11edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2010~~-06-~~14 03~~:49:00 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-01-26 13:23:12 UTC</tt>.

: The original revision id was <tt>~~148685161~~</tt>.

: The original revision id was <tt>196242112</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=11 tone equal temperament=

11-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.

===Theory===

Compared to 12edo, the intervals of 11edo are stretched:

* The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.

* The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.

* The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."

* The "major third," at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.

* The "perfect fourth," at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.

11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat quite a bit with harmonic timbres.

|| Harmonic || 8 || || 9 || || 11 || || 14 || || 16 ||

|| JI interval from 1/1 || 1/1 = 0 cents || || 9/8 = 204 || || 11/8 = 551 || || 7/4 = 969 || || 2/1 = 1200 ||

|| nearest 11edo interval || 0\11edo = 0 cents || || 2\11 = 218 || || 5\11 = 545 || || 9\11 = 982 || || 11\11 = 1200 ||

|| difference || 0 || || +14 || || -6 || || +13 || || 0 ||

|| JI interval between || || 9:8 = 204 cents || || 11:9 = 347 || || 14/11 = 418 || || 8:7 = 231 || ||

|| nearest 11edo interval || || 2\11 = 218 || || 3\11 = 327 || || 4\11 = 436 || || 2\11 = 218 || ||

|| difference || || +14 || || -20 || || +18 || || -13 || ||

===MOS Scales===

Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.

2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.

3\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.

4\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.

5\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.

See [[11edo Modes]]

===Compositions===

[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html|Turquoise Dabo Girl]] by [[Bill Sethares]] (spectrally bent synth ens.)

[[http://www.h-pi.com/mp3/Prelude11ET.mp3|Prelude11ET]] by [[Aaron Andrew Hunt|Aaron Hunt]] (neo-Baroque)

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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"><html><head><title>11edo</title></head><body><h1 id="toc0"><a name="x11 tone equal temperament"></a>11 tone equal temperament</h1>

11-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.

<h3 id="toc1"><a name="x11 tone equal temperament--Theory"></a>Theory</h3>

~~See~~ <a class="~~wiki_link~~" ~~href~~="/11edo~~%20Modes~~">~~11edo Modes~~</a>

Compared to 12edo, the intervals of 11edo are stretched:

<ul><li>The &quot;minor second,&quot; at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The &quot;major second,&quot; at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a &quot;bluesy&quot; seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The &quot;minor third,&quot; at 327.27 cents, is rather sharp and encroaching upon &quot;neutral third.&quot;</li><li>The &quot;major third,&quot; at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.</li><li>The &quot;perfect fourth,&quot; at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.</li></ul>

11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat quite a bit with harmonic timbres.

<tr>

<td>Harmonic

</td>

<td>8

</td>

<td>

</td>

<td>9

</td>

<td>

</td>

<td>11

</td>

<td>

</td>

<td>14

</td>

<td>

</td>

<td>16

</td>

</tr>

<tr>

<td>JI interval from 1/1

</td>

<td>1/1 = 0 cents

</td>

<td>

</td>

<td>9/8 = 204

</td>

<td>

</td>

<td>11/8 = 551

</td>

<td>

</td>

<td>7/4 = 969

</td>

<td>

</td>

<td>2/1 = 1200

</td>

</tr>

<tr>

<td>nearest 11edo interval

</td>

<td>0\11edo = 0 cents

</td>

<td>

</td>

<td>2\11 = 218

</td>

<td>

</td>

<td>5\11 = 545

</td>

<td>

</td>

<td>9\11 = 982

</td>

<td>

</td>

<td>11\11 = 1200

</td>

</tr>

<tr>

<td>difference

</td>

<td>0

</td>

<td>

</td>

<td>+14

</td>

<td>

</td>

<td>-6

</td>

<td>

</td>

<td>+13

</td>

<td>

</td>

<td>0

</td>

</tr>

<tr>

<td>JI interval between

</td>

<td>

</td>

<td>9:8 = 204 cents

</td>

<td>

</td>

<td>11:9 = 347

</td>

<td>

</td>

<td>14/11 = 418

</td>

<td>

</td>

<td>8:7 = 231

</td>

<td>

</td>

</tr>

<tr>

<td>nearest 11edo interval

</td>

<td>

</td>

<td>2\11 = 218

</td>

<td>

</td>

<td>3\11 = 327

</td>

<td>

</td>

<td>4\11 = 436

</td>

<td>

</td>

<td>2\11 = 218

</td>

<td>

</td>

</tr>

<tr>

<td>difference

</td>

<td>

</td>

<td>+14

</td>

<td>

</td>

<td>-20

</td>

<td>

</td>

<td>+18

</td>

<td>

</td>

<td>-13

</td>

<td>

</td>

</tr>

</table>

<h3 id="toc2"><a name="x11 tone equal temperament--MOS Scales"></a>MOS Scales</h3>

Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.

<h3 id="~~toc2~~"><a name="x11 tone equal temperament--Compositions"></a>Compositions</h3>

2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.

<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow">Turquoise Dabo Girl</a> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (spectrally bent synth ens.)

3\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.

4\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.

5\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.

See <a class="wiki_link" href="/11edo%20Modes">11edo Modes</a>

<h3 id="toc3"><a name="x11 tone equal temperament--Compositions"></a>Compositions</h3>

<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow">Turquoise Dabo Girl</a> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (spectrally bent synth ens.)

<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude11ET.mp3" rel="nofollow">Prelude11ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Hunt</a> (neo-Baroque)

<a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/complist.html" rel="nofollow">The Stuffed Ones</a> by <a class="wiki_link" href="/Christopher%20Bailey">Christopher Bailey</a> (keyboards concréte)

<a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839070" rel="nofollow">conversation is</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>. Text is a sentence borrowed from a paper by Larry Richards, set to an 11-tone row. For guitar &amp; voice.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-14 03:49:00 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-01-26 13:23:12 UTC</tt>.<br>
-: The original revision id was <tt>148685161</tt>.<br>
+: The original revision id was <tt>196242112</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=11 tone equal temperament=
+-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.
 ===Theory===
+Compared to 12edo, the intervals of 11edo are stretched:
+* The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.
+* The "major second," at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.
+* The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."
+* The "major third," at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.
+* The "perfect fourth," at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.
+edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat quite a bit with harmonic timbres.
+|| Harmonic || 8 ||   || 9 ||   || 11 ||   || 14 ||   || 16 ||
+|| JI interval from 1/1 || 1/1 = 0 cents ||   || 9/8 = 204 ||   || 11/8 = 551 ||   || 7/4 = 969 ||   || 2/1 = 1200 ||
+|| nearest 11edo interval || 0\11edo = 0 cents ||   || 2\11 = 218 ||   || 5\11 = 545 ||   || 9\11 = 982 ||   || 11\11 = 1200 ||
+|| difference || 0 ||   || +14 ||   || -6 ||   || +13 ||   || 0 ||
+|| JI interval between ||   || 9:8 = 204 cents ||   || 11:9 = 347 ||   || 14/11 = 418 ||   || 8:7 = 231 ||   ||
+|| nearest 11edo interval ||   || 2\11 = 218 ||   || 3\11 = 327 ||   || 4\11 = 436 ||   || 2\11 = 218 ||   ||
+|| difference ||   || +14 ||   || -20 ||   || +18 ||   || -13 ||   ||
+===MOS Scales===
+Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.
+\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.
+\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.
+\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.
+\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.
 See [[11edo Modes]]
 ===Compositions===
 [[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html|Turquoise Dabo Girl]] by [[Bill Sethares]] (spectrally bent synth ens.)
 [[http://www.h-pi.com/mp3/Prelude11ET.mp3|Prelude11ET]] by [[Aaron Andrew Hunt|Aaron Hunt]] (neo-Baroque)
@@ Line 19: / Line 49: @@
 <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;11edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x11 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11 tone equal temperament&lt;/h1&gt;
   &lt;br /&gt;
+-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x11 tone equal temperament--Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h3&gt;
-  See &lt;a class="wiki_link" href="/11edo%20Modes"&gt;11edo Modes&lt;/a&gt;&lt;br /&gt;
+  &lt;br /&gt;
+Compared to 12edo, the intervals of 11edo are stretched:&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;The &amp;quot;minor second,&amp;quot; at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.&lt;/li&gt;&lt;li&gt;The &amp;quot;major second,&amp;quot; at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a &amp;quot;bluesy&amp;quot; seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.&lt;/li&gt;&lt;li&gt;The &amp;quot;minor third,&amp;quot; at 327.27 cents, is rather sharp and encroaching upon &amp;quot;neutral third.&amp;quot;&lt;/li&gt;&lt;li&gt;The &amp;quot;major third,&amp;quot; at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.&lt;/li&gt;&lt;li&gt;The &amp;quot;perfect fourth,&amp;quot; at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat quite a bit with harmonic timbres.&lt;br /&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;JI interval from 1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1/1 = 0 cents&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/8 = 204&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/8 = 551&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/4 = 969&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2/1 = 1200&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;nearest 11edo interval&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0\11edo = 0 cents&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2\11 = 218&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5\11 = 545&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9\11 = 982&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11\11 = 1200&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;difference&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;+14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;+13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;JI interval between&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9:8 = 204 cents&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11:9 = 347&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/11 = 418&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8:7 = 231&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;nearest 11edo interval&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2\11 = 218&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3\11 = 327&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4\11 = 436&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2\11 = 218&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;difference&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;+14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;+18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x11 tone equal temperament--MOS Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;MOS Scales&lt;/h3&gt;
+ &lt;br /&gt;
+Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x11 tone equal temperament--Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h3&gt;
+\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.&lt;br /&gt;
-  &lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow"&gt;Turquoise Dabo Girl&lt;/a&gt; by &lt;a class="wiki_link" href="/Bill%20Sethares"&gt;Bill Sethares&lt;/a&gt; (spectrally bent synth ens.)&lt;br /&gt;
+\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.&lt;br /&gt;
+\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.&lt;br /&gt;
+\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.&lt;br /&gt;
+&lt;br /&gt;
+See &lt;a class="wiki_link" href="/11edo%20Modes"&gt;11edo Modes&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x11 tone equal temperament--Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Compositions&lt;/h3&gt;
+  &lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow"&gt;Turquoise Dabo Girl&lt;/a&gt; by &lt;a class="wiki_link" href="/Bill%20Sethares"&gt;Bill Sethares&lt;/a&gt; (spectrally bent synth ens.)&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude11ET.mp3" rel="nofollow"&gt;Prelude11ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Hunt&lt;/a&gt; (neo-Baroque)&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/complist.html" rel="nofollow"&gt;The Stuffed Ones&lt;/a&gt; by &lt;a class="wiki_link" href="/Christopher%20Bailey"&gt;Christopher Bailey&lt;/a&gt; (keyboards concréte)&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839070" rel="nofollow"&gt;conversation is&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;. Text is a sentence borrowed from a paper by Larry Richards, set to an 11-tone row. For guitar &amp;amp; voice.&lt;/body&gt;&lt;/html&gt;</pre></div>