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{{interwiki
{{Interwiki
| en = Harmonic series
| de = Obertonreihe
| de = Obertonreihe
| en = Overtone series
| es =  
| ja =
| ko = 배음렬
| ro = Seria armonică
| zh = 泛音列
}}
}}
{{Wikipedia|Harmonic series (music)}}
{{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 '''harmonic series''' is a sequence of notes 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").
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.


Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage are 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.
 
[[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]]
 
== 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'''.


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


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.
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.


== Music based on the harmonic series ==
== Music based on the harmonic series ==
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One might compose with the harmonic series by, for instance:
One might compose with the harmonic series by, for instance:
* Tuning to the first several harmonics over one fundamental;
* 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, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);
* 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".)
* 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".)


== Some individual compositions ==
== Music ==
; [[Richard Burdick]]
* [http://www.i-ching-music.com/FREE102.html ''Planetary Ripples'']{{dead link}}
 
; [[Folkart Slovakia]] ([http://www.fujara.sk/audio_samples.htm site])
* Various played with Fujara (slovak overtone flute)
 
; {{W|Georg Friedrich Haas}}
* String Quartet No.2, mm. 1~57
 
; [[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}}
 
; [[Norbert Oldani]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]''{{dead link}}
 
; [[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]
 
; [[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]
 
; [[SoundWell]] ([http://www.soundwell.com/en/music site])
* Various ("Snake" overtone flute)
 
; [[Spectral Voices]] ([http://www.spectralvoices.com/ site])
* Various (meditative new age with overtone singing)


* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]''{{dead link}} by [[Norbert Oldani]]
; [[Stimmhorn]] ([http://www.stimmhorn.ch/ site])
* [http://mysterybear.net/article/18/threnody Threnody]{{dead link}} ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Threnody.mp3 play]''{{dead link}} by [[Dave Seidel]]
* Various (experimental alphorn and yodeling combined with overtone singing)
* [http://mysterybear.net/article/22/owllight Owllight]{{dead link}} ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Owllight.mp3 play]''{{dead link}} by Dave Seidel
 
* [http://mysterybear.net/article/23/palimpsest Palimsest]{{dead link}} ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Palimpsest.mp3 play]''{{dead link}} by Dave Seidel
; {{W|Karlheinz Stockhausen}}
* [http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/immanent.html Immanent Sphere]{{dead link}} ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/ImmanentSphere.mp3 play]''{{dead link}} by [[William Sethares]]
* {{W|Stimmung|''Stimmung''}} (1968)
* [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}} by [[Dave Hill]]
* {{W|Sternklang|''Sternklang''}} (1971)
* [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]]
 
* [http://www.i-ching-music.com/FREE102.html Planetary Ripples]{{dead link}} by Richard Burdick
; [[Cam Taylor]]
* [http://en.wikipedia.org/wiki/Stimmung Stimmung] by Karlheinz Stockhausen
* [https://www.youtube.com/watch?v=ECLEbVXoTvA Harmonic series 4-8, 8-16 and 16-32 on the Lumatone] (2022)
* [http://www.southern.com/southern/band/BRANC/disc.html Symphony No.3 (Gloria)]{{dead link}} by [http://www.glennbranca.com/ Glenn Branca]
 
* Various by [http://en.wikipedia.org/wiki/Georg_Friedrich_Haas Georg Friedrich Haas]
; [[Chris Vaisvil]]
* Various played with [http://www.fujara.sk/audio_samples.htm Fujara] (slovak overtone flute)
* ''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 by [http://www.soundwell.com/en/music SoundWell] ("Snake" overtone flute)
 
* Various by [http://www.spectralvoices.com/ Spectral Voices] (meditative new age with overtone singing)
; {{W|Glenn Branca}} ([http://www.glennbranca.com/ site])
* Various by [http://www.stimmhorn.ch/ Stimmhorn] (experimental alphorn and yodeling combined with overtone singing)
* ''Symphony No. 3 "Gloria"'' (1983)


== See also ==
== See also ==
* [[Subharmonic series]]
* [[Overtone scales]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Isoharmonic chords]]
* [[Isoharmonic chords]]
* [[First Five Octaves of the Harmonic Series]]
* [[List of octave-reduced harmonics]]
* [[Overtone scales]]
* [[List of overtones]]
* [[Prime harmonic series]]
* [[Prime harmonic series]]
* [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]
* [[Kite's thoughts on the V-I cadence in higher prime limits]]
* [[Harmonics 128–256|8th octave overtone tuning]]


== External links ==
== External links ==
 
* [[Wikipedia: Spectral music]]
* [http://en.wikipedia.org/wiki/Spectral_music Spectral music article on Wikipedia]
* [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.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.
* [http://www.overtone.cc Overtone music network] - a portal for overtone music.
* [http://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.
* [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.
     
* [[Noah Jordan]] videos:
** [https://www.youtube.com/watch?v=iyceyPMJAb8 All Harmonics Within One Octave (1–64) | Harmonic Series Explained Visually] (2026)
** [https://www.youtube.com/watch?v=DAUeGio1Fdg How Prime Harmonics Fill the Octave (≤1024) — Microtonal & Just Intonation Visualization] (2026)
 
[[Category:Harmonic]]
[[Category:Harmonic]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Overview]]
[[Category:Terms]]
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