# Overtone series

(Redirected from Harmonic series)

## Music based on the overtone series

The overtone series can be mathematically generated by frequency ratios 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.

The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.

Steps between adjacent members of either series are called "superparticular," and they appear in the form (n+1)/n, e.g. 4/3, 28/27, 33/32...

In just intonation theory, the overtone series is often treated as the foundation of consonance. The chord of nature is the name sometimes given to the overtone series, or the series up to a certain stopping point, regarded as a chord.

One might compose with the overtone series by, for instance:

• Tuning to the first several overtones over one fundamental.
• Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16, 12 through 24, 20 through 40... see overtone scales).
• Tuning to the overtones of the overtones.
• Tuning to the overtones of the overtones & the undertones of the undertones. (This can produce complex scales such as Harry Partch's 43-tone Monophonic; this kind of thing is more often called "just intonation" than "overtone music".)