23edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-05-28 22:18:41 UTC</tt>.<br>

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:01:05 UTC</tt>.<br>

: The original revision id was <tt>~~232644562~~</tt>.<br>

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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">=<span style="color: #007a1b; display: block;">23 tone equal temperament</span>=

23et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit [[k*N subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.

23-EDO was proposed by ethnomusicologist [[http://en.wikipedia.org/wiki/Erich_von_Hornbostel|Erich von Hornbostel]] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.

23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.

Like 9-EDO, 16-EDO, and 25-EDO, one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three sharp 4/3's with 5/1 (related to the Armodue system). This means mapping 3/2 to 13 degrees of 23, and results in a 7-note "anti-diatonic" scale of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes (3 3 3 1 3 3 3 3 1).

However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_~~(music_critic)~~|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.

However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.

==Intervals==

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|| 22 || 1147.8261 ||

[[image:Ciclo_Icositrifonía.png width="341" height="344" caption="Intervallic Cicle of 23 steps Equal per Octave"]]

==Commas==

23 EDO tempers out the following commas. (Note: This assumes the val < 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).

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

|| 135/128 || | -7 3 1 > || 92.18 || Major Chroma || Major Limma || Pelogic Comma ||

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

|| 36/35 || | 2 2 -1 -1 > || 48.77 || Septimal Quarter Tone || || ||

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

|| 4000/3969 || | 5 -4 3 -2 > || 13.47 || Octagar || || ||

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

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

|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma || || ||

===INSTRUMENTS===

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=Compositions=

[[http://home.vicnet.net.au/~~~epoetry~~/family.mp3|The Family Supper]] by Warren Burt

[[http://home.vicnet.net.au/%7Eepoetry/family.mp3|The Family Supper]] by Warren Burt

__Allegro Moderato__ by Easley Blackwood

[[http://www.youtube.com/watch?v=Hqst8MaRiYM|Icositriphonic Heptatonic MOS]] by Igliashon Jones

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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>23edo</title></head><body><h1 id="toc0"><a name="x23 tone equal temperament"></a><span style="color: #007a1b; display: block;">23 tone equal temperament</span></h1>

<br />

23et, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*23 subgroup</a> 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. <br />

23et, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*23 subgroup</a> 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.<br />

<br />

23-EDO was proposed by ethnomusicologist <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Erich_von_Hornbostel" rel="nofollow">Erich von Hornbostel</a> as the result of continuing a circle of &quot;blown&quot; fifths of ~678-cent fifths that (he argued) resulted from &quot;overblowing&quot; a bamboo pipe.<br />

<br />

23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23. <br />

23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.<br />

<br />

Like 9-EDO, 16-EDO, and 25-EDO, one way to treat 23-EDO is as a Pelogic temperament, tempering out the &quot;comma&quot; of 135/128 and equating three sharp 4/3's with 5/1 (related to the Armodue system). This means mapping 3/2 to 13 degrees of 23, and results in a 7-note &quot;anti-diatonic&quot; scale of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes (3 3 3 1 3 3 3 3 1).<br />

<br />

However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_~~(music_critic)~~" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. <br />

However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br />

<br />

<h2 id="toc1"><a name="x23 tone equal temperament-Intervals"></a>Intervals</h2>

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</table>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 344px; width: 341px;" /></td></tr><tr><td class="imageCaption">Intervallic Cicle of 23 steps Equal per Octave</td></tr></table><br />

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 344px; width: 341px;" /></td></tr><tr><td class="imageCaption">Intervallic Cicle of 23 steps Equal per Octave</td></tr></table><br />

<h2 id="toc2"><a name="x23 tone equal temperament-Commas"></a>Commas</h2>

23 EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br />

<tr>

<th>Comma<br />

</th>

<th>Monzo<br />

</th>

<th>Value (Cents)<br />

</th>

</th>

</th>

</th>

</tr>

<tr>

</td>

</td>

</td>

<td>Major Chroma<br />

</td>

<td>Major Limma<br />

</td>

<td>Pelogic Comma<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Kleisma<br />

</td>

<td>Semicomma Majeur<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Septimal Quarter Tone<br />

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Avicennma<br />

</td>

<td>Avicenna's Enharmonic Diesis<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Octagar<br />

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Porwell<br />

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Ptolemisma<br />

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>Werckisma<br />

</td>

</td>

</td>

</tr>

</table>

<br />

<h3 id="~~toc2~~"><a name="x23 tone equal temperament-~~Intervals~~-INSTRUMENTS"></a>INSTRUMENTS</h3>

<h3 id="toc3"><a name="x23 tone equal temperament-Commas-INSTRUMENTS"></a>INSTRUMENTS</h3>

<img src="/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 182px; width: 560px;" /><br />

<img src="/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 182px; width: 560px;" /><br />

<em>An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.</em><br />

<br />

<img src="/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 237px; width: 533px;" /><br />

<img src="/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 237px; width: 533px;" /><br />

<em>An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.</em><br />

<br />

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2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1<br />

<br />

<h1 id="~~toc3~~"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc4"><a name="Compositions"></a>Compositions</h1>

<a class="wiki_link_ext" href="http://home.vicnet.net.au/~~~epoetry~~/family.mp3" rel="nofollow">The Family Supper</a> by Warren Burt<br />

<a class="wiki_link_ext" href="http://home.vicnet.net.au/%7Eepoetry/family.mp3" rel="nofollow">The Family Supper</a> by Warren Burt<br />

<u>Allegro Moderato</u> by Easley Blackwood<br />

<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Hqst8MaRiYM" rel="nofollow">Icositriphonic Heptatonic MOS</a> by Igliashon Jones<br />

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<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/boogie_pie.mp3" rel="nofollow">Boogie Pie</a></span>by Aaron Krister Johnson<br />

<br />

<h1 id="~~toc4~~"><a name="Books"></a>Books</h1>

<h1 id="toc5"><a name="Books"></a>Books</h1>

<img src="/file/view/Libro_Icositrif%C3%B3nico.PNG/163031733/Libro_Icositrif%C3%B3nico.PNG" alt="Libro_Icositrifónico.PNG" title="Libro_Icositrifónico.PNG" /><br />

<img src="/file/view/Libro_Icositrif%C3%B3nico.PNG/163031733/Libro_Icositrif%C3%B3nico.PNG" alt="Libro_Icositrifónico.PNG" title="Libro_Icositrifónico.PNG" /><br />

<br />

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

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

<br />

<img src="/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/567x297/Teclado_Icositrif%C3%B3nico.PNG" alt="Teclado_Icositrifónico.PNG" title="Teclado_Icositrifónico.PNG" style="height: 297px; width: 567px;" /><br />

<img src="/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/567x297/Teclado_Icositrif%C3%B3nico.PNG" alt="Teclado_Icositrifónico.PNG" title="Teclado_Icositrifónico.PNG" style="height: 297px; width: 567px;" /><br />

<em>A prototype for Armodue 1/3-tone Keyboard, Armodue-Hornbostel Family Temperaments.</em></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:genewardsmith|genewardsmith]] and made on <tt>2011-05-28 22:18:41 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:01:05 UTC</tt>.<br>
-: The original revision id was <tt>232644562</tt>.<br>
+: The original revision id was <tt>233344668</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>
 <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">=&lt;span style="color: #007a1b; display: block;"&gt;23 tone equal temperament&lt;/span&gt;=
 et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit [[k*N subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.
 -EDO was proposed by ethnomusicologist [[http://en.wikipedia.org/wiki/Erich_von_Hornbostel|Erich von Hornbostel]] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.
 -EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.
 Like 9-EDO, 16-EDO, and 25-EDO, one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three sharp 4/3's with 5/1 (related to the Armodue system). This means mapping 3/2 to 13 degrees of 23, and results in a 7-note "anti-diatonic" scale of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes (3 3 3 1 3 3 3 3 1).
-However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_(music_critic)|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.
+However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.
 ==Intervals==
@@ Line 44: / Line 44: @@
 || 22 || 1147.8261 ||
 [[image:Ciclo_Icositrifonía.png width="341" height="344" caption="Intervallic Cicle of 23 steps Equal per Octave"]]
+==Commas==
+EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).
+||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 135/128 || | -7 3 1 &gt; || 92.18 || Major Chroma || Major Limma || Pelogic Comma ||
+|| 15625/15552 || | -6 -5 6 &gt; || 8.11 || Kleisma || Semicomma Majeur ||   ||
+|| 36/35 || | 2 2 -1 -1 &gt; || 48.77 || Septimal Quarter Tone ||   ||   ||
+|| 525/512 || | -9 1 2 1 &gt; || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||   ||
+|| 4000/3969 || | 5 -4 3 -2 &gt; || 13.47 || Octagar ||   ||   ||
+|| 6144/6125 || | 11 1 -3 -2 &gt; || 5.36 || Porwell ||   ||   ||
+|| 100/99 || | 2 -2 2 0 -1 &gt; || 17.40 || Ptolemisma ||   ||   ||
+|| 441/440 || | -3 2 -1 2 -1 &gt; || 3.93 || Werckisma ||   ||   ||
 ===INSTRUMENTS===
@@ Line 94: / Line 105: @@
 =Compositions=
-[[http://home.vicnet.net.au/~epoetry/family.mp3|The Family Supper]] by Warren Burt
+[[http://home.vicnet.net.au/%7Eepoetry/family.mp3|The Family Supper]] by Warren Burt
 __Allegro Moderato__ by Easley Blackwood
 [[http://www.youtube.com/watch?v=Hqst8MaRiYM|Icositriphonic Heptatonic MOS]] by Igliashon Jones
@@ Line 112: / Line 123: @@
 <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;23edo&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="x23 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #007a1b; display: block;"&gt;23 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-et, or 23-EDO, is a tuning system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*23 subgroup&lt;/a&gt; 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. &lt;br /&gt;
+et, or 23-EDO, is a tuning system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. If to this subgroup is added the commas of 17-limit 46et, the larger 17-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*23 subgroup&lt;/a&gt; 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.&lt;br /&gt;
 &lt;br /&gt;
 -EDO was proposed by ethnomusicologist &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Erich_von_Hornbostel" rel="nofollow"&gt;Erich von Hornbostel&lt;/a&gt; as the result of continuing a circle of &amp;quot;blown&amp;quot; fifths of ~678-cent fifths that (he argued) resulted from &amp;quot;overblowing&amp;quot; a bamboo pipe.&lt;br /&gt;
 &lt;br /&gt;
--EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23. &lt;br /&gt;
+-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.&lt;br /&gt;
 &lt;br /&gt;
 Like 9-EDO, 16-EDO, and 25-EDO, one way to treat 23-EDO is as a Pelogic temperament, tempering out the &amp;quot;comma&amp;quot; of 135/128 and equating three sharp 4/3's with 5/1 (related to the Armodue system). This means mapping 3/2 to 13 degrees of 23, and results in a 7-note &amp;quot;anti-diatonic&amp;quot; scale of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes (3 3 3 1 3 3 3 3 1).&lt;br /&gt;
 &lt;br /&gt;
-However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &amp;quot;anti-pentatonic&amp;quot;) and 4 1 4 1 4 4 1 4 (the &amp;quot;quarter-tone&amp;quot; version of the Blackwood/&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_(music_critic)" rel="nofollow"&gt;Rapoport&lt;/a&gt;/Wilson 13-EDO &amp;quot;subminor&amp;quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &amp;quot;4/3&amp;quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. &lt;br /&gt;
+However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &amp;quot;anti-pentatonic&amp;quot;) and 4 1 4 1 4 4 1 4 (the &amp;quot;quarter-tone&amp;quot; version of the Blackwood/&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow"&gt;Rapoport&lt;/a&gt;/Wilson 13-EDO &amp;quot;subminor&amp;quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &amp;quot;4/3&amp;quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x23 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h2&gt;
@@ Line 272: / Line 283: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:158:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cicle of 23 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cicle of 23 steps Equal per Octave&amp;quot; style=&amp;quot;height: 344px; width: 341px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 344px; width: 341px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cicle of 23 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:158 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:288:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cicle of 23 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cicle of 23 steps Equal per Octave&amp;quot; style=&amp;quot;height: 344px; width: 341px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/341x344/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 344px; width: 341px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cicle of 23 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:288 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x23 tone equal temperament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Commas&lt;/h2&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).&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;135/128&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;92.18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major Chroma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major Limma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Pelogic Comma&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;36/35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 2 -1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;48.77&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Septimal Quarter Tone&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;4000/3969&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -4 3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.47&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Octagar&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;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;441/440&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 2 -1 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Werckisma&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;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x23 tone equal temperament-Intervals-INSTRUMENTS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;INSTRUMENTS&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x23 tone equal temperament-Commas-INSTRUMENTS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;INSTRUMENTS&lt;/h3&gt;
-  &lt;!-- ws:start:WikiTextLocalImageRule:159:&amp;lt;img src=&amp;quot;/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 182px; width: 560px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 182px; width: 560px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:159 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextLocalImageRule:289:&amp;lt;img src=&amp;quot;/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 182px; width: 560px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Icositriphonic_Bass.JPG/206711470/560x182/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 182px; width: 560px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:289 --&gt;&lt;br /&gt;
 &lt;em&gt;An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:160:&amp;lt;img src=&amp;quot;/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 237px; width: 533px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 237px; width: 533px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:160 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:290:&amp;lt;img src=&amp;quot;/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 237px; width: 533px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Icositriphonic_Guitar.PNG/206712964/533x237/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 237px; width: 533px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:290 --&gt;&lt;br /&gt;
 &lt;em&gt;An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
@@ Line 322: / Line 466: @@
 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Compositions&lt;/h1&gt;
-  &lt;a class="wiki_link_ext" href="http://home.vicnet.net.au/~epoetry/family.mp3" rel="nofollow"&gt;The Family Supper&lt;/a&gt; by Warren Burt&lt;br /&gt;
+  &lt;a class="wiki_link_ext" href="http://home.vicnet.net.au/%7Eepoetry/family.mp3" rel="nofollow"&gt;The Family Supper&lt;/a&gt; by Warren Burt&lt;br /&gt;
 &lt;u&gt;Allegro Moderato&lt;/u&gt; by Easley Blackwood&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Hqst8MaRiYM" rel="nofollow"&gt;Icositriphonic Heptatonic MOS&lt;/a&gt; by Igliashon Jones&lt;br /&gt;
@@ Line 331: / Line 475: @@
 &lt;span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/boogie_pie.mp3" rel="nofollow"&gt;Boogie Pie&lt;/a&gt;&lt;/span&gt;by Aaron Krister Johnson&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Books&lt;/h1&gt;
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 &lt;em&gt;A prototype for Armodue 1/3-tone Keyboard, Armodue-Hornbostel Family Temperaments.&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>