19edo: 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:~~vaisvil~~|~~vaisvil~~]] and made on <tt>2011-05-17 20:35:10 UTC</tt>.

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 20:43:48 UTC</tt>.

: The original revision id was <tt>~~229425236~~</tt>.

: The original revision id was <tt>233328094</tt>.

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

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

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|| 18 || 1136.84 || ||

==Commas==

19 EDO tempers out the following commas. (Note: This assumes the val < 19 30 44 53 66 70 |.)

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

|| 16875/16384 || | -14 3 4 > || 51.12 || Negri Comma || Double Augmentation Diesis || ||

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

|| 81/80 || | -4 4 -1 > || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma ||

|| 78732/78125 || | 2 9 -7 > || 13.40 || Medium Semicomma || Sensipent Comma || ||

|| 15625/15552 || | -6 -5 6 > || 8.11 || Kleisma || Semicomma Majeur || ||

|| 1792620/1787149 || | 8 14 -13 > || 5.29 || Parakleisma || || ||

|| 4830148/4822299 || | -14 -19 19 > || 2.82 || Enneadeca || 19-Tone-Comma || ||

|| 1029/1000 || | -3 1 -3 3 > || 49.49 || Keega || || ||

|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis || ||

|| 49/48 || | -4 -1 2 > || 35.70 || Slendro Diesis || || ||

|| 686/675 || | 1 -3 -2 3 > || 27.99 || Senga || || ||

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

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

|| 126/125 || | 1 2 -3 1 > || 13.79 || Septimal Semicomma || Starling Comma || ||

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

|| 19683/19600 || | -4 9 -2 -2 > || 7.32 || Cataharry || || ||

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

|| 3136/3125 || | 6 -5 2 > || 6.08 || Hemimean || || ||

|| 703125/702464 || | -11 2 7 -3 > || 1.63 || Meter || || ||

|| 4375/4374 || | -1 -7 4 1 > || 0.40 || Ragisma || || ||

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

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

|| 65536/65219 || | 16 -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 || || ||

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

|| 676/675 || | 2 -3 -2 2 > || 2.56 || Parizeksma || || ||

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<h4>Original HTML content:</h4>

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

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

<hr />

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

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For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, <a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>).

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, <a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>).

<h2 id="toc2"><a name="Theory-Intervals"></a>Intervals</h2>

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<h2 id="toc3"><a name="Theory-Commas"></a>Commas</h2>

19 EDO tempers out the following commas. (Note: This assumes the val &lt; 19 30 44 53 66 70 |.)

<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>16875/16384

</td>

<td>| -14 3 4 &gt;

</td>

<td>51.12

</td>

<td>Negri Comma

</td>

<td>Double Augmentation Diesis

</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>81/80

</td>

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

</td>

<td>21.51

</td>

<td>Syntonic Comma

</td>

<td>Didymos Comma

</td>

<td>Meantone Comma

</td>

</tr>

<tr>

<td>78732/78125

</td>

<td>| 2 9 -7 &gt;

</td>

<td>13.40

</td>

<td>Medium Semicomma

</td>

<td>Sensipent Comma

</td>

<td>

</td>

</tr>

<tr>

<td>15625/15552

</td>

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

</td>

<td>8.11

</td>

<td>Kleisma

</td>

<td>Semicomma Majeur

</td>

<td>

</td>

</tr>

<tr>

<td>1792620/1787149

</td>

<td>| 8 14 -13 &gt;

</td>

<td>5.29

</td>

<td>Parakleisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4830148/4822299

</td>

<td>| -14 -19 19 &gt;

</td>

<td>2.82

</td>

<td>Enneadeca

</td>

<td>19-Tone-Comma

</td>

<td>

</td>

</tr>

<tr>

<td>1029/1000

</td>

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

</td>

<td>49.49

</td>

<td>Keega

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>525/512

</td>

<td>| -9 1 2 1 &gt;

</td>

<td>43.41

</td>

<td>Avicennma

</td>

<td>Avicenna's Enharmonic Diesis

</td>

<td>

</td>

</tr>

<tr>

<td>49/48

</td>

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

</td>

<td>35.70

</td>

<td>Slendro Diesis

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>686/675

</td>

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

</td>

<td>27.99

</td>

<td>Senga

</td>

<td>

</td>

<td>

</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>245/243

</td>

<td>| -5 1 2 &gt;

</td>

<td>14.19

</td>

<td>Sensamagic

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>126/125

</td>

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

</td>

<td>13.79

</td>

<td>Septimal Semicomma

</td>

<td>Starling 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>19683/19600

</td>

<td>| -4 9 -2 -2 &gt;

</td>

<td>7.32

</td>

<td>Cataharry

</td>

<td>

</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>3136/3125

</td>

<td>| 6 -5 2 &gt;

</td>

<td>6.08

</td>

<td>Hemimean

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>703125/702464

</td>

<td>| -11 2 7 -3 &gt;

</td>

<td>1.63

</td>

<td>Meter

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4375/4374

</td>

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

</td>

<td>0.40

</td>

<td>Ragisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>100/99

</td>

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

</td>

<td>17.40

</td>

<td>Ptolemisma

</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 -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>91/90

</td>

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

</td>

<td>19.13

</td>

<td>Superleap

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>676/675

</td>

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

</td>

<td>2.56

</td>

<td>Parizeksma

</td>

<td>

</td>

<td>

</td>

</tr>

</table>

<h2 id="~~toc3~~"><a name="Theory-Articles"></a>Articles</h2>

<h2 id="toc4"><a name="Theory-Articles"></a>Articles</h2>

<ul><li><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">A Case For Nineteen</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow">19-Tone Theory and Applications</a> by Hubert S. Howe Jr. <a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Tunings for 19 Tone Equal Tempered Guitar</a> by William A. Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow">Microtonalism</a> by Bailey, Morrison, Pearson and Parncutt <a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory</a> <a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow">Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar</a>.</li><li><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow">Enneadecaphonic Scales for Guitar</a> by Ron Sword</li></ul>

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

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

Bucht, Saku and Huovinen, Erkki, Perceived consonance of harmonic intervals in 19-tone equal temperament, CIM04_proceedings.

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Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.

19 note per octave Ibanez conversion by Brad Smith (Indianapolis)

<img src="http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" alt="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" title="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" style="height: 600px; width: 800px;" />

<img src="http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" alt="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" title="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" style="height: 600px; width: 800px;" />

<hr />

<h1 id="~~toc5~~"><a name="Compositions"></a>Compositions</h1>

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

<a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow">The Juggler</a> by Aaron Krister Johnson

@@ 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:vaisvil|vaisvil]] and made on <tt>2011-05-17 20:35:10 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 20:43:48 UTC</tt>.<br>
-: The original revision id was <tt>229425236</tt>.<br>
+: The original revision id was <tt>233328094</tt>.<br>
-: The revision comment was: <tt></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>
@@ Line 45: / Line 45: @@
 || 18 || 1136.84 ||   ||
+==Commas==
+EDO tempers out the following commas. (Note: This assumes the val &lt; 19 30 44 53 66 70 |.)
+||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 16875/16384 || | -14 3 4 &gt; || 51.12 || Negri Comma || Double Augmentation Diesis ||   ||
+|| 3125/3072 || | -10 -1 5 &gt; || 29.61 || Small Diesis || Magic Comma ||   ||
+|| 81/80 || | -4 4 -1 &gt; || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma ||
+|| 78732/78125 || | 2 9 -7 &gt; || 13.40 || Medium Semicomma || Sensipent Comma ||   ||
+|| 15625/15552 || | -6 -5 6 &gt; || 8.11 || Kleisma || Semicomma Majeur ||   ||
+|| 1792620/1787149 || | 8 14 -13 &gt; || 5.29 || Parakleisma ||   ||   ||
+|| 4830148/4822299 || | -14 -19 19 &gt; || 2.82 || Enneadeca || 19-Tone-Comma ||   ||
+|| 1029/1000 || | -3 1 -3 3 &gt; || 49.49 || Keega ||   ||   ||
+|| 525/512 || | -9 1 2 1 &gt; || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||   ||
+|| 49/48 || | -4 -1 2 &gt; || 35.70 || Slendro Diesis ||   ||   ||
+|| 686/675 || | 1 -3 -2 3 &gt; || 27.99 || Senga ||   ||   ||
+|| 875/864 || | -5 -3 3 1 &gt; || 21.90 || Keema ||   ||   ||
+|| 245/243 || | -5 1 2 &gt; || 14.19 || Sensamagic ||   ||   ||
+|| 126/125 || | 1 2 -3 1 &gt; || 13.79 || Septimal Semicomma || Starling Comma ||   ||
+|| 225/224 || | -5 2 2 -1 &gt; || 7.71 || Septimal Kleisma || Marvel Comma ||   ||
+|| 19683/19600 || | -4 9 -2 -2 &gt; || 7.32 || Cataharry ||   ||   ||
+|| 10976/10935 || | 5 -7 -1 3 &gt; || 6.48 || Hemimage ||   ||   ||
+|| 3136/3125 || | 6 -5 2 &gt; || 6.08 || Hemimean ||   ||   ||
+|| 703125/702464 || | -11 2 7 -3 &gt; || 1.63 || Meter ||   ||   ||
+|| 4375/4374 || | -1 -7 4 1 &gt; || 0.40 || Ragisma ||   ||   ||
+|| 100/99 || | 2 -2 2 -1 &gt; || 17.40 || Ptolemisma ||   ||   ||
+|| 896/891 || | 7 -4 0 1 -1 &gt; || 9.69 || Pentacircle ||   ||   ||
+|| 65536/65219 || | 16 -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 ||   ||   ||
+|| 91/90 || | -1 -2 -1 1 1 &gt; || 19.13 || Superleap ||   ||   ||
+|| 676/675 || | 2 -3 -2 2 &gt; || 2.56 || Parizeksma ||   ||   ||
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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;19edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/9458830?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;9458830&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
-&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:13:&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:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&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;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;
+&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:15:&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:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&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;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;br /&gt;
 &lt;hr /&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;
@@ Line 102: / Line 132: @@
 For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41edo"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;
 &lt;br /&gt;
-However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, &lt;!-- ws:start:WikiTextUrlRule:371:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:371 --&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;).&lt;br /&gt;
+However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, &lt;!-- ws:start:WikiTextUrlRule:937:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:937 --&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Intervals&lt;/h2&gt;
@@ Line 272: / Line 302: @@
 &lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Theory-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h2&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 19 30 44 53 66 70 |.)&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;16875/16384&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -14 3 4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;51.12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Negri Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Double Augmentation Diesis&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;81/80&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 4 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.51&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Syntonic Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Didymos Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Meantone Comma&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;78732/78125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 9 -7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Medium Semicomma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Sensipent 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;15625/15552&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -6 -5 6 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Kleisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Semicomma Majeur&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1792620/1787149&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 8 14 -13 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Parakleisma&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;4830148/4822299&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -14 -19 19 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.82&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Enneadeca&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19-Tone-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;1029/1000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 1 -3 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49.49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Keega&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;525/512&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -9 1 2 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;43.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Avicennma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Avicenna's Enharmonic Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;49/48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 -1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35.70&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Slendro Diesis&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;686/675&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 -3 -2 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Senga&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;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;245/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -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;126/125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 2 -3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Septimal Semicomma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Starling 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;19683/19600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 9 -2 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Cataharry&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;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;3136/3125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 -5 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.08&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Hemimean&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;703125/702464&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -11 2 7 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Meter&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;4375/4374&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 -7 4 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ragisma&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 -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;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 -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;91/90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 -2 -1 1 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;tr&gt;
+        &lt;td&gt;676/675&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -3 -2 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.56&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Parizeksma&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;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Theory-Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Articles&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Theory-Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Articles&lt;/h2&gt;
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 &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow"&gt;A Case For Nineteen&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;19-Tone Theory and Applications&lt;/a&gt; by Hubert S. Howe Jr. &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow"&gt;Tunings for 19 Tone Equal Tempered Guitar&lt;/a&gt; by William A. Sethares &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow"&gt;Microtonalism&lt;/a&gt; by Bailey, Morrison, Pearson and Parncutt &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow"&gt;19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow"&gt;Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow"&gt;Enneadecaphonic Scales for Guitar&lt;/a&gt; by Ron Sword&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;References&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;References&lt;/h2&gt;
   &lt;br /&gt;
 Bucht, Saku and Huovinen, Erkki, &lt;em&gt;Perceived consonance of harmonic intervals in 19-tone equal temperament&lt;/em&gt;, CIM04_proceedings.&lt;br /&gt;
@@ Line 283: / Line 712: @@
 Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.&lt;br /&gt;
 note per octave Ibanez conversion by Brad Smith (Indianapolis)&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextRemoteImageRule:598:&amp;lt;img src=&amp;quot;http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 600px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" alt="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" title="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" style="height: 600px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:598 --&gt;&lt;br /&gt;
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 &lt;hr /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Compositions&lt;/h1&gt;
   &lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow"&gt;The Juggler&lt;/a&gt; &lt;/span&gt; by Aaron Krister Johnson&lt;br /&gt;