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In acoustics and telecommunication, the 'harmonic' of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is ''f'', the harmonics have frequency 2''f'', 3''f'', 4''f'', etc. The harmonics have the property that they are all periodic at the signal frequency, and due to the properties of Fourier series, the sum of the signal and its harmonics is also periodic at that frequency.
Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics.
Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are often perceived as unpleasant.
The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as inharmonics. Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics.
The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:

''1f''	440 Hz	fundamental frequency	first harmonic
''2f''	880 Hz	first overtone	second harmonic
''3f''	1320 Hz	second overtone	third harmonic
''4f''	1760 Hz	third overtone	fourth harmonic

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. Harmonics may be used to check at a unison the tuning of strings that 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 Overtone singing, which uses harmonics.
Harmonics may be either used or considered as the basis of 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 bowing technique halfway between hitting and bowing the strings. Composer Lawrence Ball uses harmonics to generate music electronically.
The fundamental frequency is the reciprocal of the period of the periodic phenomenon.

Contents

Harmonics on stringed instruments

See also

Harmonics on stringed instruments

The following table displays the stop points on a stringed instrument, such as the guitar, at which gentle touching of a
string will force it into a harmonic mode when vibrated. 3rd bridge guitars are guitars that have an additional bridge with which these harmonics are essential to create volume on the inverse-side when a string is attacked on the counterpart.

harmonic	stop note	harmonic note	cents	reduced cents
2	octave	P8	1200.0	0.0
3	just perfect fifth	P8 + P5	1902.0	702.0
4	just perfect fourth	2P8	2400.0	0.0
5	just major third	2P8 + just M3	2786.3	386.3
6	just minor third	2P8 + P5	3102.0	702.0
7	septimal minor third	2P8 + septimal m7	3368.8	968.8
8	septimal major second	3P8	3600.0	0.0
9	Pythagorean major second	3P8 + pyth M2	3803.9	203.9
10	just minor whole tone	3P8 + just M3	3986.3	386.3
11	greater unidecimal neutral second	3P8 + just M3 + GUN2	4151.3	551.3
12	lesser unidecimal neutral second	3P8 + P5	4302.0	702.0
13	tridecimal 2/3-tone	3P8 + P5 + T23T	4440.5	840.5
14	2/3-tone	3P8 + P5 + septimal m3	4568.8	968.8
15	septimal (or major) diatonic semitone	3P8 + P5 + just M3	4688.3	1088.3
16	just (or minor) diatonic semitone	4P8	4800.0	0.0

See also

★ 3rd bridge guitar

★ Artificial harmonic

★ Fourier series

★ Fundamental frequency

★ Harmonic oscillator

★ Harmonic series (music)

★ Harmony

★ Inharmonic

★ Just intonation

★ Moodswinger

★ Overtones

★ Pure tone

★ Stretched octave

★ Tap harmonic

★ Xenharmonic

★ Singing bowl

★ Pinch harmonic

★ Aristoxenus