MicrotonalTheory: Difference between revisions

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[[toc|flat]]
=Theory: Inventions that shape understanding= 

Theories are [[http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf|not discoveries but inventions]] of humans, which often bring forth //new ways of experiencing//. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories.)

=Reality tunnels into microtonality= 
* [[JustIntonation|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, tonality diamonds, eikosany, etc.
* [[Equal Temperaments|Equal]] tunings: each one a subtle monoculture of intervals
* In Western common practice music, the (somewhat forgotten) use of [[historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave
* Musics of traditional cultures
** [[Arabic, Turkish, Persian]]
** [[Indian]] (North, South)
** African
** Thai
** Indonesian (Java, Bali)
** Ancient Greek, [[http://orthodoxwiki.org/Byzantine_Chant#The_scale|Byzantine]]
* [[Regular Temperaments]] (including Linear Temperaments): a reality bending just intonation and equal temperaments towards one another, fleshed out in the past decade or so
* [[MOSScales|Moment of Symmetry]], brought to you by Erv Wilson
* [[Empirical]]. This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.
* [[tetrachord|Tetrachordal Scales]], which use divided fourths as building blocks for composition.
* [[isoharmonic chords|Isoharmonic chords/scales]]
* [[Pretty Pictures]] that represent scales in one way or another
* [[Notation]] (pretty pictures for a the purpose of writing music down)
* the notion of a [[Scalesmith]] who //builds// scales, with various methods, perhaps for single occasions
** Counter-intuitive, random, arbitrary scales
** Numerology-based, computationally demanding scales
** Scale stretching
** Acoustically-based (resonant frequencies of performance space, for example)
* ([[Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)
* [[Redundancy]] in a tuning system

=External links= 
== == 
* Tonalsoft [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Encyclopedia of microtonal music theory]] - a whole sea of information on the topic, covering both historical tuning theories and modern developments
* [[http://microtonalismo.com|Microtonalismo]] - Web microtonal
* [[http://www.bikexprt.com/music/tunebibl.htm|A bibliography on musical tunings and temperaments]], compiled by John S. Allen
* [[Huygens-Fokker]] Foundation's [[http://www.xs4all.nl/%7Ehuygensf/doc/bib.html|Tuning & temperament bibliography]], hyperlinked and updated by Manuel op de Coul
* The [[http://www.untwelve.org|UnTwelve]] website has some pages of theoretical interest, including a [[http://www.untwelve.org/what.html|fascinating article]] authored by Margo Schulter

Original HTML content:

<html><head><title>MicrotonalTheory</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Theory: Inventions that shape understanding">Theory: Inventions that shape understanding</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Reality tunnels into microtonality">Reality tunnels into microtonality</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory: Inventions that shape understanding"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory: Inventions that shape understanding</h1>
 <br />
Theories are <a class="wiki_link_ext" href="http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf" rel="nofollow">not discoveries but inventions</a> of humans, which often bring forth <em>new ways of experiencing</em>. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories.)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Reality tunnels into microtonality"></a><!-- ws:end:WikiTextHeadingRule:2 -->Reality tunnels into microtonality</h1>
 <ul><li><a class="wiki_link" href="/JustIntonation">Just Intonation</a>: an infinite world of rational numbers and numerous models: the harmonic series, tonality diamonds, eikosany, etc.</li><li><a class="wiki_link" href="/Equal%20Temperaments">Equal</a> tunings: each one a subtle monoculture of intervals</li><li>In Western common practice music, the (somewhat forgotten) use of <a class="wiki_link" href="/historical%20temperaments">historical temperaments</a> (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musics of traditional cultures<ul><li><a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, Persian</a></li><li><a class="wiki_link" href="/Indian">Indian</a> (North, South)</li><li>African</li><li>Thai</li><li>Indonesian (Java, Bali)</li><li>Ancient Greek, <a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow">Byzantine</a></li></ul></li><li><a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a> (including Linear Temperaments): a reality bending just intonation and equal temperaments towards one another, fleshed out in the past decade or so</li><li><a class="wiki_link" href="/MOSScales">Moment of Symmetry</a>, brought to you by Erv Wilson</li><li><a class="wiki_link" href="/Empirical">Empirical</a>. This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li><a class="wiki_link" href="/tetrachord">Tetrachordal Scales</a>, which use divided fourths as building blocks for composition.</li><li><a class="wiki_link" href="/isoharmonic%20chords">Isoharmonic chords/scales</a></li><li><a class="wiki_link" href="/Pretty%20Pictures">Pretty Pictures</a> that represent scales in one way or another</li><li><a class="wiki_link" href="/Notation">Notation</a> (pretty pictures for a the purpose of writing music down)</li><li>the notion of a <a class="wiki_link" href="/Scalesmith">Scalesmith</a> who <em>builds</em> scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>(<a class="wiki_link" href="/Corollaries">Corollaries</a>, traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li><a class="wiki_link" href="/Redundancy">Redundancy</a> in a tuning system</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:4 -->External links</h1>
 <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
 <ul><li>Tonalsoft <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Encyclopedia of microtonal music theory</a> - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li><a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow">Microtonalismo</a> - Web microtonal</li><li><a class="wiki_link_ext" href="http://www.bikexprt.com/music/tunebibl.htm" rel="nofollow">A bibliography on musical tunings and temperaments</a>, compiled by John S. Allen</li><li><a class="wiki_link" href="/Huygens-Fokker">Huygens-Fokker</a> Foundation's <a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/bib.html" rel="nofollow">Tuning &amp; temperament bibliography</a>, hyperlinked and updated by Manuel op de Coul</li><li>The <a class="wiki_link_ext" href="http://www.untwelve.org" rel="nofollow">UnTwelve</a> website has some pages of theoretical interest, including a <a class="wiki_link_ext" href="http://www.untwelve.org/what.html" rel="nofollow">fascinating article</a> authored by Margo Schulter</li></ul></body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2011-04-04 23:07:46 UTC</tt>.<br>
+: This revision was by author [[User:lobawad|lobawad]] and made on <tt>2011-05-12 05:51:21 UTC</tt>.<br>
-: The original revision id was <tt>217168270</tt>.<br>
+: The original revision id was <tt>227779140</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 33: / Line 33: @@
 ** Numerology-based, computationally demanding scales
 ** Scale stretching
+** Acoustically-based (resonant frequencies of performance space, for example)
 * ([[Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)
 * [[Redundancy]] in a tuning system
@@ Line 50: / Line 51: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Reality tunnels into microtonality"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Reality tunnels into microtonality&lt;/h1&gt;
-  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/JustIntonation"&gt;Just Intonation&lt;/a&gt;: an infinite world of rational numbers and numerous models: the harmonic series, tonality diamonds, eikosany, etc.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal&lt;/a&gt; tunings: each one a subtle monoculture of intervals&lt;/li&gt;&lt;li&gt;In Western common practice music, the (somewhat forgotten) use of &lt;a class="wiki_link" href="/historical%20temperaments"&gt;historical temperaments&lt;/a&gt; (meantones, well temperaments) with 12 or more unequal notes per octave&lt;/li&gt;&lt;li&gt;Musics of traditional cultures&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, Persian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indian"&gt;Indian&lt;/a&gt; (North, South)&lt;/li&gt;&lt;li&gt;African&lt;/li&gt;&lt;li&gt;Thai&lt;/li&gt;&lt;li&gt;Indonesian (Java, Bali)&lt;/li&gt;&lt;li&gt;Ancient Greek, &lt;a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow"&gt;Byzantine&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt; (including Linear Temperaments): a reality bending just intonation and equal temperaments towards one another, fleshed out in the past decade or so&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt;, brought to you by Erv Wilson&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Empirical"&gt;Empirical&lt;/a&gt;. This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/tetrachord"&gt;Tetrachordal Scales&lt;/a&gt;, which use divided fourths as building blocks for composition.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/isoharmonic%20chords"&gt;Isoharmonic chords/scales&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pretty%20Pictures"&gt;Pretty Pictures&lt;/a&gt; that represent scales in one way or another&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt; (pretty pictures for a the purpose of writing music down)&lt;/li&gt;&lt;li&gt;the notion of a &lt;a class="wiki_link" href="/Scalesmith"&gt;Scalesmith&lt;/a&gt; who &lt;em&gt;builds&lt;/em&gt; scales, with various methods, perhaps for single occasions&lt;ul&gt;&lt;li&gt;Counter-intuitive, random, arbitrary scales&lt;/li&gt;&lt;li&gt;Numerology-based, computationally demanding scales&lt;/li&gt;&lt;li&gt;Scale stretching&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(&lt;a class="wiki_link" href="/Corollaries"&gt;Corollaries&lt;/a&gt;, traces left by other reality tunnels, which by themselves are completely trivial and obvious)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Redundancy"&gt;Redundancy&lt;/a&gt; in a tuning system&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/JustIntonation"&gt;Just Intonation&lt;/a&gt;: an infinite world of rational numbers and numerous models: the harmonic series, tonality diamonds, eikosany, etc.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal&lt;/a&gt; tunings: each one a subtle monoculture of intervals&lt;/li&gt;&lt;li&gt;In Western common practice music, the (somewhat forgotten) use of &lt;a class="wiki_link" href="/historical%20temperaments"&gt;historical temperaments&lt;/a&gt; (meantones, well temperaments) with 12 or more unequal notes per octave&lt;/li&gt;&lt;li&gt;Musics of traditional cultures&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, Persian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indian"&gt;Indian&lt;/a&gt; (North, South)&lt;/li&gt;&lt;li&gt;African&lt;/li&gt;&lt;li&gt;Thai&lt;/li&gt;&lt;li&gt;Indonesian (Java, Bali)&lt;/li&gt;&lt;li&gt;Ancient Greek, &lt;a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow"&gt;Byzantine&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt; (including Linear Temperaments): a reality bending just intonation and equal temperaments towards one another, fleshed out in the past decade or so&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt;, brought to you by Erv Wilson&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Empirical"&gt;Empirical&lt;/a&gt;. This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/tetrachord"&gt;Tetrachordal Scales&lt;/a&gt;, which use divided fourths as building blocks for composition.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/isoharmonic%20chords"&gt;Isoharmonic chords/scales&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pretty%20Pictures"&gt;Pretty Pictures&lt;/a&gt; that represent scales in one way or another&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt; (pretty pictures for a the purpose of writing music down)&lt;/li&gt;&lt;li&gt;the notion of a &lt;a class="wiki_link" href="/Scalesmith"&gt;Scalesmith&lt;/a&gt; who &lt;em&gt;builds&lt;/em&gt; scales, with various methods, perhaps for single occasions&lt;ul&gt;&lt;li&gt;Counter-intuitive, random, arbitrary scales&lt;/li&gt;&lt;li&gt;Numerology-based, computationally demanding scales&lt;/li&gt;&lt;li&gt;Scale stretching&lt;/li&gt;&lt;li&gt;Acoustically-based (resonant frequencies of performance space, for example)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(&lt;a class="wiki_link" href="/Corollaries"&gt;Corollaries&lt;/a&gt;, traces left by other reality tunnels, which by themselves are completely trivial and obvious)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Redundancy"&gt;Redundancy&lt;/a&gt; in a tuning system&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;External links&lt;/h1&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt; &lt;/h2&gt;
   &lt;ul&gt;&lt;li&gt;Tonalsoft &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow"&gt;Encyclopedia of microtonal music theory&lt;/a&gt; - a whole sea of information on the topic, covering both historical tuning theories and modern developments&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow"&gt;Microtonalismo&lt;/a&gt; - Web microtonal&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.bikexprt.com/music/tunebibl.htm" rel="nofollow"&gt;A bibliography on musical tunings and temperaments&lt;/a&gt;, compiled by John S. Allen&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Huygens-Fokker"&gt;Huygens-Fokker&lt;/a&gt; Foundation's &lt;a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/bib.html" rel="nofollow"&gt;Tuning &amp;amp; temperament bibliography&lt;/a&gt;, hyperlinked and updated by Manuel op de Coul&lt;/li&gt;&lt;li&gt;The &lt;a class="wiki_link_ext" href="http://www.untwelve.org" rel="nofollow"&gt;UnTwelve&lt;/a&gt; website has some pages of theoretical interest, including a &lt;a class="wiki_link_ext" href="http://www.untwelve.org/what.html" rel="nofollow"&gt;fascinating article&lt;/a&gt; authored by Margo Schulter&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

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