22edo: Difference between revisions
Wikispaces>xenjacob **Imported revision 269078952 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 269079752 - 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:xenjacob|xenjacob]] and made on <tt>2011-10-27 05: | : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2011-10-27 05:21:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>269079752</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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The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent [[3-limit]] fifth, thus making 22edo a "super-pythagorean" system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the [[7-limit]] ; the [[subminor third]] comes close to [[7_6|7/6]] and the [[supermajor third]] to [[9_7|9/7]]. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and [[8_7|8/7]], and the m2 falling close to a quarter-tone. | The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent [[3-limit]] fifth, thus making 22edo a "super-pythagorean" system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the [[7-limit]] ; the [[subminor third]] comes close to [[7_6|7/6]] and the [[supermajor third]] to [[9_7|9/7]]. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and [[8_7|8/7]], and the m2 falling close to a quarter-tone. | ||
How to Notate 22edo in Sagittal | ===How to Notate 22edo in Sagittal=== | ||
When 22edo is treated as a | 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: | ||
[[image:22edo.png]] | [[image:22edo.png]] | ||
This notation is consistent with Sagittal's notation of 5-limit JI harmony: "major" 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma. | |||
===11edo=== | ===11edo=== | ||
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|| < 22 35 51 62 76 81 | ||</pre></div> | || < 22 35 51 62 76 81 | ||</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>22edo</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>22edo</title></head><body><!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1> | ||
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The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent <a class="wiki_link" href="/3-limit">3-limit</a> fifth, thus making 22edo a &quot;super-pythagorean&quot; system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the <a class="wiki_link" href="/7-limit">7-limit</a> ; the <a class="wiki_link" href="/subminor%20third">subminor third</a> comes close to <a class="wiki_link" href="/7_6">7/6</a> and the <a class="wiki_link" href="/supermajor%20third">supermajor third</a> to <a class="wiki_link" href="/9_7">9/7</a>. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and <a class="wiki_link" href="/8_7">8/7</a>, and the m2 falling close to a quarter-tone.<br /> | The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent <a class="wiki_link" href="/3-limit">3-limit</a> fifth, thus making 22edo a &quot;super-pythagorean&quot; system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the <a class="wiki_link" href="/7-limit">7-limit</a> ; the <a class="wiki_link" href="/subminor%20third">subminor third</a> comes close to <a class="wiki_link" href="/7_6">7/6</a> and the <a class="wiki_link" href="/supermajor%20third">supermajor third</a> to <a class="wiki_link" href="/9_7">9/7</a>. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and <a class="wiki_link" href="/8_7">8/7</a>, and the m2 falling close to a quarter-tone.<br /> | ||
<br /> | <br /> | ||
How to Notate 22edo in Sagittal< | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"></a><!-- ws:end:WikiTextHeadingRule:10 -->How to Notate 22edo in Sagittal</h3> | ||
<br /> | <br /> | ||
When 22edo is treated as a | 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:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:778:&lt;img src=&quot;/file/view/22edo.png/269078624/22edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /><!-- ws:end:WikiTextLocalImageRule:778 --><br /> | ||
This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Theory-Properties of 22 equal temperament-11edo"></a><!-- ws:end:WikiTextHeadingRule:12 -->11edo</h3> | ||
<br /> | <br /> | ||
As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 can be notated as every other note of 22.<br /> | As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 can be notated as every other note of 22.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Theory-External links"></a><!-- ws:end:WikiTextHeadingRule:14 -->External links</h2> | ||
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<a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a><br /> | <a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:16 -->References</h2> | ||
<br /> | <br /> | ||
Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | ||
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<br /> | <br /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:18 -->Compositions</h1> | ||
<br /> | <br /> | ||
<ul><li><a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a></li><li><a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow">Glassic</a> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a> by Paul Erlich and Ara Sarkissian (jazz)</li><li><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">Dragged by a Storm Across the Desert Years</a> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><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">Numerology</a> by Iglashion Jones (progressive metal)</li><li><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">Revenge of the inorganic compounds</a> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a> - youtube</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a><ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf">Sagittal score of Sunday Pipes</a></li></ul></li></ul><br /> | <ul><li><a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a></li><li><a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow">Glassic</a> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a> by Paul Erlich and Ara Sarkissian (jazz)</li><li><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">Dragged by a Storm Across the Desert Years</a> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><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">Numerology</a> by Iglashion Jones (progressive metal)</li><li><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">Revenge of the inorganic compounds</a> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a> - youtube</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a><ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf">Sagittal score of Sunday Pipes</a></li></ul></li></ul><br /> | ||