Harmonic

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 component pitches of a harmonic tone which sound at whole number multiples above, or "within", the named note being played on a musical instrument. Non-whole number multiples are called partials or inharmonic overtones. It is the amplitude and placement of harmonics and partials which give different instruments different timbre (despite not usually being detected seperately by the untrained human ear), and the seperate trajectories of the overtones of two instruments playing in unison is what allows one to perceive them as seperate. Bells have more clearly perceptible harmonics and partials than most instruments.

The name 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. This series is called the harmonic series. For instance, when one plays an A440Hz, "A" refers to the fundamental or first harmonic, but this sound also contains the second harmonic, 880Hz, the third, 1320Hz, and so on, at varying amplitudes.

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, inharmonic. See also: harmonic series

This article incorporates material from Federal Standard 1037C