Harmonic series (music)

Pitched musical instruments are usually based on a harmonic oscillator such as a string or a column of air. Both can and do oscillate at numerous frequencies simultaneously. Because of the self-filtering nature of resonance, these frequencies are mostly limited to integer multiples of the lowest possible frequency, and such multiples form the harmonic series.

Harmonics and tuning

If the first 15 harmonics are transposed into the span of one octave, they approximate what the West has adopted as the major scale based on the fundamental tone. The Western chromatic scale has been modified into twelve equal semitones, and in relation to that scale, many of the harmonics are slightly out of tune, and the 7th, 11th, and 13th harmonics are significantly so. In the late 1930s, composer Paul Hindemith ranked musical intervals according to their relative dissonance based on these and similar harmonic relationships.

Related Topics:
Transposed - Octave - Major scale - Semitones - Paul Hindemith - Dissonance

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Below is a comparison between the first 20 harmonics and their equivalent frequencies in the 12-tone equal-tempered scale. Orange-tinted fields highlight differences greater than 5 cents, which is the "just noticeable difference" for the human ear. (Because physical characteristics of musical instruments cause significant variations from these theoretical values, they should not be used for tuning without adjusting for those variations.)

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