This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Harmonic series
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-27 03:10:29 UTC</tt>.<br>
| de = Obertonreihe
: The original revision id was <tt>576000995</tt>.<br>
| es =
: The revision comment was: <tt>link to blog entry as well</tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| ko = 배음렬
<h4>Original Wikitext content:</h4>
| ro = Seria armonică
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Music based on the overtone series=
| zh = 泛音列
}}
{{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.
Steps between adjacent members of either series are called "[[superparticular]]," and they appear in the form (n+1)/n, eg. 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.
In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.
One might compose with the overtone series by, for instance:
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.
* 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, [[otones12-24|12 through 24]], [[otones20-40|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 "[[JustIntonation|just intonation]]" than "overtone music".)
== ==
[[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]]
==External links==
[[http://en.wikipedia.org/wiki/Spectral_music|Spectral music article on wikipedia]]
== Chord of nature ==
[[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
{{Wikipedia|Klang (music)}}
[[http://www.overtone.cc|Overtone music network]] - a portal for overtone music.
Treated as a [[chord]], the harmonic series is sometimes called the '''chord of nature'''; in German this has been called the '''Klang'''.
[[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.
==Some individual compositions==
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.
//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3|Drone Inside An Harmonic Series]]// by [[Norbert Oldani]]
== Segments ==
[[http://mysterybear.net/article/18/threnody|Threnody]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Threnody.mp3|play]]// by [[Dave Seidel]]
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.
[[http://mysterybear.net/article/22/owllight|Owllight]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Owllight.mp3|play]]// by Dave Seidel
[[http://mysterybear.net/article/23/palimpsest|Palimsest]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Palimpsest.mp3|play]]// by Dave Seidel
[[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]]
[[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]]
[[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]] by Richard Burdick
[[http://en.wikipedia.org/wiki/Stimmung|Stimmung]] by Karlheinz Stockhausen
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://www.southern.com/southern/band/BRANC/disc.html|Symphony No.3 (Gloria)]] by [[http://www.glennbranca.com/|Glenn Branca]]
Various by [[http://en.wikipedia.org/wiki/Georg_Friedrich_Haas|Georg Friedrich Haas]]
Various played with [[http://www.fujara.sk/audio_samples.htm|Fujara]] (slovak overtone flute)
== Music based on the harmonic series ==
Various by [[http://www.soundwell.com/music-e.htm|SoundWell]] ("Snake" overtone flute)
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.
Various by [[http://www.spectralvoices.com/review.htm|Spectral Voices]] (meditative new age with overtone singing)
Various by [[http://www.stimmhorn.ch/|Stimmhorn]] (experimental alphorn and yodeling combined with overtone singing)
==See also:==
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]]).
* [[Isoharmonic Chords]]
* [[First Five Octaves of the Harmonic Series]]
One might compose with the harmonic series by, for instance:
* [[Overtone Scales]]
* Tuning to the first several harmonics over one fundamental;
* [[ListOfOvertones]]
* 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]].
* [[The Prime Harmonic Series]]
* 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".)
* [[Harmonic]]</pre></div>
<h4>Original HTML content:</h4>
== Music ==
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>OverToneSeries</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Music based on the overtone series"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music based on the overtone series</h1>
The overtone series can be mathematically generated by <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">frequency ratios</a> 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.<br />
The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.<br />
Steps between adjacent members of either series are called &quot;<a class="wiki_link" href="/superparticular">superparticular</a>,&quot; and they appear in the form (n+1)/n, eg. 4/3, 28/27, 33/32...<br />
* Various played with Fujara (slovak overtone flute)
<br />
In just intonation theory, the overtone series is often treated as the foundation of consonance. The <a class="wiki_link" href="/chord%20of%20nature">chord of nature</a> is the name sometimes given to the overtone series, or the series up to a certain stopping point, regarded as a chord.<br />
; {{W|Georg Friedrich Haas}}
<br />
* String Quartet No.2, mm. 1~57
One might compose with the overtone series by, for instance:<br />
<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, <a class="wiki_link" href="/otones12-24">12 through 24</a>, <a class="wiki_link" href="/otones20-40">20 through 40</a>... see <a class="wiki_link" href="/Overtone%20Scales">Overtone Scales</a>).</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 <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>'s 43-tone Monophonic; this kind of thing is more often called &quot;<a class="wiki_link" href="/JustIntonation">just intonation</a>&quot; than &quot;overtone music&quot;.)</li></ul><br />
* [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}}
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Music based on the overtone series-External links"></a><!-- ws:end:WikiTextHeadingRule:4 -->External links</h2>
<br />
; [[Norbert Oldani]]
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Spectral_music" rel="nofollow">Spectral music article on wikipedia</a><br />
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]''{{dead link}}
<a class="wiki_link_ext" href="http://www.naturton-musik.de/" rel="nofollow">www.naturton-musik.de</a> - 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<br />
<a class="wiki_link_ext" href="http://www.overtone.cc" rel="nofollow">Overtone music network</a> - a portal for overtone music.<br />
; [[Dave Seidel]]
<a class="wiki_link_ext" href="http://www.xing.com/net/overtonenetwork" rel="nofollow">Oberton-Netzwerk (Xing)</a> - german-speaking group dedicated to overtone music on the social network platform <a class="wiki_link_ext" href="http://www.xing.com" rel="nofollow">Xing</a>. Microtonal music in general is welcome, too.<br />
<a class="wiki_link_ext" href="http://www.i-ching-music.com/FREE102.html" rel="nofollow">Planetary Ripples</a> by Richard Burdick<br />
* Various (meditative new age with overtone singing)
<br />
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Stimmung" rel="nofollow">Stimmung</a> by Karlheinz Stockhausen<br />
* Various (experimental alphorn and yodeling combined with overtone singing)
Various by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a><br />
<br />
; {{W|Karlheinz Stockhausen}}
Various played with <a class="wiki_link_ext" href="http://www.fujara.sk/audio_samples.htm" rel="nofollow">Fujara</a> (slovak overtone flute)<br />
* {{W|Stimmung|''Stimmung''}} (1968)
Various by <a class="wiki_link_ext" href="http://www.soundwell.com/music-e.htm" rel="nofollow">SoundWell</a> (&quot;Snake&quot; overtone flute)<br />
* {{W|Sternklang|''Sternklang''}} (1971)
Various by <a class="wiki_link_ext" href="http://www.spectralvoices.com/review.htm" rel="nofollow">Spectral Voices</a> (meditative new age with overtone singing)<br />
Various by <a class="wiki_link_ext" href="http://www.stimmhorn.ch/" rel="nofollow">Stimmhorn</a> (experimental alphorn and yodeling combined with overtone singing)<br />
; [[Cam Taylor]]
<br />
* [https://www.youtube.com/watch?v=ECLEbVXoTvA Harmonic series 4-8, 8-16 and 16-32 on the Lumatone] (2022)
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Music based on the overtone series-See also:"></a><!-- ws:end:WikiTextHeadingRule:8 -->See also:</h2>
<ul><li><a class="wiki_link" href="/Isoharmonic%20Chords">Isoharmonic Chords</a></li><li><a class="wiki_link" href="/First%20Five%20Octaves%20of%20the%20Harmonic%20Series">First Five Octaves of the Harmonic Series</a></li><li><a class="wiki_link" href="/Overtone%20Scales">Overtone Scales</a></li><li><a class="wiki_link" href="/ListOfOvertones">ListOfOvertones</a></li><li><a class="wiki_link" href="/The%20Prime%20Harmonic%20Series">The Prime Harmonic Series</a></li><li><a class="wiki_link" href="/Harmonic">Harmonic</a></li></ul></body></html></pre></div>
* [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.
* [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)
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.
Harmonic series on A, partials 1 to 16, notated in HEJI.
Treated as a chord, the harmonic series is sometimes called the chord of nature; in German this has been called the Klang.
The q-limit chord of nature is 1:2:3:4:…:q up to some odd number q, and is the basic q-limitotonality which can be equated via 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.
A segment whose last harmonic is twice its first, n::2n, spans one octave and can be repeated at the octave to form a scale. These are the overtone scales. Several have their own pages, for example 8::16, 12::24 and 16::32. Used as a scale, the segment n::2n is also called mode n of the harmonic series.
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 segment of the harmonic series for use as a scale. For instance: 8::16, 12::24, 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".)
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
Oberton-Netzwerk (Xing)[dead link] - German-speaking group dedicated to overtone music on the social network platform Xing. Microtonal music in general is welcome, too.
