An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. Usually the first overtone is the second harmonic, the second overtone is the third harmonic, etc.

Use of the term overtone is generally confined to acoustic waves, especially in applications related to music. Despite confused usage, an overtone is either a harmonic or a partial. A harmonic is an integer multiple of the fundamental frequency. A partial or inharmonic overtone is a non-integer multiple of a fundamental frequency.

An example of harmonic overtones:

f	440 Hz	fundamental tone	first harmonic
2f	880 Hz	first overtone	second harmonic
3f	1320 Hz	second overtone	third harmonic

Unlike harmonics, overtones are not necessarily exact multiples of the fundamental frequency. Not all musical instruments have overtones that match their harmonics, as described earlier in this note. The sharpness or flatness of their overtones is one of the elements that contributes to their sound; this also has the effect of making their waveforms not perfectly periodic.

Since the harmonic series is an arithmetic series (1f, 2f, 3f, 4f...), and the octave, or octave series, is a geometric series (f, 2×f, 2×2×f, 2×2×2×f...), this causes the overtone series to divide the octave into increasingly smaller parts as it ascends.

The overtones of a sound determine its sound quality or timbre and its spectra.

Contrast with fundamental.

See also

• harmonic series (music)
• just intonation
• xenharmonic
• stretched octave

Source: originally from Federal Standard 1037C, but edited.

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