22edo: Difference between revisions

Wikispaces>mbattaglia1
**Imported revision 287849378 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 299587190 - 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>2011-12-21 02:34:07 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-08 01:01:30 UTC</tt>.<br>
: The original revision id was <tt>287849378</tt>.<br>
: The original revision id was <tt>299587190</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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* Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - [[http://www.angelfire.com/mo/oljare/midicomp.html|MIDI files]]
* Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - [[http://www.angelfire.com/mo/oljare/midicomp.html|MIDI files]]
** [[http://xenharmonic.wikispaces.com/file/view/sunday3.pdf|Sagittal score of Sunday Pipes]]
** [[http://xenharmonic.wikispaces.com/file/view/sunday3.pdf|Sagittal score of Sunday Pipes]]
* [[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.


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When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:&lt;br /&gt;
When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:781:&amp;lt;img src=&amp;quot;/file/view/22edo.png/269078624/22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:781 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:783:&amp;lt;img src=&amp;quot;/file/view/22edo.png/269078624/22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:783 --&gt;&lt;br /&gt;
This notation is consistent with Sagittal's notation of 5-limit JI harmony: &amp;quot;major&amp;quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.&lt;br /&gt;
This notation is consistent with Sagittal's notation of 5-limit JI harmony: &amp;quot;major&amp;quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Compositions&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Compositions&lt;/h1&gt;
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  &lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/~chris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&gt;&lt;/span&gt; by Paul Erlich and &lt;a class="wiki_link" href="/Ara%20Sarkissian"&gt;Ara Sarkissian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow"&gt;Dragged by a Storm Across the Desert Years&lt;/a&gt;&lt;/span&gt; by * &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Jones&lt;/a&gt; (synth with electric guitar)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow"&gt;Numerology&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow"&gt;Revenge of the inorganic compounds&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow"&gt;My Crazy Aunt Sophie&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;. Blatantly xenharmonic piano.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow"&gt;where words are said to mean&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp;amp; the following pieces by Andrew are for 22-tone guitar &amp;amp; voice.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow"&gt;I've come with a bucket of roses&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow"&gt;one drop of rain&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow"&gt;being a&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow"&gt;my own house&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 17&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt;&lt;/span&gt; Mussorgsky-Smith&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow"&gt;Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity&lt;/a&gt;&lt;/span&gt; - youtube&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow"&gt;Improvisation in 22-equal temperament&lt;/a&gt;&lt;/span&gt;, Mike Battaglia - youtube&lt;/li&gt;&lt;li&gt;Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - &lt;a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow"&gt;MIDI files&lt;/a&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/~chris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&gt;&lt;/span&gt; by Paul Erlich and &lt;a class="wiki_link" href="/Ara%20Sarkissian"&gt;Ara Sarkissian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow"&gt;Dragged by a Storm Across the Desert Years&lt;/a&gt;&lt;/span&gt; by * &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Jones&lt;/a&gt; (synth with electric guitar)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow"&gt;Numerology&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow"&gt;Revenge of the inorganic compounds&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow"&gt;My Crazy Aunt Sophie&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;. Blatantly xenharmonic piano.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow"&gt;where words are said to mean&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp;amp; the following pieces by Andrew are for 22-tone guitar &amp;amp; voice.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow"&gt;I've come with a bucket of roses&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow"&gt;one drop of rain&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow"&gt;being a&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow"&gt;my own house&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 17&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt;&lt;/span&gt; Mussorgsky-Smith&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow"&gt;Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity&lt;/a&gt;&lt;/span&gt; - youtube&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow"&gt;Improvisation in 22-equal temperament&lt;/a&gt;&lt;/span&gt;, Mike Battaglia - youtube&lt;/li&gt;&lt;li&gt;Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - &lt;a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow"&gt;MIDI files&lt;/a&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;