Harmonic series

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The harmonic series, also known as the overtone series, is a series of pitches produced naturally by the systematic division of a standing wave into pure ratios. This standing wave can be a vibrating string or a column of air. The most basic ratio, 1:1, is analogous to the fundamental frequency of the vibrating medium. This is the lowest note in the example below and can potentially start at any pitch. The second note, one octave higher, is the next basic ratio, 1:2, which in a vibrating string or column of air is half it's full length. The rest of the series is comprised similarly, with ratios 1:3, 1:4, 1:5, theoretically to infinity.

<music> \cadenzaOn \meterOff \clef bass c,,4 s16 c'4 s16 g'4 \clef treble c e g beh c d e fih g aeh aih b c cis d dis e </music> A harmonic series beginning on C

Because the series is pure and today's musical scale is based on equal temperament, our ears will perceive many of the notes of the series as being "out of tune." Examples include the 7th harmonic, 11th, 13th, 14th, and others. These have been approximated using quarter tone notation above.