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| 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-10-17 12:32:02 UTC</tt>.<br>
| | | de = Obertonreihe |
| : The original revision id was <tt>95821664</tt>.<br>
| | | es = |
| : The revision comment was: <tt></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"). |
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| 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.
| | 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.
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| Steps between adjacent members of either series are called "superparticular," & they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...
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| In just intonation theory, the overtone series is often treated as the foundation of consonance. | | In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance. |
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| 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.
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| * 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]]...).
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| * Tuning to the overtones of the overtones.
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| * 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".)
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| == ==
| | [[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]] |
| ==External links==
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| [[http://en.wikipedia.org/wiki/Spectral_music|Spectral music article on wikipedia]]
| | == Chord of nature == |
| [[http://www.overtone.cc|Overtone music network]] - a portal for overtone music. | | {{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'''. |
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| ==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. |
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| [[http://en.wikipedia.org/wiki/Stimmung|Stimmung]] by Karlheinz Stockhausen
| | == Segments == |
| [[http://www.southern.com/southern/band/BRANC/disc.html|Symphony No.3 (Gloria)]] by [[http://www.glennbranca.com/|Glenn Branca]]
| | 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. |
| Various by [[http://en.wikipedia.org/wiki/Georg_Friedrich_Haas|Georg Friedrich Haas]]
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| Various played with [[http://www.fujara.sk/audio_samples.htm|Fujara]] (slovak overtone flute)
| | 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. |
| Various by [[http://www.soundwell.com/music-e.htm|SoundWell]] ("Snake" overtone flute)
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| Various by [[http://www.spectralvoices.com/review.htm|Spectral Voices]] (meditative new age with overtone singing)
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| Various by [[http://www.stimmhorn.ch/|Stimmhorn]] (experimental alphorn and yodeling combined with overtone singing)
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| [[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/immanent.html|Immanent Sphere]] by William Sethares
| | == Music based on the harmonic series == |
| [[http://mysterybear.net/article/23/palimpsest|Palimsest]] by Dave Seidel
| | 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://mysterybear.net/article/22/owllight|Owllight]] by Dave Seidel | |
| [[http://mysterybear.net/article/18/threnody|Threnody]] by Dave Seidel
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| [[http://www.i-ching-music.com/FREE102.html|Planetary Ripples]] by Richard Burdick
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| ==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]]). |
| [[ListOfOvertones]]</pre></div>
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| <h4>Original HTML content:</h4>
| | One might compose with the harmonic series by, for instance: |
| <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>
| | * Tuning to the first several harmonics over one fundamental; |
| <br />
| | * 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 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.<br />
| | * 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".) |
| The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.<br />
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| Steps between adjacent members of either series are called &quot;superparticular,&quot; &amp; they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...<br /> | | == Music == |
| <br />
| | ; [[Richard Burdick]] |
| In just intonation theory, the overtone series is often treated as the foundation of consonance.<br />
| | * [http://www.i-ching-music.com/FREE102.html ''Planetary Ripples'']{{dead link}} |
| <br />
| | |
| One might compose with the overtone series by, for instance:<br /> | | ; [[Folkart Slovakia]] ([http://www.fujara.sk/audio_samples.htm site]) |
| <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>...).</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 />
| | * Various played with Fujara (slovak overtone flute) |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h2>
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| <!-- 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>
| | ; {{W|Georg Friedrich Haas}} |
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| | * String Quartet No.2, mm. 1~57 |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Spectral_music" rel="nofollow">Spectral music article on wikipedia</a><br />
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| <a class="wiki_link_ext" href="http://www.overtone.cc" rel="nofollow">Overtone music network</a> - a portal for overtone music.<br />
| | ; [[Dave Hill]] |
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| | * [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:6:&lt;h2&gt; --><h2 id="toc3"><a name="Music based on the overtone series-Some individual compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Some individual compositions</h2>
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| <br />
| | ; [[Norbert Oldani]] |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Stimmung" rel="nofollow">Stimmung</a> by Karlheinz Stockhausen<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.southern.com/southern/band/BRANC/disc.html" rel="nofollow">Symphony No.3 (Gloria)</a> by <a class="wiki_link_ext" href="http://www.glennbranca.com/" rel="nofollow">Glenn Branca</a><br />
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| Various by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a><br />
| | ; [[Dave Seidel]] |
| <br />
| | * [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] |
| Various played with <a class="wiki_link_ext" href="http://www.fujara.sk/audio_samples.htm" rel="nofollow">Fujara</a> (slovak overtone flute)<br />
| | * [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] |
| 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 />
| | * [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] |
| 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 />
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| 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 />
| | ; [[William Sethares]] |
| <br />
| | * ''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] |
| <a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/immanent.html" rel="nofollow">Immanent Sphere</a> by William Sethares<br />
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| <a class="wiki_link_ext" href="http://mysterybear.net/article/23/palimpsest" rel="nofollow">Palimsest</a> by Dave Seidel<br />
| | ; [[SoundWell]] ([http://www.soundwell.com/en/music site]) |
| <a class="wiki_link_ext" href="http://mysterybear.net/article/22/owllight" rel="nofollow">Owllight</a> by Dave Seidel<br />
| | * Various ("Snake" overtone flute) |
| <a class="wiki_link_ext" href="http://mysterybear.net/article/18/threnody" rel="nofollow">Threnody</a> by Dave Seidel<br />
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| <a class="wiki_link_ext" href="http://www.i-ching-music.com/FREE102.html" rel="nofollow">Planetary Ripples</a> by Richard Burdick<br />
| | ; [[Spectral Voices]] ([http://www.spectralvoices.com/ site]) |
| <br />
| | * Various (meditative new age with overtone singing) |
| <!-- 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>
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| <a class="wiki_link" href="/ListOfOvertones">ListOfOvertones</a></body></html></pre></div>
| | ; [[Stimmhorn]] ([http://www.stimmhorn.ch/ site]) |
| | * Various (experimental alphorn and yodeling combined with overtone singing) |
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| | ; {{W|Karlheinz Stockhausen}} |
| | * {{W|Stimmung|''Stimmung''}} (1968) |
| | * {{W|Sternklang|''Sternklang''}} (1971) |
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| | ; [[Cam Taylor]] |
| | * [https://www.youtube.com/watch?v=ECLEbVXoTvA Harmonic series 4-8, 8-16 and 16-32 on the Lumatone] (2022) |
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| | ; [[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] |
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| | ; {{W|Glenn Branca}} ([http://www.glennbranca.com/ site]) |
| | * ''Symphony No. 3 "Gloria"'' (1983) |
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| | == 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]] |
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| | == External links == |
| | * [[Wikipedia: Spectral music]] |
| | * [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) |
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| | [[Category:Harmonic]] |
| | [[Category:Listen]] |
| | [[Category:Terms]] |