# Harmonic series

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The harmonic series is a sequence of tones generated by whole-number frequency ratios over a fundamental: 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1… ad infinitum. Each member of this series is a harmonic (which is short for "harmonic partial").

Note that the terms overtone and overtone series are not quite synonymous with harmonic and harmonic series, respectively, although interchangeable usage is also attested. Technically speaking, overtone series excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard.

In just intonation theory, the harmonic series is often treated as the foundation of consonance.

The subharmonic series (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.

## Music based on the harmonic series

The chord of nature is the name sometimes given to the harmonic series, or the series up to a certain stopping point, regarded as a chord.

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

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

• Tuning to the first several harmonics over one fundamental;
• Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance harmonics 8 though 16, 12 through 24, 20 through 40... see overtone scales);
• 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".)

## Music

Richard Burdick
Folkart Slovakia (site)
• Various played with Fujara (slovak overtone flute)
Georg Friedrich Haas
• Various[which?]
Dave Hill
Norbert Oldani
Dave Seidel
William Sethares
SoundWell (site)
• Various ("Snake" overtone flute)
Spectral Voices (site)
• Various (meditative new age with overtone singing)
Stimmhorn (site)
• Various (experimental alphorn and yodeling combined with overtone singing)
Karlheinz Stockhausen
Chris Vaisvil
• Rock Trio in Harmonic Series (2016) – blog | play
Glenn Branca (site)
• Symphony No. 3 "Gloria" (1983)