An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency.
Use of the term overtone is generally confined to acoustic waves, especially in applications related to music. Overtone is used similarly and differently from the terms harmonic and partial. Often they are used interchangably, otherwise a partial is a non-integer multiple of a fundamental frequency, as opposed to harmonics, which are integer multiples of the fundamental. An overtone is either a partial or a harmonic, and partial thus refers to the inharmonic overtones.
The first overtone is usually roughly twice the frequency of the fundamental, and thus then corresponds to the second harmonic; the second overtone is usually roughly three times the frequency of the fundamental, and thus then corresponds to the third harmonic, etc.
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 overtone series is an arithmetic series (f1, f2, f3, f4...), and the octave, or octave series, is a geometric series (f, 2f, 2×2×f, 2×2×2×f...), this causes the overtone series to divide the octave into increasingly smaller parts as it ascends.
Source: originally from Federal Standard 1037C, but edited.