15edo: Difference between revisions

Line 1:

<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:jdfreivald|jdfreivald]] and made on <tt>2011-05-~~10 22~~:05:01 UTC</tt>.

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 19:49:07 UTC</tt>.

: The original revision id was <tt>~~227352684~~</tt>.

: The original revision id was <tt>233316194</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>

Line 14:

""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]]). 15-ET matches the [[11_8|11:8]] and [[16_11|16:11]] ratios, and does not match the [[7_5|7:5]] or [[10_7|10:7]] tritone."

==Commas ~~tempered~~ (~~an incomplete list~~)~~:==~~

==Commas==

256/243, | 8 -5 >

15 EDO tempers out the following commas. (Note: This assumes the val < 15 24 35 42 52 56 |.)

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

|| 256/243 || | 8 -5 > || 90.22 || Limma || Pythagorean Minor 2nd || ||

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

|| 128/125 || | 7 0 -3 > || 41.06 || Diesis || Augmented Comma || ||

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

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

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

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

|| 64827/64000 || | -9 3 -3 4 > || 22.23 || Squalentine || || ||

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

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

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

|| 1029/1024 || | -10 1 0 3 > || 8.43 || Gamelisma || || ||

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

|| 250047/250000 || | -4 6 -6 3 > || 0.33 || Landscape Comma || || ||

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

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

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

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

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

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

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

|| 3025/3024 || | -4 -3 2 -1 2 > || 0.57 || Lehmerisma || || ||

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

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

Additional notes:

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Line 75:

&quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>). 15-ET matches the <a class="wiki_link" href="/11_8">11:8</a> and <a class="wiki_link" href="/16_11">16:11</a> ratios, and does not match the <a class="wiki_link" href="/7_5">7:5</a> or <a class="wiki_link" href="/10_7">10:7</a> tritone.&quot;

<h2 id="toc1"><a name="x15 tone equal temperament-Commas ~~tempered (an incomplete list):~~"></a>Commas ~~tempered~~ (~~an incomplete list~~):</h2>

<h2 id="toc1"><a name="x15 tone equal temperament-Commas"></a>Commas</h2>

256/243, | 8 -5 &gt;

15 EDO tempers out the following commas. (Note: This assumes the val &lt; 15 24 35 42 52 56 |.)

<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>256/243

</td>

<td>| 8 -5 &gt;

</td>

<td>90.22

</td>

<td>Limma

</td>

<td>Pythagorean Minor 2nd

</td>

<td>

</td>

</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>128/125

</td>

<td>| 7 0 -3 &gt;

</td>

<td>41.06

</td>

<td>Diesis

</td>

<td>Augmented 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>1029/1000

</td>

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

</td>

<td>49.49

</td>

<td>Keega

</td>

<td>

</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>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>64827/64000

</td>

<td>| -9 3 -3 4 &gt;

</td>

<td>22.23

</td>

<td>Squalentine

</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>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>4000/3969

</td>

<td>| 5 -4 3 -2 &gt;

</td>

<td>13.47

</td>

<td>Octagar

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>1029/1024

</td>

<td>| -10 1 0 3 &gt;

</td>

<td>8.43

</td>

<td>Gamelisma

</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>250047/250000

</td>

<td>| -4 6 -6 3 &gt;

</td>

<td>0.33

</td>

<td>Landscape Comma

</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>121/120

</td>

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

</td>

<td>14.37

</td>

<td>Biyatisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>176/175

</td>

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

</td>

<td>9.86

</td>

<td>Valinorsma

</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>441/440

</td>

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

</td>

<td>3.93

</td>

<td>Werckisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4000/3993

</td>

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

</td>

<td>3.03

</td>

<td>Wizardharry

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>3025/3024

</td>

<td>| -4 -3 2 -1 2 &gt;

</td>

<td>0.57

</td>

<td>Lehmerisma

</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>

Additional notes:

Line 56:

Line 440:

<img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" />(15-tone Classical Guitar by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a> / Sword Guitars)

<img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" />(15-tone Classical Guitar by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a> / Sword Guitars)

<h1 id="toc2"><a name="Theory"></a>Theory</h1>

Line 64:

Line 448:

<h1 id="toc3"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<a href="http://www.ronsword.com" rel="nofollow"><img src="http://ronsword.com/images/Pendecaphonic_coversm.jpg" alt="external image Pendecaphonic_coversm.jpg" title="external image Pendecaphonic_coversm.jpg" style="height: 149px; width: 112px;" /></a><a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ronald. &quot;Pendecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.</a> - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions

<a href="http://www.ronsword.com" rel="nofollow"><img src="http://ronsword.com/images/Pendecaphonic_coversm.jpg" alt="external image Pendecaphonic_coversm.jpg" title="external image Pendecaphonic_coversm.jpg" style="height: 149px; width: 112px;" /></a><a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ronald. &quot;Pendecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.</a> - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions

<h2 id="toc4"><a name="Practical Theory / Books-Compositions"></a>Compositions</h2>

<a class="wiki_link_ext" href="http://teamouse.googlepages.com/MizarianPorcupineOverture.mp3" rel="nofollow">Mizarian Porcupine Overture</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a> (<a class="wiki_link_ext" href="http://teamouse.googlepages.com/home" rel="nofollow">Herman Miller</a>) (<a class="wiki_link" href="/Regular%20Temperaments#porcupine">porcupine</a> chord progressions)

@@ 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:jdfreivald|jdfreivald]] and made on <tt>2011-05-10 22:05:01 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 19:49:07 UTC</tt>.<br>
-: The original revision id was <tt>227352684</tt>.<br>
+: The original revision id was <tt>233316194</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 14: / Line 14: @@
 ""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]]). 15-ET matches the [[11_8|11:8]] and [[16_11|16:11]] ratios, and does not match the [[7_5|7:5]] or [[10_7|10:7]] tritone."
-==Commas tempered (an incomplete list):==
+==Commas==
-/243, | 8 -5 &gt;
+EDO tempers out the following commas. (Note: This assumes the val &lt; 15 24 35 42 52 56 |.)
+||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 256/243 || | 8 -5 &gt; || 90.22 || Limma || Pythagorean Minor 2nd ||   ||
+|| 250/243 || | 1 -5 3 &gt; || 49.17 || Maximal Diesis || Porcupine Comma ||   ||
+|| 128/125 || | 7 0 -3 &gt; || 41.06 || Diesis || Augmented Comma ||   ||
+|| 15625/15552 || | -6 -5 6 &gt; || 8.11 || Kleisma || Semicomma Majeur ||   ||
+|| 1029/1000 || | -3 1 -3 3 &gt; || 49.49 || Keega ||   ||   ||
+|| 49/48 || | -4 -1 2 &gt; || 35.70 || Slendro Diesis ||   ||   ||
+|| 64/63 || | 6 -2 0 -1 &gt; || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
+|| 64827/64000 || | -9 3 -3 4 &gt; || 22.23 || Squalentine ||   ||   ||
+|| 875/864 || | -5 -3 3 1 &gt; || 21.90 || Keema ||   ||   ||
+|| 126/125 || | 1 2 -3 1 &gt; || 13.79 || Septimal Semicomma || Starling Comma ||   ||
+|| 4000/3969 || | 5 -4 3 -2 &gt; || 13.47 || Octagar ||   ||   ||
+|| 1029/1024 || | -10 1 0 3 &gt; || 8.43 || Gamelisma ||   ||   ||
+|| 6144/6125 || | 11 1 -3 -2 &gt; || 5.36 || Porwell ||   ||   ||
+|| 250047/250000 || | -4 6 -6 3 &gt; || 0.33 || Landscape Comma ||   ||   ||
+|| 100/99 || | 2 -2 2 -1 &gt; || 17.40 || Ptolemisma ||   ||   ||
+|| 121/120 || | -3 -1 -1 2 &gt; || 14.37 || Biyatisma ||   ||   ||
+|| 176/175 || | 4 -2 -1 1 &gt; || 9.86 || Valinorsma ||   ||   ||
+|| 65536/65219 || | 16 -2 -3 &gt; || 8.39 || Orgonisma ||   ||   ||
+|| 385/384 || | -7 -1 1 1 1 &gt; || 4.50 || Keenanisma ||   ||   ||
+|| 441/440 || | -3 2 -1 2 -1 &gt; || 3.93 || Werckisma ||   ||   ||
+|| 4000/3993 || | 5 -1 3 -3 &gt; || 3.03 || Wizardharry ||   ||   ||
+|| 3025/3024 || | -4 -3 2 -1 2 &gt; || 0.57 || Lehmerisma ||   ||   ||
+|| 91/90 || | -1 -2 -1 1 1 &gt; || 19.13 || Superleap ||   ||   ||
+|| 676/675 || | 2 -3 -2 2 &gt; || 2.56 || Parizeksma ||   ||   ||
 Additional notes:
@@ Line 48: / Line 75: @@
 &amp;quot;&amp;quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of &lt;a class="wiki_link" href="/5edo"&gt;5 equal divisions of the octave&lt;/a&gt; (or five scales of &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;). 15-ET matches the &lt;a class="wiki_link" href="/11_8"&gt;11:8&lt;/a&gt; and &lt;a class="wiki_link" href="/16_11"&gt;16:11&lt;/a&gt; ratios, and does not match the &lt;a class="wiki_link" href="/7_5"&gt;7:5&lt;/a&gt; or &lt;a class="wiki_link" href="/10_7"&gt;10:7&lt;/a&gt; tritone.&amp;quot;&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="x15 tone equal temperament-Commas tempered (an incomplete list):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Commas tempered (an incomplete list):&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x15 tone equal temperament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Commas&lt;/h2&gt;
-/243, | 8 -5 &amp;gt;&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 15 24 35 42 52 56 |.)&lt;br /&gt;
+&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;256/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 8 -5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;90.22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Limma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Pythagorean Minor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&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;128/125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 7 0 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;41.06&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Augmented 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;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;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;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;64827/64000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -9 3 -3 4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22.23&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Squalentine&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;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;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;1029/1024&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -10 1 0 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gamelisma&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;250047/250000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 6 -6 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Landscape Comma&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;121/120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 -1 -1 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 -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;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;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;tr&gt;
+        &lt;td&gt;4000/3993&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -1 3 -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;3025/3024&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 -3 2 -1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Lehmerisma&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;
 Additional notes:&lt;br /&gt;
@@ Line 56: / Line 440: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:10:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_15edoclassicalsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:10 --&gt;(&lt;em&gt;15-tone Classical Guitar by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/em&gt; / &lt;em&gt;Sword Guitars&lt;/em&gt;)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:362:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_15edoclassicalsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:362 --&gt;(&lt;em&gt;15-tone Classical Guitar by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/em&gt; / &lt;em&gt;Sword Guitars&lt;/em&gt;)&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Theory&lt;/h1&gt;
@@ Line 64: / Line 448: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Practical Theory / Books&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:12:&amp;lt;a href=&amp;quot;http://www.ronsword.com&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/Pendecaphonic_coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 149px; width: 112px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/Pendecaphonic_coversm.jpg" alt="external image Pendecaphonic_coversm.jpg" title="external image Pendecaphonic_coversm.jpg" style="height: 149px; width: 112px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:12 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow"&gt;Sword, Ronald. &amp;quot;Pendecaphonic Scales for Guitar&amp;quot; IAAA Press, UK-USA. First Ed: June 2009.&lt;/a&gt; - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:364:&amp;lt;a href=&amp;quot;http://www.ronsword.com&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/Pendecaphonic_coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 149px; width: 112px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/Pendecaphonic_coversm.jpg" alt="external image Pendecaphonic_coversm.jpg" title="external image Pendecaphonic_coversm.jpg" style="height: 149px; width: 112px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:364 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow"&gt;Sword, Ronald. &amp;quot;Pendecaphonic Scales for Guitar&amp;quot; IAAA Press, UK-USA. First Ed: June 2009.&lt;/a&gt; - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Practical Theory / Books-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;&lt;/h2&gt;
   &lt;a class="wiki_link_ext" href="http://teamouse.googlepages.com/MizarianPorcupineOverture.mp3" rel="nofollow"&gt;Mizarian Porcupine Overture&lt;/a&gt; by &lt;a class="wiki_link" href="/Herman%20Miller"&gt;Herman Miller&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://teamouse.googlepages.com/home" rel="nofollow"&gt;Herman Miller&lt;/a&gt;) (&lt;a class="wiki_link" href="/Regular%20Temperaments#porcupine"&gt;porcupine&lt;/a&gt; chord progressions)&lt;br /&gt;