22edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 21:53:36 UTC</tt>.

: The original revision id was <tt>~~216121588~~</tt>.

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: The revision comment was: <tt>Added comma table.</tt>

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<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">[[toc|flat]]

----

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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 [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), 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 a utonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], 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 [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.

===Commas===

22 EDO tempers out the following commas. (Note: This assumes the val < 22 35 51 62 76 81 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

|| 250/243 || | 1 -5 3 > || 49.17 || Maximal Diesis || Porcupine Comma || ||

|| 3125/3072 || | -10 -1 5 > || 29.61 || Small Diesis || Magic Comma || ||

|| 2048/2025 || | 11 -4 -2 > || 19.55 || Diaschisma || || ||

|| 2109375/2097152 || | -21 3 7 > || 10.06 || Semicomma || Fokker Comma || ||

|| 9193891/9143623 || | 32 -7 -9 > || 9.49 |||| Escapade Comma || ||

|| 4758837/4757272 || | -53 10 16 > || 0.57 || Kwazy || || ||

|| 50/49 || | 1 0 2 -2 > || 34.98 || Tritonic Diesis || Jubilisma || ||

|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||

|| 875/864 || | -5 -3 3 1 > || 21.90 || Keema || || ||

|| 2430/2401 || | 1 5 1 -4 > || 20.79 || Nuwell || || ||

|| 245/243 || | 0 -5 1 2 > || 14.19 || Sensamagic || || ||

|| 1728/1715 || | 6 3 -1 -3 > || 13.07 || Orwellisma || Orwell Comma || ||

|| 225/224 || | -5 2 2 -1 > || 7.71 || Septimal Kleisma || Marvel Comma || ||

|| 10976/10935 || | 5 -7 -1 3 > || 6.48 || Hemimage || || ||

|| 6144/6125 || | 11 1 -3 -2 > || 5.36 || Porwell || || ||

|| 65625/65536 || | -16 1 5 1 > || 2.35 || Horwell || || ||

|| 420175/419904 || | -6 -8 2 5 > || 1.12 || Wizma || || ||

|| 99/98 || | -1 2 0 -2 1 > || 17.58 || Mothwellsma || || ||

|| 100/99 || | 2 -2 2 0 -1 > || 17.40 || Ptolemisma || || ||

|| 121/120 || | -3 -1 -1 0 2 > || 14.37 || Biyatisma || || ||

|| 176/175 || | 4 0 -2 -1 1 > || 9.86 || Valinorsma || || ||

|| 896/891 || | 7 -4 0 1 -1 > || 9.69 || Pentacircle || || ||

|| 65536/65219 || | 16 0 0 -2 -3 > || 8.39 || Orgonisma || || ||

|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma || || ||

|| 540/539 || | 2 3 1 -2 -1 > || 3.21 || Swetisma || || ||

|| 4000/3993 || | 5 -1 3 0 -3 > || 3.03 || Wizardharry || || ||

|| 9801/9800 || | -3 4 -2 -2 2 > || 0.18 || Kalisma || Gauss' Comma || ||

|| 91/90 || | -1 -2 -1 1 0 1 > || 19.13 || Superleap || || ||

===A Superpythagorean System===

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==External links==

[[http://lumma.org/tuning/erlich/erlich-decatonic.pdf

[[http://lumma.org/tuning/erlich/erlich-decatonic.pdf|Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']]

|Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']]

==References==

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[[http://soundclick.com/share?songid=8839060|being a]] by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).

[[http://soundclick.com/share?songid=8839071|my own house]] by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).

[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith</pre></div>

[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith

|| < 22 35 51 62 76 81 | ||

</pre></div>

<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><a href="#Theory">Theory</a> | <a href="#Compositions">Compositions</a>

<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><a href="#Theory">Theory</a> | <a href="#Compositions">Compositions</a>

~~ ~~

<hr />

<h1 id="toc0"><a name="Theory"></a>Theory</h1>

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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 <a class="wiki_link" href="/50_49">50/49</a>, (the <a class="wiki_link" href="/jubilee%20comma">jubilee comma</a>), and <a class="wiki_link" href="/64_63">64/63</a>, (the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>), 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 a utonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>, 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 <a class="wiki_link" href="/orwell%20comma">orwell comma</a>; and the <a class="wiki_link" href="/orwell%20tetrad">orwell tetrad</a> is also a chord of 22-et.

<h3 id="toc2"><a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"></a>A Superpythagorean System</h3>

<h3 id="toc2"><a name="Theory-Properties of 22 equal temperament-Commas"></a>Commas</h3>

22 EDO tempers out the following commas. (Note: This assumes the val &lt; 22 35 51 62 76 81 |.)

<tr>

<th>Comma

</th>

<th>Monzo

</th>

<th>Value (Cents)

</th>

<th>Name 1

</th>

<th>Name 2

</th>

<th>Name 3

</th>

</tr>

<tr>

<td>250/243

</td>

<td>| 1 -5 3 &gt;

</td>

<td>49.17

</td>

<td>Maximal Diesis

</td>

<td>Porcupine Comma

</td>

<td>

</td>

</tr>

<tr>

<td>3125/3072

</td>

<td>| -10 -1 5 &gt;

</td>

<td>29.61

</td>

<td>Small Diesis

</td>

<td>Magic Comma

</td>

<td>

</td>

</tr>

<tr>

<td>2048/2025

</td>

<td>| 11 -4 -2 &gt;

</td>

<td>19.55

</td>

<td>Diaschisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>2109375/2097152

</td>

<td>| -21 3 7 &gt;

</td>

<td>10.06

</td>

<td>Semicomma

</td>

<td>Fokker Comma

</td>

<td>

</td>

</tr>

<tr>

<td>9193891/9143623

</td>

<td>| 32 -7 -9 &gt;

</td>

<td>9.49

</td>

<td colspan="2">Escapade Comma

</td>

<td>

</td>

</tr>

<tr>

<td>4758837/4757272

</td>

<td>| -53 10 16 &gt;

</td>

<td>0.57

</td>

<td>Kwazy

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>50/49

</td>

<td>| 1 0 2 -2 &gt;

</td>

<td>34.98

</td>

<td>Tritonic Diesis

</td>

<td>Jubilisma

</td>

<td>

</td>

</tr>

<tr>

<td>64/63

</td>

<td>| 6 -2 0 -1 &gt;

</td>

<td>27.26

</td>

<td>Septimal Comma

</td>

<td>Archytas' Comma

</td>

<td>Leipziger Komma

</td>

</tr>

<tr>

<td>875/864

</td>

<td>| -5 -3 3 1 &gt;

</td>

<td>21.90

</td>

<td>Keema

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>2430/2401

</td>

<td>| 1 5 1 -4 &gt;

</td>

<td>20.79

</td>

<td>Nuwell

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>245/243

</td>

<td>| 0 -5 1 2 &gt;

</td>

<td>14.19

</td>

<td>Sensamagic

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>1728/1715

</td>

<td>| 6 3 -1 -3 &gt;

</td>

<td>13.07

</td>

<td>Orwellisma

</td>

<td>Orwell Comma

</td>

<td>

</td>

</tr>

<tr>

<td>225/224

</td>

<td>| -5 2 2 -1 &gt;

</td>

<td>7.71

</td>

<td>Septimal Kleisma

</td>

<td>Marvel Comma

</td>

<td>

</td>

</tr>

<tr>

<td>10976/10935

</td>

<td>| 5 -7 -1 3 &gt;

</td>

<td>6.48

</td>

<td>Hemimage

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>6144/6125

</td>

<td>| 11 1 -3 -2 &gt;

</td>

<td>5.36

</td>

<td>Porwell

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>65625/65536

</td>

<td>| -16 1 5 1 &gt;

</td>

<td>2.35

</td>

<td>Horwell

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>420175/419904

</td>

<td>| -6 -8 2 5 &gt;

</td>

<td>1.12

</td>

<td>Wizma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>99/98

</td>

<td>| -1 2 0 -2 1 &gt;

</td>

<td>17.58

</td>

<td>Mothwellsma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>100/99

</td>

<td>| 2 -2 2 0 -1 &gt;

</td>

<td>17.40

</td>

<td>Ptolemisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>121/120

</td>

<td>| -3 -1 -1 0 2 &gt;

</td>

<td>14.37

</td>

<td>Biyatisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>176/175

</td>

<td>| 4 0 -2 -1 1 &gt;

</td>

<td>9.86

</td>

<td>Valinorsma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>896/891

</td>

<td>| 7 -4 0 1 -1 &gt;

</td>

<td>9.69

</td>

<td>Pentacircle

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>65536/65219

</td>

<td>| 16 0 0 -2 -3 &gt;

</td>

<td>8.39

</td>

<td>Orgonisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>385/384

</td>

<td>| -7 -1 1 1 1 &gt;

</td>

<td>4.50

</td>

<td>Keenanisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>540/539

</td>

<td>| 2 3 1 -2 -1 &gt;

</td>

<td>3.21

</td>

<td>Swetisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4000/3993

</td>

<td>| 5 -1 3 0 -3 &gt;

</td>

<td>3.03

</td>

<td>Wizardharry

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>9801/9800

</td>

<td>| -3 4 -2 -2 2 &gt;

</td>

<td>0.18

</td>

<td>Kalisma

</td>

<td>Gauss' Comma

</td>

<td>

</td>

</tr>

<tr>

<td>91/90

</td>

<td>| -1 -2 -1 1 0 1 &gt;

</td>

<td>19.13

</td>

<td>Superleap

</td>

<td>

</td>

<td>

</td>

</tr>

</table>

<h3 id="toc3"><a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"></a>A Superpythagorean System</h3>

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.

<h3 id="~~toc3~~"><a name="Theory-Properties of 22 equal temperament-11edo"></a>11edo</h3>

<h3 id="toc4"><a name="Theory-Properties of 22 equal temperament-11edo"></a>11edo</h3>

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).

<h2 id="~~toc4~~"><a name="Theory-External links"></a>External links</h2>

<h2 id="toc5"><a name="Theory-External links"></a>External links</h2>

<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>

<h2 id="~~toc5~~"><a name="Theory-References"></a>References</h2>

<h2 id="toc6"><a name="Theory-References"></a>References</h2>

Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]

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<hr />

<h1 id="~~toc6~~"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc7"><a name="Compositions"></a>Compositions</h1>

<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>

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<a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).

<a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).

<a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith</body></html></pre></div>

<a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith

<tr>

<td>&lt; 22 35 51 62 76 81 |

</td>

</tr>

</table>

</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>2011-04-01 02:41:40 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 21:53:36 UTC</tt>.<br>
-: The original revision id was <tt>216121588</tt>.<br>
+: The original revision id was <tt>233342942</tt>.<br>
-: The revision comment was: <tt>some links added</tt><br>
+: The revision comment was: <tt>Added comma table.</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">[[toc|flat]]
 ----
@@ Line 26: / Line 25: @@
 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 [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), 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 a utonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], 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 [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.
+===Commas===
+EDO tempers out the following commas. (Note: This assumes the val &lt; 22 35 51 62 76 81 |.)
+||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 250/243 || | 1 -5 3 &gt; || 49.17 || Maximal Diesis || Porcupine Comma ||   ||
+|| 3125/3072 || | -10 -1 5 &gt; || 29.61 || Small Diesis || Magic Comma ||   ||
+|| 2048/2025 || | 11 -4 -2 &gt; || 19.55 || Diaschisma ||   ||   ||
+|| 2109375/2097152 || | -21 3 7 &gt; || 10.06 || Semicomma || Fokker Comma ||   ||
+|| 9193891/9143623 || | 32 -7 -9 &gt; || 9.49 |||| Escapade Comma ||   ||
+|| 4758837/4757272 || | -53 10 16 &gt; || 0.57 || Kwazy ||   ||   ||
+|| 50/49 || | 1 0 2 -2 &gt; || 34.98 || Tritonic Diesis || Jubilisma ||   ||
+|| 64/63 || | 6 -2 0 -1 &gt; || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
+|| 875/864 || | -5 -3 3 1 &gt; || 21.90 || Keema ||   ||   ||
+|| 2430/2401 || | 1 5 1 -4 &gt; || 20.79 || Nuwell ||   ||   ||
+|| 245/243 || | 0 -5 1 2 &gt; || 14.19 || Sensamagic ||   ||   ||
+|| 1728/1715 || | 6 3 -1 -3 &gt; || 13.07 || Orwellisma || Orwell Comma ||   ||
+|| 225/224 || | -5 2 2 -1 &gt; || 7.71 || Septimal Kleisma || Marvel Comma ||   ||
+|| 10976/10935 || | 5 -7 -1 3 &gt; || 6.48 || Hemimage ||   ||   ||
+|| 6144/6125 || | 11 1 -3 -2 &gt; || 5.36 || Porwell ||   ||   ||
+|| 65625/65536 || | -16 1 5 1 &gt; || 2.35 || Horwell ||   ||   ||
+|| 420175/419904 || | -6 -8 2 5 &gt; || 1.12 || Wizma ||   ||   ||
+|| 99/98 || | -1 2 0 -2 1 &gt; || 17.58 || Mothwellsma ||   ||   ||
+|| 100/99 || | 2 -2 2 0 -1 &gt; || 17.40 || Ptolemisma ||   ||   ||
+|| 121/120 || | -3 -1 -1 0 2 &gt; || 14.37 || Biyatisma ||   ||   ||
+|| 176/175 || | 4 0 -2 -1 1 &gt; || 9.86 || Valinorsma ||   ||   ||
+|| 896/891 || | 7 -4 0 1 -1 &gt; || 9.69 || Pentacircle ||   ||   ||
+|| 65536/65219 || | 16 0 0 -2 -3 &gt; || 8.39 || Orgonisma ||   ||   ||
+|| 385/384 || | -7 -1 1 1 1 &gt; || 4.50 || Keenanisma ||   ||   ||
+|| 540/539 || | 2 3 1 -2 -1 &gt; || 3.21 || Swetisma ||   ||   ||
+|| 4000/3993 || | 5 -1 3 0 -3 &gt; || 3.03 || Wizardharry ||   ||   ||
+|| 9801/9800 || | -3 4 -2 -2 2 &gt; || 0.18 || Kalisma || Gauss' Comma ||   ||
+|| 91/90 || | -1 -2 -1 1 0 1 &gt; || 19.13 || Superleap ||   ||   ||
 ===A Superpythagorean System===
@@ Line 36: / Line 66: @@
 ==External links==
-[[http://lumma.org/tuning/erlich/erlich-decatonic.pdf
+[[http://lumma.org/tuning/erlich/erlich-decatonic.pdf|Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']]
-|Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']]
 ==References==
@@ Line 59: / Line 88: @@
 [[http://soundclick.com/share?songid=8839060|being a]] by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).
 [[http://soundclick.com/share?songid=8839071|my own house]] by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).
-[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith</pre></div>
+[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith
+&lt;span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 613px; width: 1px;"&gt;
+|| &lt; 22 35 51 62 76 81 | ||
+&lt;/span&gt;</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&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:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&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:16:&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:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&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;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;br /&gt;
-&lt;br /&gt;
 &lt;hr /&gt;
 &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;
@@ Line 81: / Line 112: @@
 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 a utonal 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;
 &lt;br /&gt;
-&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-A Superpythagorean System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;A Superpythagorean System&lt;/h3&gt;
+&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-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Commas&lt;/h3&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 22 35 51 62 76 81 |.)&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Comma&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Monzo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Value (Cents)&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 1&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 2&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 3&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;250/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 -5 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Maximal Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Porcupine Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3125/3072&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -10 -1 5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29.61&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Small Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Magic Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2048/2025&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 11 -4 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Diaschisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2109375/2097152&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -21 3 7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10.06&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Semicomma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Fokker Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9193891/9143623&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 32 -7 -9 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Escapade Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4758837/4757272&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -53 10 16 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Kwazy&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;50/49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 0 2 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;34.98&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Tritonic Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Jubilisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;64/63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.26&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Septimal Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Archytas' Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Leipziger Komma&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;875/864&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Keema&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2430/2401&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 5 1 -4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Nuwell&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;245/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 -5 1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Sensamagic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1728/1715&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 3 -1 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.07&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Orwellisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Orwell Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;225/224&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 2 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Septimal Kleisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Marvel Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;10976/10935&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -7 -1 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Hemimage&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6144/6125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 11 1 -3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Porwell&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;65625/65536&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -16 1 5 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Horwell&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;420175/419904&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -6 -8 2 5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Wizma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;99/98&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 2 0 -2 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17.58&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Mothwellsma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;100/99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -2 2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ptolemisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;121/120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 -1 -1 0 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Biyatisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;176/175&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 4 0 -2 -1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Valinorsma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;896/891&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 7 -4 0 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Pentacircle&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;65536/65219&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 16 0 0 -2 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Orgonisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;385/384&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Keenanisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;540/539&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 3 1 -2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Swetisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4000/3993&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -1 3 0 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Wizardharry&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9801/9800&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 4 -2 -2 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Kalisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gauss' Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;91/90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 -2 -1 1 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19.13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Superleap&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&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-A Superpythagorean System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;A Superpythagorean System&lt;/h3&gt;
   &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;
 &lt;br /&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-11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11edo&lt;/h3&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-11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11edo&lt;/h3&gt;
   &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).&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;External links&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;External links&lt;/h2&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;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;References&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;References&lt;/h2&gt;
   &lt;br /&gt;
 Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]&lt;br /&gt;
@@ Line 99: / Line 541: @@
 &lt;br /&gt;
 &lt;hr /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Compositions&lt;/h1&gt;
   &lt;br /&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;br /&gt;
@@ Line 113: / Line 555: @@
 &lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow"&gt;being a&lt;/a&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow"&gt;my own house&lt;/a&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;br /&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;/body&gt;&lt;/html&gt;</pre></div>
+&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;br /&gt;
+&lt;span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 613px; width: 1px;"&gt;&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&amp;lt; 22 35 51 62 76 81 |&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>