Harmonic

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This article is about the components of sound. In mathematics, see harmonic (mathematics).

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 a sine wave, it is an integer 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-integer 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.

Sample for a harmonic series:

1f 440 Hz fundamental frequency first harmonic
2f 880 Hz first overtone second harmonic
3f 1320 Hz second overtone third harmonic

Amplitudes are varying.

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 Overtone 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 bowing technique halfway between hitting and bowing the strings.

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

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Harmonics on Stringed Instruments

The following table displays the stop points on a stringed instrument, such as the violin, at which gentle touching of a string will force it into a harmonic mode when vibrated.

harmonic stop note harmonic note cents reduced cents
2 octave P8 1200 0
3 just perfect fifth P8 + P5 1901.95500 701.95500
4 just perfect fourth 2P8 2400 0
5 just major third 2P8 + just M3 2786.31371 386.31371
6 just minor third 2P8 + P5 3101.95500 701.95500
7 septimal minor third 2P8 + septimal m7 3368.82591 968.82591
8 septimal major second 3P8 3600 0
9 pythagorean major second 3P8 + pyth M2 3803.91000 203.91000
10 just minor whole tone 3P8 + just M3 3986.31371 386.31371
11 greater unidecimal neutral second 3P8 + just M3 + GUN2 4151.31794 551.31794
12 lesser unidecimal neutral second 3P8 + P5 4301.95500 701.955
13 tridecimal 2/3-tone 3P8 + P5 + T23T 4440.52766 840.52766
14 2/3-tone 3P8 + P5 + septimal m3 4568.82591 968.82591
15 septimal (or major) diatonic semitone 3P8 + P5 + just M3 4688.26871 1088.26871
16 just (or minor) diatonic semitone 4P8 4800 0


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See also

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External links

es:Armónico nl:Harmonische ja:倍音 pl:Składowa harmoniczna pt:Harmônica

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