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=Music based on the overtone series=
{{Interwiki
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{{Wikipedia|Harmonic series (music)}}
The '''harmonic series''' is a sequence of [[pitch|tones]] generated by whole-number frequency [[ratio]]s 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").


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


The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.
In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.  


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


In just intonation theory, the overtone series is often treated as the foundation of consonance. The [[chord_of_nature|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.
[[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]]


One might compose with the overtone series by, for instance:
== Chord of nature ==
{{Wikipedia|Klang (music)}}
Treated as a [[chord]], the harmonic series is sometimes called the '''chord of nature'''; in German this has been called the '''Klang'''.


<ul><li>Tuning to the first several overtones over one fundamental.</li><li>Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone_scales|Overtone Scales]]).</li><li>Tuning to the overtones of the overtones.</li><li>Tuning to the overtones of the overtones &amp; the undertones of the undertones. (This can produce complex scales such as [[Harry_Partch|Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "[[JustIntonation|just intonation]]" than "overtone music".)</li></ul>
The ''q''-limit chord of nature is 1:2:3:4:…:''q'' up to some odd number ''q'', and is the basic ''q''-[[limit]] [[Otonality and utonality|otonality]] which can be equated via [[Octave reduction|octave equivalence]] to other versions of the complete ''q''-limit otonal chord.


== ==
== Segments ==
A ''segment'' of the harmonic series is a run of consecutive harmonics. It is written ''a''::''b'' for the harmonics ''a'' through ''b''. For example, 4::8 consists of the harmonics 4, 5, 6, 7 and 8, which as a chord is 4:5:6:7:8. Relative to its lowest member, the segment ''a''::''b'' has the frequency ratios ''a''/''a'', (''a''+1)/''a'', …, ''b''/''a''; the steps between its members are [[superparticular]] ratios.


==External links==
A segment whose last harmonic is twice its first, ''n''::2''n'', spans one octave and can be repeated at the octave to form a scale. These are the [[overtone scale]]s. Several have their own pages, for example [[Harmonics 8–16|8::16]], [[Harmonics 12–24|12::24]] and [[Harmonics 16–32|16::32]]. Used as a scale, the segment ''n''::2''n'' is also called mode ''n'' of the harmonic series.


[http://en.wikipedia.org/wiki/Spectral_music Spectral music article on wikipedia]
== 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.


[http://www.naturton-musik.de/ www.naturton-musik.de] - web site dedicated to overtone music (by austrian composer Johannes Kotschy) - a lot of theory material and practical guides to write music based on the overtone series
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]]).


[http://www.overtone.cc Overtone music network] - a portal for overtone music.
One might compose with the harmonic series by, for instance:
* Tuning to the first several harmonics over one fundamental;
* Tuning to an octave-repeating segment of the harmonic series for use as a scale. For instance: [[Harmonics 8–16|8::16]], [[Harmonics 12–24|12::24]], [[Harmonics 20–40|20::40]], ... See [[overtone scale]].
* 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".)


[http://www.xing.com/net/overtonenetwork Oberton-Netzwerk (Xing)] - german-speaking group dedicated to overtone music on the social network platform [http://www.xing.com Xing]. Microtonal music in general is welcome, too.
== Music ==
; [[Richard Burdick]]
* [http://www.i-ching-music.com/FREE102.html ''Planetary Ripples'']{{dead link}}


==Some individual compositions==
; [[Folkart Slovakia]] ([http://www.fujara.sk/audio_samples.htm site])
* Various played with Fujara (slovak overtone flute)


''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]'' by [[Norbert_Oldani|Norbert Oldani]]
; {{W|Georg Friedrich Haas}}
* String Quartet No.2, mm. 1~57


[http://mysterybear.net/article/18/threnody Threnody] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Threnody.mp3 play]'' by [[Dave_Seidel|Dave Seidel]]
; [[Dave Hill]]
* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Chord Progression on the Harmonic Overtone Series'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play]{{dead link}}


[http://mysterybear.net/article/22/owllight Owllight] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Owllight.mp3 play]'' by Dave Seidel
; [[Norbert Oldani]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]''{{dead link}}


[http://mysterybear.net/article/23/palimpsest Palimsest] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Palimpsest.mp3 play]'' by Dave Seidel
; [[Dave Seidel]]
* [http://mysterybear.net/article/18/threnody ''Threnody'']{{dead link}} [https://web.archive.org/web/20201127015923/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Threnody.mp3 play]
* [http://mysterybear.net/article/22/owllight ''Owllight'']{{dead link}} [https://web.archive.org/web/20201127012201/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Owllight.mp3 play]
* [http://mysterybear.net/article/23/palimpsest ''Palimsest'']{{dead link}} [https://web.archive.org/web/20201127012920/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Palimpsest.mp3 play]


[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/immanent.html Immanent Sphere] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/ImmanentSphere.mp3 play]'' by [[William_Sethares|William Sethares]]
; [[William Sethares]]
* ''Immanent Sphere'' – [https://sethares.engr.wisc.edu/mp3s/immanent.html detail] | [https://web.archive.org/web/20201127013148/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/ImmanentSphere.mp3 play]


[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Chord Progression on the Harmonic Overtone Series] ''[http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play]'' by [[Dave_Hill|Dave Hill]]
; [[SoundWell]] ([http://www.soundwell.com/en/music site])
* Various ("Snake" overtone flute)


[http://chrisvaisvil.com/rock-trio-in-harmonic-series/ Rock Trio in Harmonic Series] [http://micro.soonlabel.com/harmonic_series/Nevadatite20160226_harmonic_band.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]]
; [[Spectral Voices]] ([http://www.spectralvoices.com/ site])
* Various (meditative new age with overtone singing)


[http://www.i-ching-music.com/FREE102.html Planetary Ripples] by Richard Burdick
; [[Stimmhorn]] ([http://www.stimmhorn.ch/ site])
* Various (experimental alphorn and yodeling combined with overtone singing)


[http://en.wikipedia.org/wiki/Stimmung Stimmung] by Karlheinz Stockhausen
; {{W|Karlheinz Stockhausen}}
* {{W|Stimmung|''Stimmung''}} (1968)
* {{W|Sternklang|''Sternklang''}} (1971)


[http://www.southern.com/southern/band/BRANC/disc.html Symphony No.3 (Gloria)] by [http://www.glennbranca.com/ Glenn Branca]
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=ECLEbVXoTvA Harmonic series 4-8, 8-16 and 16-32 on the Lumatone] (2022)


Various by [http://en.wikipedia.org/wiki/Georg_Friedrich_Haas Georg Friedrich Haas]
; [[Chris Vaisvil]]
* ''Rock Trio in Harmonic Series'' (2016) – [http://chrisvaisvil.com/rock-trio-in-harmonic-series/ blog] | [http://micro.soonlabel.com/harmonic_series/Nevadatite20160226_harmonic_band.mp3 play]


Various played with [http://www.fujara.sk/audio_samples.htm Fujara] (slovak overtone flute)
; {{W|Glenn Branca}} ([http://www.glennbranca.com/ site])
* ''Symphony No. 3 "Gloria"'' (1983)


Various by [http://www.soundwell.com/music-e.htm SoundWell] ("Snake" overtone flute)
== See also ==
* [[Overtone scales]]
* [[Gallery of just intervals]]
* [[Isoharmonic chords]]
* [[List of octave-reduced harmonics]]
* [[Prime harmonic series]]
* [[Kite's thoughts on the V-I cadence in higher prime limits]]
* [[Harmonics 128–256|8th octave overtone tuning]]


Various by [http://www.spectralvoices.com/review.htm Spectral Voices] (meditative new age with overtone singing)
== External links ==
 
* [[Wikipedia: Spectral music]]
Various by [http://www.stimmhorn.ch/ Stimmhorn] (experimental alphorn and yodeling combined with overtone singing)
* [http://www.naturton-musik.de/ www.naturton-musik.de]{{dead link}} - web site dedicated to overtone music (by Austrian composer Johannes Kotschy) - a lot of theory material and practical guides to write music based on the overtone series
 
* [http://www.overtone.cc Overtone music network] - a portal for overtone music.
==See also:==
* [https://www.xing.com/net/overtonenetwork Oberton-Netzwerk (Xing)]{{dead link}} - German-speaking group dedicated to overtone music on the social network platform [http://www.xing.com Xing]. Microtonal music in general is welcome, too.
<ul><li>[[isoharmonic_chords|Isoharmonic Chords]]</li><li>[[First_Five_Octaves_of_the_Harmonic_Series|First Five Octaves of the Harmonic Series]]</li><li>[[overtone_scales|Overtone Scales]]</li><li>[[ListOfOvertones|ListOfOvertones]]</li><li>[[The_Prime_Harmonic_Series|The Prime Harmonic Series]]</li><li>[[Harmonic|Harmonic]]</li></ul>      [[Category:harmonic]]
* [[Noah Jordan]] videos:
[[Category:harmonic_series]]
** [https://www.youtube.com/watch?v=iyceyPMJAb8 All Harmonics Within One Octave (1–64) | Harmonic Series Explained Visually] (2026)
[[Category:ji]]
** [https://www.youtube.com/watch?v=DAUeGio1Fdg How Prime Harmonics Fill the Octave (≤1024) — Microtonal & Just Intonation Visualization] (2026)
[[Category:just]]
 
[[Category:listen]]
[[Category:Harmonic]]
[[Category:overtone]]
[[Category:Listen]]
[[Category:overview]]
[[Category:Terms]]
[[Category:people]]
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