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 separately by the untrained human ear), and the separate trajectories of the overtones of two instruments playing in unison is what allows one to perceive them as separate. Bells have more clearly perceptible 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. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics by string players, which have an eerie quality, as well as being high in pitch which are located on the nodes of the strings. Harmonics may be used to check at a unison the tuning of strings which are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see throat singing, which uses harmonics.
Harmonics may be used as the basis of just intonation systems or considered as the basis of all just intonation systems. Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowinging technique halfway between hitting and bowing the strings.
This article incorporates material from Federal Standard 1037C