13edo: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 391132644 - Original comment: Reverted to Dec 6, 2012 6:15 am: revert** |
Wikispaces>mbattaglia1 **Imported revision 391132734 - 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:mbattaglia1|mbattaglia1]] and made on <tt>2012-12-11 00: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-12-11 00:26:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>391132734</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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=**Compositions**= | =**Compositions**= | ||
<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]] | <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]] | ||
<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]] | <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]] | ||
<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]] | <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]] | ||
<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]] | <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]] <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://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]] | ||
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[[http://soundcloud.com/cityoftheasleep/farthur|Farthur]] by City of the Asleep | [[http://soundcloud.com/cityoftheasleep/farthur|Farthur]] by 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]] | ||
<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]] | <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]] | ||
<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]] | <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]] | ||
<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]] | <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]] | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.seraph.it/dep/det/13Miles.mp3|13 Miles]]//</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/ca5de720a48c401bcab8fc82c3b81ddc-152.html|blog entry]]) | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/13Miles.mp3|13 Miles]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/ca5de720a48c401bcab8fc82c3b81ddc-152.html|blog entry]]) | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.seraph.it/dep/det/FastAndFurious13.mp3|Fast And Furious 13]]//</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/d2849db485fe3de42e769dad4db3a6ac-153.html|blog entry]]) | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/FastAndFurious13.mp3|Fast And Furious 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/d2849db485fe3de42e769dad4db3a6ac-153.html|blog entry]]) | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.seraph.it/dep/det/SazDul13.mp3|SazDul 13]]//</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/bb5f0dcff57ba4fc56fcf50f54f10e4b-154.html|blog entry]]) | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/SazDul13.mp3|SazDul 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/bb5f0dcff57ba4fc56fcf50f54f10e4b-154.html|blog entry]]) | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.seraph.it/dep/det/Thirteenstan.mp3|Thirteenstan]]//</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/2cd2657e7fc17cdbe44dcd5fc255a951-155.html|blog entry]]) | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/Thirteenstan.mp3|Thirteenstan]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/2cd2657e7fc17cdbe44dcd5fc255a951-155.html|blog entry]]) | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.seraph.it/dep/det/Concertina13.mp3|Concertina 13]]//</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/3e06afae9b0565b3bc0f39581683cfa7-156.html|blog entry]]) | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/Concertina13.mp3|Concertina 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/3e06afae9b0565b3bc0f39581683cfa7-156.html|blog entry]]) | ||
[[@http://soundcloud.com/xenvotta/sets/votta-liber-stellarum-for/|Liber Stellarum]] by [[@http://www.alvotta.net|Alfredo Votta]] | [[@http://soundcloud.com/xenvotta/sets/votta-liber-stellarum-for/|Liber Stellarum]] by [[@http://www.alvotta.net|Alfredo Votta]] | ||
= | =Chuckles McGee's 13-EDO diatonic approaches= | ||
From a temperament perspective, we can probably make the "best" use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping <1 -1| (for 5 and 13), corresponding to the 3rd horogram above. This gives rise to "Sephiroth" modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping <2 3| (for 11 and 13). This corresponds to the 2nd horogram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament). | From a temperament perspective, we can probably make the "best" use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping <1 -1| (for 5 and 13), corresponding to the 3rd horogram above. This gives rise to "Sephiroth" modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping <2 3| (for 11 and 13). This corresponds to the 2nd horogram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament). | ||
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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:21:&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:21 --><!-- ws:start:WikiTextTocRule:22: --><a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="# | <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:21:&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:21 --><!-- ws:start:WikiTextTocRule:22: --><a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Chuckles McGee's 13-EDO diatonic approaches">Chuckles McGee's 13-EDO diatonic approaches</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#toc8"> </a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | ||
<!-- ws:end:WikiTextTocRule:32 --><!-- 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"> | <!-- ws:end:WikiTextTocRule:32 --><!-- 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"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | </script><!-- ws:end:WikiTextMediaRule:0 --><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> | ||
<br /> | <br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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 /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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 /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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 /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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 /> | ||
| Line 381: | Line 381: | ||
<a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/farthur" rel="nofollow">Farthur</a> by City of the Asleep<br /> | <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/farthur" rel="nofollow">Farthur</a> by City of the Asleep<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 /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name=" | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Chuckles McGee's 13-EDO diatonic approaches"></a><!-- ws:end:WikiTextHeadingRule:13 -->Chuckles McGee's 13-EDO diatonic approaches</h1> | ||
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From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horogram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horogram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horogram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horogram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | ||