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Harmonic series (music)

Harmonic series of a string with terms written as reciprocals (2/1 written as 1/2)
First eight harmonics on C.
An illustration of the harmonic series in musical notation. The numbers above the harmonic indicate the number of cents' difference from equal temperament (rounded to the nearest cent). Blue notes are flat and red notes are sharp.
Harmonics on C, 1 to 32.  Play 

A harmonic series is the sequence of sounds where the base frequency of each sound is an integral multiple of the lowest base frequency.

Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series (see harmonic series (mathematics)).

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