant, awaiting technical review.
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