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In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integral multiple of the fundamental frequency. For a sine wave, it is an integral multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.

In musical terms, harmonics are notes which sound at higher frequencies that the note being played on a musical instrument. It is harmonics which give different instruments different qualities of tone, although they are usually not detected by the untrained human ear. Bells have more clearly perceptible harmonics than most instruments.

The frequency of the note played is the fundamental frequency or the first harmonic, the second harmonic is twice the fundamental frequency, the third harmonic is thrice the fundamental frequency, and so on. The series of notes which thus develops is called the harmonic series.

In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g.recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. On string instruments it is often used to produce very pure sounding notes which have an eerie quality, as well as being high in pitch.

The fundamental frequency is the reciprocal of the period of the periodic phenomenon.

Contrast with: fundamental, overtone.

This article incorporates material from Federal Standard 1037C

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