22edo: Difference between revisions

Wikispaces>xenjacob
**Imported revision 269079752 - Original comment: **
Wikispaces>vaisvil
**Imported revision 269120442 - 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 05:21:22 UTC</tt>.<br>
: This revision was by author [[User:vaisvil|vaisvil]] and made on <tt>2011-10-27 08:52:44 UTC</tt>.<br>
: The original revision id was <tt>269079752</tt>.<br>
: The original revision id was <tt>269120442</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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** [[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]]


|| &lt; 22 35 51 62 76 81 | ||</pre></div>
|| &lt; 22 35 51 62 76 81 | ||
 
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<h4>Original HTML content:</h4>
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:21:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;hr /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Theory&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Theory&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
In music, &lt;em&gt;22 equal temperament&lt;/em&gt;, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
In music, &lt;em&gt;22 equal temperament&lt;/em&gt;, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
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See also: &lt;a class="wiki_link" href="/22edo%20Solfege"&gt;22edo Solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Tetrachords"&gt;22edo Tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Modes"&gt;22edo Modes&lt;/a&gt;&lt;br /&gt;
See also: &lt;a class="wiki_link" href="/22edo%20Solfege"&gt;22edo Solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Tetrachords"&gt;22edo Tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Modes"&gt;22edo Modes&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-Properties of 22 equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Properties of 22 equal temperament&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-Properties of 22 equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Properties of 22 equal temperament&lt;/h2&gt;
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  &lt;br /&gt;
Possibly the most striking characteristic of 22-et to those not used to it is that it does &lt;strong&gt;not&lt;/strong&gt; &amp;quot;temper out&amp;quot; the syntonic comma of 81/80, and therefore is not a system of &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; temperament. It does, however, temper out the diaschisma, 2048/2025, the magic comma or small diesis, 3125/3072, and the porcupine comma, or maximal diesis, 250/243. In a diaschismic system, such as 12-et or 22-et, the &lt;a class="wiki_link" href="/diatonic%20tritone"&gt;diatonic tritone&lt;/a&gt; &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, which is a major third above a &lt;a class="wiki_link" href="/major%20whole%20tone"&gt;major whole tone&lt;/a&gt; representing &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, is equated to its inverted form, &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;. That the magic comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; system, where five major thirds make up a perfect fifth. That the porcupine comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#porcupine"&gt;porcupine&lt;/a&gt; system, where three &lt;a class="wiki_link" href="/minor%20whole%20tone"&gt;minor whole tone&lt;/a&gt;s (&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; tones) give a fourth, and five give a minor sixth.&lt;br /&gt;
Possibly the most striking characteristic of 22-et to those not used to it is that it does &lt;strong&gt;not&lt;/strong&gt; &amp;quot;temper out&amp;quot; the syntonic comma of 81/80, and therefore is not a system of &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; temperament. It does, however, temper out the diaschisma, 2048/2025, the magic comma or small diesis, 3125/3072, and the porcupine comma, or maximal diesis, 250/243. In a diaschismic system, such as 12-et or 22-et, the &lt;a class="wiki_link" href="/diatonic%20tritone"&gt;diatonic tritone&lt;/a&gt; &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, which is a major third above a &lt;a class="wiki_link" href="/major%20whole%20tone"&gt;major whole tone&lt;/a&gt; representing &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, is equated to its inverted form, &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;. That the magic comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; system, where five major thirds make up a perfect fifth. That the porcupine comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#porcupine"&gt;porcupine&lt;/a&gt; system, where three &lt;a class="wiki_link" href="/minor%20whole%20tone"&gt;minor whole tone&lt;/a&gt;s (&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; tones) give a fourth, and five give a minor sixth.&lt;br /&gt;
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In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, (the &lt;a class="wiki_link" href="/jubilee%20comma"&gt;jubilee comma&lt;/a&gt;), and &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, (the &lt;a class="wiki_link" href="/septimal%20comma"&gt;septimal comma&lt;/a&gt;), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritons of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the &lt;a class="wiki_link" href="/orwell%20comma"&gt;orwell comma&lt;/a&gt;; and the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; is also a chord of 22-et.&lt;br /&gt;
In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, (the &lt;a class="wiki_link" href="/jubilee%20comma"&gt;jubilee comma&lt;/a&gt;), and &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, (the &lt;a class="wiki_link" href="/septimal%20comma"&gt;septimal comma&lt;/a&gt;), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritons of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the &lt;a class="wiki_link" href="/orwell%20comma"&gt;orwell comma&lt;/a&gt;; and the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; is also a chord of 22-et.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Theory-Properties of 22 equal temperament-Linear Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Linear Temperaments&lt;/h3&gt;
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&lt;/table&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Theory-Properties of 22 equal temperament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Commas&lt;/h3&gt;
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  22 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 22 35 51 62 76 81 |.)&lt;br /&gt;
  22 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 22 35 51 62 76 81 |.)&lt;br /&gt;


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&lt;/table&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;A Superpythagorean System&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;A Superpythagorean System&lt;/h3&gt;
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The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; fifth, thus making 22edo a &amp;quot;super-pythagorean&amp;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 &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; ; the &lt;a class="wiki_link" href="/subminor%20third"&gt;subminor third&lt;/a&gt; comes close to &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; and the &lt;a class="wiki_link" href="/supermajor%20third"&gt;supermajor third&lt;/a&gt; to &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, and the m2 falling close to a quarter-tone.&lt;br /&gt;
The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; fifth, thus making 22edo a &amp;quot;super-pythagorean&amp;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 &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; ; the &lt;a class="wiki_link" href="/subminor%20third"&gt;subminor third&lt;/a&gt; comes close to &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; and the &lt;a class="wiki_link" href="/supermajor%20third"&gt;supermajor third&lt;/a&gt; to &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, and the m2 falling close to a quarter-tone.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;How to Notate 22edo in Sagittal&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;How to Notate 22edo in Sagittal&lt;/h3&gt;
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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:778:&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:778 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:779:&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:779 --&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:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Theory-Properties of 22 equal temperament-11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11edo&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Theory-Properties of 22 equal temperament-11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;11edo&lt;/h3&gt;
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As 22 is divisible by 11, a 22edo instrument can play any music in &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, 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.&lt;br /&gt;
As 22 is divisible by 11, a 22edo instrument can play any music in &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, 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.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;External links&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;External links&lt;/h2&gt;
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&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow"&gt;Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow"&gt;Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;References&lt;/h2&gt;
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Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]&lt;br /&gt;
Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]&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;
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&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&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;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&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; 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;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; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&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; 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;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; 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;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; 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;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; 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;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; 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;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; 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;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; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&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; Mussorgsky-Smith&lt;/li&gt;&lt;li&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; - youtube&lt;/li&gt;&lt;li&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;, 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;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&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;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&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; 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;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; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&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; 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;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; 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;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; 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;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; 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;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; 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;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; 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;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; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&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; Mussorgsky-Smith&lt;/li&gt;&lt;li&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; - youtube&lt;/li&gt;&lt;li&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;, 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;
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