13edo: Difference between revisions
Wikispaces>vaisvil **Imported revision 305045202 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 311590024 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-15 22:10:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>311590024</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=**Compositions**= | =**Compositions**= | ||
[[http://www.microtonalmusic.net/audio/slowdance13edo.mp3|Slow Dance]] by [[http://danielthompson.blogspot.com/|Daniel Thompson]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.microtonalmusic.net/audio/slowdance13edo.mp3|Slow Dance]]</span> by [[http://danielthompson.blogspot.com/|Daniel Thompson]] | ||
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3|Prelude in 13ET]] by [[Aaron Andrew Hunt]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3|Prelude in 13ET]]</span> by [[Aaron Andrew Hunt]] | ||
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/13ET.mp3|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/13ET.mp3|Two-Part Invention in 13ET]]</span> by [[Aaron Andrew Hunt]] | ||
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/triskaidekaphobia.mp3|Triskaidekaphobia]] by [[http://www.io.com/%7Ehmiller/music/|Herman Miller]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/triskaidekaphobia.mp3|Triskaidekaphobia]]</span> by [[http://www.io.com/%7Ehmiller/music/|Herman Miller]] | ||
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin13tet.mp3|play]] by [[Andrew Heathwaite]] | [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin13tet.mp3|play]]</span> by [[Andrew Heathwaite]] | ||
[[@http://cityoftheasleep.bandcamp.com/track/broken-dream-jar|Broken Dream Jar]] by [[IgliashonJones|City of the Asleep]] | [[@http://cityoftheasleep.bandcamp.com/track/broken-dream-jar|Broken Dream Jar]] by [[IgliashonJones|City of the Asleep]] | ||
[[@http://www.last.fm/music/City+of+the+Asleep/Map+of+an+Internal+Landscape/Blinding+White+Darkness|Blinding White Darkness]] by [[IgliashonJones|City of the Asleep]] | [[@http://www.last.fm/music/City+of+the+Asleep/Map+of+an+Internal+Landscape/Blinding+White+Darkness|Blinding White Darkness]] by [[IgliashonJones|City of the Asleep]] | ||
[[@http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm|Upsidedown and Backwards: Explorations in 13-tone Equal Temperament]] by [[http://www.elvenminstrel.com/|David J. Finnamore]] | [[@http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm|Upsidedown and Backwards: Explorations in 13-tone Equal Temperament]] by [[http://www.elvenminstrel.com/|David J. Finnamore]] | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3|Comets Over Flatland 11]] by [[Randy Winchester]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3|Comets Over Flatland 11]]</span> by [[Randy Winchester]] | ||
[[http://micro.soonlabel.com/13edo/20120225-midiaxe-prelude-for-synthesizer-in-13-equal.mp3|Prelude for Synthesizer in 13 Equal]] by [[Chris Vaisvil]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/13edo/20120225-midiaxe-prelude-for-synthesizer-in-13-equal.mp3|Prelude for Synthesizer in 13 Equal]]</span> by [[Chris Vaisvil]] | ||
[[http://micro.soonlabel.com/13edo/muon_catalyzed_fusion_13_edo.mp3|Muon Catalyzed Fusion]] by [[Chris Vaisvil | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/13edo/muon_catalyzed_fusion_13_edo.mp3|Muon Catalyzed Fusion]]</span> by [[Chris Vaisvil]] | ||
]] | |||
=Igliashon's 13-EDO diatonic approaches= | =Igliashon's 13-EDO diatonic approaches= | ||
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[[image:Archeotonic.png]] | [[image:Archeotonic.png]] | ||
[[image:Oneirotonic.png]] | [[image:Oneirotonic.png]] | ||
=Mapping to Standard Keyboards= | |||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. | |||
Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. | |||
Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use. | |||
|| 1 || 6 || 11 || 3 || 8 || (13) || 5 || 10 || 2 || 7 || 12 || 4 || 9 || 1 || Place in Chain of 730 cent intervals || | |||
|| X || * || || * || * || || * || || * || * || || * || || X || Marked are the octatonic scales (X=Sarnathian) || | |||
|| || * || || * || * || || * || || X || * || || * || * || || || | |||
|| || * || || X || * || || * || * || || * || || * || * || || || | |||
|| || * || * || || * || || * || * || || * || || X || * || || || | |||
|| || * || * || || * || || X || * || || * || * || || * || || || | |||
|| **D** || Eb || E || **F** || Gb || || **G** || Ab || **A** || Bb || B || **C** || Db || **D** || Keeps the pentatonic scale on the white keys || | |||
|| **A** || Bb || B || **C** || Db || || **D** || Eb || **E** || F || Gb || **G** || Ab || **A** || // || | |||
|| **E** || F || Gb || **G** || Ab || || **A** || Bb || **B** || C || Db || **D** || Eb || **E** || // || | |||
|| **B** || C || Db || **D** || Eb || || **E** || F || **Gb** || G || Ab || **A** || Bb || **B** || // || | |||
|| C || Db || D || Eb || E || || F || Gb || G || Ab || A || Bb || B || C || Puts the missing key between a semitone || | |||
|| G || Ab || A || Bb || B || || C || Db || D || Eb || E || F || Gb || G || // (if that were to be valuable in any way) || | |||
= = | |||
= = | |||
=Commas= | =Commas= | ||
13 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 13 21 30 36 45 48 |.) | 13 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 13 21 30 36 45 48 |.) | ||
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||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= ||</pre></div> | ||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<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>13edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>13edo</title></head><body><!-- ws:start:WikiTextTocRule:23:&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:23 --><!-- ws:start:WikiTextTocRule:24: --><a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Igliashon's 13-EDO diatonic approaches">Igliashon's 13-EDO diatonic approaches</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#toc8"> </a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#toc9"> </a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/12670900?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;12670900&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | ||
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Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:777:&lt;img src=&quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:777 --><br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:780:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13edo%20horograms.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13edo horograms.pdf&quot; title=&quot;File: 13edo horograms.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /></a><div><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf">13edo horograms.pdf</a><br /><ul><li><a href="/file/detail/13edo%20horograms.pdf">Details</a></li><li><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf">Download</a></li><li style="color: #666">242 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:780 --><br /> | ||
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:11 --><strong>Compositions</strong></h1> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:11 --><strong>Compositions</strong></h1> | ||
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<a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/13ET.mp3" rel="nofollow">Two-Part Invention in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/13ET.mp3" rel="nofollow">Two-Part Invention in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/triskaidekaphobia.mp3" rel="nofollow">Triskaidekaphobia</a> by <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/music/" rel="nofollow">Herman Miller</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/triskaidekaphobia.mp3" rel="nofollow">Triskaidekaphobia</a></span> by <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/music/" rel="nofollow">Herman Miller</a><br /> | ||
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265" rel="nofollow">Spikey Hair in 13tET</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin13tet.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br /> | <a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265" rel="nofollow">Spikey Hair in 13tET</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin13tet.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br /> | ||
<a class="wiki_link_ext" href="http://cityoftheasleep.bandcamp.com/track/broken-dream-jar" rel="nofollow" target="_blank">Broken Dream Jar</a> by <a class="wiki_link" href="/IgliashonJones">City of the Asleep</a><br /> | <a class="wiki_link_ext" href="http://cityoftheasleep.bandcamp.com/track/broken-dream-jar" rel="nofollow" target="_blank">Broken Dream Jar</a> by <a class="wiki_link" href="/IgliashonJones">City of the Asleep</a><br /> | ||
<a class="wiki_link_ext" href="http://www.last.fm/music/City+of+the+Asleep/Map+of+an+Internal+Landscape/Blinding+White+Darkness" rel="nofollow" target="_blank">Blinding White Darkness</a> by <a class="wiki_link" href="/IgliashonJones">City of the Asleep</a><br /> | <a class="wiki_link_ext" href="http://www.last.fm/music/City+of+the+Asleep/Map+of+an+Internal+Landscape/Blinding+White+Darkness" rel="nofollow" target="_blank">Blinding White Darkness</a> by <a class="wiki_link" href="/IgliashonJones">City of the Asleep</a><br /> | ||
<a class="wiki_link_ext" href="http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm" rel="nofollow" target="_blank">Upsidedown and Backwards: Explorations in 13-tone Equal Temperament</a> by <a class="wiki_link_ext" href="http://www.elvenminstrel.com/" rel="nofollow">David J. Finnamore</a><br /> | <a class="wiki_link_ext" href="http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm" rel="nofollow" target="_blank">Upsidedown and Backwards: Explorations in 13-tone Equal Temperament</a> by <a class="wiki_link_ext" href="http://www.elvenminstrel.com/" rel="nofollow">David J. Finnamore</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3" rel="nofollow">Comets Over Flatland 11</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3" rel="nofollow">Comets Over Flatland 11</a></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/13edo/20120225-midiaxe-prelude-for-synthesizer-in-13-equal.mp3" rel="nofollow">Prelude for Synthesizer in 13 Equal</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/13edo/20120225-midiaxe-prelude-for-synthesizer-in-13-equal.mp3" rel="nofollow">Prelude for Synthesizer in 13 Equal</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/13edo/muon_catalyzed_fusion_13_edo.mp3" rel="nofollow">Muon Catalyzed Fusion</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/13edo/muon_catalyzed_fusion_13_edo.mp3" rel="nofollow">Muon Catalyzed Fusion</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Igliashon's 13-EDO diatonic approaches"></a><!-- ws:end:WikiTextHeadingRule:13 -->Igliashon's 13-EDO diatonic approaches</h1> | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Igliashon's 13-EDO diatonic approaches"></a><!-- ws:end:WikiTextHeadingRule:13 -->Igliashon's 13-EDO diatonic approaches</h1> | ||
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<br /> | <br /> | ||
To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:15 -->Mapping to Standard Keyboards</h1> | ||
<br /> | |||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. <br /> | |||
<br /> | |||
Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. <br /> | |||
<br /> | |||
Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use.<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td>(13)<br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td>12<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>Place in Chain of 730 cent intervals<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>X<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>X<br /> | |||
</td> | |||
<td>Marked are the octatonic scales (X=Sarnathian)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>X<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>X<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>X<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>X<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>*<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><strong>D</strong><br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td><strong>F</strong><br /> | |||
</td> | |||
<td>Gb<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><strong>G</strong><br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td><strong>A</strong><br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | |||
<td><strong>C</strong><br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td><strong>D</strong><br /> | |||
</td> | |||
<td>Keeps the pentatonic scale on the white keys<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><strong>A</strong><br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | |||
<td><strong>C</strong><br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><strong>D</strong><br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td><strong>E</strong><br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>Gb<br /> | |||
</td> | |||
<td><strong>G</strong><br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td><strong>A</strong><br /> | |||
</td> | |||
<td><em><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><strong>E</strong><br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>Gb<br /> | |||
</td> | |||
<td><strong>G</strong><br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><strong>A</strong><br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td><strong>B</strong><br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td><strong>D</strong><br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td><strong>E</strong><br /> | |||
</td> | |||
<td></em><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><strong>B</strong><br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td><strong>D</strong><br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><strong>E</strong><br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td><strong>Gb</strong><br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td><strong>A</strong><br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td><strong>B</strong><br /> | |||
</td> | |||
<td><em><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>C<br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>Gb<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>Puts the missing key between a semitone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>G<br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>Gb<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td></em> (if that were to be valuable in any way)<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><!-- ws:end:WikiTextHeadingRule:17 --> </h1> | |||
<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9"><!-- ws:end:WikiTextHeadingRule:19 --> </h1> | |||
<!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc10"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:21 -->Commas</h1> | |||
13 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<br /> | 13 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<br /> | ||