Porcupine: 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:genewardsmith|genewardsmith]] and made on <tt>2013-11-11 10:50:06 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-11 11:24:13 UTC</tt>.

: The original revision id was <tt>~~467983132~~</tt>.

: The original revision id was <tt>467993484</tt>.

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

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

Line 47:

|| 14/11 || 161.751 ||

|| 7/5 || 162.047 ||

|| 5\37 || 162.162 ||

|| 11/8 || 162.171 13- and 15-limit minimax ||

|| 8\59 || 162.712 ||

|| 5/4 || 162.737 5-limit minimax ||

|| 15/14 || 162.897 ||

Line 61:

Line 63:

|| 11/9 || 173.704 ||

|| 16/13 || 179.736 ||

|| 10/9 || 182.404 ||

===Spectrum of Porcupinefish Tunings===

|| 12/11 || 150.637 ||

|| 6/5 || 157.821 ||

|| 2\15 || 160.000 ||

|| 18/13 || 160.307 ||

|| 15/13 || 160.860 ||

|| 8/7 || 161.471 ||

|| 13/12 || 161.531 ||

|| 14/11 || 161.751 ||

|| 7/5 || 162.047 ||

|| 14/13 || 162.100 ||

|| 13/10 || 162.149 ||

|| 5\37 || 162.162 ||

|| 11/8 || 162.171 ||

|| 16/13 || 162.322 ||

|| 13/11 || 162.368 13- and 15-limit minimax ||

|| 8\59 || 162.712 ||

|| 5/4 || 162.737 ||

|| 15/14 || 162.897 ||

|| 7/6 || 162.986 ||

|| 3\22 || 163.636 ||

|| 9/7 || 163.743 ||

|| 16/15 || 163.966 ||

|| 11/10 || 165.004 ||

|| 4\29 || 165.517 ||

|| 15/11 || 165.762 ||

|| 4/3 || 166.015 ||

|| 11/9 || 173.704 ||

|| 10/9 || 182.404 ||

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Line 383:

</td>

<td>162.047

</td>

</tr>

<tr>

<td>5\37

</td>

<td>162.162

</td>

</tr>

Line 357:

Line 395:

</td>

<td>162.171 13- and 15-limit minimax

</td>

</tr>

<tr>

<td>8\59

</td>

<td>162.712

</td>

</tr>

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<h2 id="~~toc2~~"><a name="x-History"></a>History</h2>

<h3 id="toc2"><a name="x-Spectrum of Porcupine Tunings by Eigenmonzos-Spectrum of Porcupinefish Tunings"></a>Spectrum of Porcupinefish Tunings</h3>

<tr>

<td>12/11

</td>

<td>150.637

</td>

</tr>

<tr>

<td>6/5

</td>

<td>157.821

</td>

</tr>

<tr>

<td>2\15

</td>

<td>160.000

</td>

</tr>

<tr>

<td>18/13

</td>

<td>160.307

</td>

</tr>

<tr>

<td>15/13

</td>

<td>160.860

</td>

</tr>

<tr>

<td>8/7

</td>

<td>161.471

</td>

</tr>

<tr>

<td>13/12

</td>

<td>161.531

</td>

</tr>

<tr>

<td>14/11

</td>

<td>161.751

</td>

</tr>

<tr>

<td>7/5

</td>

<td>162.047

</td>

</tr>

<tr>

<td>14/13

</td>

<td>162.100

</td>

</tr>

<tr>

<td>13/10

</td>

<td>162.149

</td>

</tr>

<tr>

<td>5\37

</td>

<td>162.162

</td>

</tr>

<tr>

<td>11/8

</td>

<td>162.171

</td>

</tr>

<tr>

<td>16/13

</td>

<td>162.322

</td>

</tr>

<tr>

<td>13/11

</td>

<td>162.368 13- and 15-limit minimax

</td>

</tr>

<tr>

<td>8\59

</td>

<td>162.712

</td>

</tr>

<tr>

<td>5/4

</td>

<td>162.737

</td>

</tr>

<tr>

<td>15/14

</td>

<td>162.897

</td>

</tr>

<tr>

<td>7/6

</td>

<td>162.986

</td>

</tr>

<tr>

<td>3\22

</td>

<td>163.636

</td>

</tr>

<tr>

<td>9/7

</td>

<td>163.743

</td>

</tr>

<tr>

<td>16/15

</td>

<td>163.966

</td>

</tr>

<tr>

<td>11/10

</td>

<td>165.004

</td>

</tr>

<tr>

<td>4\29

</td>

<td>165.517

</td>

</tr>

<tr>

<td>15/11

</td>

<td>165.762

</td>

</tr>

<tr>

<td>4/3

</td>

<td>166.015

</td>

</tr>

<tr>

<td>11/9

</td>

<td>173.704

</td>

</tr>

<tr>

<td>10/9

</td>

<td>182.404

</td>

</tr>

</table>

<h2 id="toc3"><a name="x-History"></a>History</h2>

Porcupine temperament/scales were discovered by <a class="wiki_link" href="/Dave%20Keenan">Dave Keenan</a>, but didn't have a name until <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a> mentioned that his Mizarian Porcupine Overture in 15-tET had a section that pumps the 250:243 comma. Although this music did not use a Porcupine MOS or MODMOS (which would have 7 or 8 notes), the name was adopted for such scales as well, once the essentially one-to-one relationship between vanishing commas and sequences of DE scales was fully evident. It was clear that even though Herman's piece was in 15, 22 was a porcupine tuning par excellence, and that was an interesting development in itself.

<h2 id="~~toc3~~"><a name="x-See also"></a>See also</h2>

<h2 id="toc4"><a name="x-See also"></a>See also</h2>

<a class="wiki_link" href="/Chords%20of%20porcupine">Chords of porcupine</a>

<a class="wiki_link" href="/Porcupine%20Notation">Porcupine Notation</a>

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<a class="wiki_link" href="/Porcupine%20Album%20Project">Porcupine Album Project</a>

<h2 id="~~toc4~~"><a name="x-Musical examples"></a>Musical examples</h2>

<h2 id="toc5"><a name="x-Musical examples"></a>Musical examples</h2>

<ul><li>&quot;<a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow">Mizarian Porcupine Overture</a>&quot;, Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>&quot;<a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a>&quot;, Paul Erlich, <a class="wiki_link" href="/22edo">22edo</a> (at least the beginning part is in porcupine).</li><li>&quot;<a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a>&quot;, Gene Ward Smith and Modest Mussorgsky, <a class="wiki_link" href="/22edo">22edo</a>.</li><li>&quot;<a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow">being a</a>&quot;, Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3" rel="nofollow">Playing Gently with Miller's Porcupine</a>, <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow">15 Porcupines in India</a>, Sarangi, Tambura and Sitar improvisation by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow">15 Quills</a> piano solo by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3" rel="nofollow">Prickly Side of Love</a> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow">Porcupine Organ Composition</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a href="http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3');">Among Other Things 2</a> by Petr Pařízek</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3" rel="nofollow">Porcupine Comma Pump</a>, by Jake Freivald</li></ul><h2 id="~~toc5~~"><a name="x-Images"></a>Images</h2>

<ul><li>&quot;<a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow">Mizarian Porcupine Overture</a>&quot;, Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>&quot;<a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a>&quot;, Paul Erlich, <a class="wiki_link" href="/22edo">22edo</a> (at least the beginning part is in porcupine).</li><li>&quot;<a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a>&quot;, Gene Ward Smith and Modest Mussorgsky, <a class="wiki_link" href="/22edo">22edo</a>.</li><li>&quot;<a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow">being a</a>&quot;, Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3" rel="nofollow">Playing Gently with Miller's Porcupine</a>, <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow">15 Porcupines in India</a>, Sarangi, Tambura and Sitar improvisation by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow">15 Quills</a> piano solo by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3" rel="nofollow">Prickly Side of Love</a> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow">Porcupine Organ Composition</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a href="http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3');">Among Other Things 2</a> by Petr Pařízek</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3" rel="nofollow">Porcupine Comma Pump</a>, by Jake Freivald</li></ul><h2 id="toc6"><a name="x-Images"></a>Images</h2>

<img src="/file/view/porcupine8.jpg/272051226/porcupine8.jpg" alt="porcupine8.jpg" title="porcupine8.jpg" /></body></html></pre></div>

<img src="/file/view/porcupine8.jpg/272051226/porcupine8.jpg" alt="porcupine8.jpg" title="porcupine8.jpg" /></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>2013-11-11 10:50:06 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-11 11:24:13 UTC</tt>.<br>
-: The original revision id was <tt>467983132</tt>.<br>
+: The original revision id was <tt>467993484</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 47: / Line 47: @@
 || 14/11 || 161.751 ||
 || 7/5 || 162.047 ||
+|| 5\37 || 162.162 ||
 || 11/8 || 162.171 13- and 15-limit minimax ||
+|| 8\59 || 162.712 ||
 || 5/4 || 162.737 5-limit minimax ||
 || 15/14 || 162.897 ||
@@ Line 61: / Line 63: @@
 || 11/9 || 173.704 ||
 || 16/13 || 179.736 ||
+|| 10/9 || 182.404 ||
+===Spectrum of Porcupinefish Tunings===
+|| 12/11 || 150.637 ||
+|| 6/5 || 157.821 ||
+|| 2\15 || 160.000 ||
+|| 18/13 || 160.307 ||
+|| 15/13 || 160.860 ||
+|| 8/7 || 161.471 ||
+|| 13/12 || 161.531 ||
+|| 14/11 || 161.751 ||
+|| 7/5 || 162.047 ||
+|| 14/13 || 162.100 ||
+|| 13/10 || 162.149 ||
+|| 5\37 || 162.162 ||
+|| 11/8 || 162.171 ||
+|| 16/13 || 162.322 ||
+|| 13/11 || 162.368 13- and 15-limit minimax ||
+|| 8\59 || 162.712 ||
+|| 5/4 || 162.737 ||
+|| 15/14 || 162.897 ||
+|| 7/6 || 162.986 ||
+|| 3\22 || 163.636 ||
+|| 9/7 || 163.743 ||
+|| 16/15 || 163.966 ||
+|| 11/10 || 165.004 ||
+|| 4\29 || 165.517 ||
+|| 15/11 || 165.762 ||
+|| 4/3 || 166.015 ||
+|| 11/9 || 173.704 ||
 || 10/9 || 182.404 ||
@@ Line 351: / Line 383: @@
 &lt;/td&gt;
          &lt;td&gt;162.047&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5\37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.162&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 357: / Line 395: @@
 &lt;/td&gt;
          &lt;td&gt;162.171 13- and 15-limit minimax&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8\59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.712&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 446: / Line 490: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-History"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;History&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Spectrum of Porcupine Tunings by Eigenmonzos-Spectrum of Porcupinefish Tunings"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Spectrum of Porcupinefish Tunings&lt;/h3&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;12/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;150.637&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;157.821&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2\15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;160.000&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;18/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;160.307&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;15/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;160.860&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;161.471&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;13/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;161.531&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;14/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;161.751&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;7/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.047&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;14/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.100&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;13/10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.149&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5\37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.162&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.171&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;16/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.322&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;13/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.368 13- and 15-limit minimax&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8\59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.712&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.737&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;15/14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.897&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162.986&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3\22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;163.636&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;163.743&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;16/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;163.966&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;11/10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;165.004&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4\29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;165.517&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;15/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;165.762&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;166.015&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;11/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;173.704&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;10/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;182.404&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-History"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;History&lt;/h2&gt;
   Porcupine temperament/scales were discovered by &lt;a class="wiki_link" href="/Dave%20Keenan"&gt;Dave Keenan&lt;/a&gt;, but didn't have a name until &lt;a class="wiki_link" href="/Herman%20Miller"&gt;Herman Miller&lt;/a&gt; mentioned that his Mizarian Porcupine Overture in 15-tET had a section that pumps the 250:243 comma. Although this music did not use a Porcupine MOS or MODMOS (which would have 7 or 8 notes), the name was adopted for such scales as well, once the essentially one-to-one relationship between vanishing commas and sequences of DE scales was fully evident. It was clear that even though Herman's piece was in 15, 22 was a porcupine tuning par excellence, and that was an interesting development in itself.&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="x-See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;See also&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;See also&lt;/h2&gt;
   &lt;a class="wiki_link" href="/Chords%20of%20porcupine"&gt;Chords of porcupine&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/Porcupine%20Notation"&gt;Porcupine Notation&lt;/a&gt;&lt;br /&gt;
@@ Line 455: / Line 674: @@
 &lt;a class="wiki_link" href="/Porcupine%20Album%20Project"&gt;Porcupine Album Project&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Musical examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Musical examples&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Musical examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Musical examples&lt;/h2&gt;
-  &lt;ul&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow"&gt;Mizarian Porcupine Overture&lt;/a&gt;&amp;quot;, Herman Miller, 1999. (15edo, namesake of the temperament)&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow"&gt;Glassic&lt;/a&gt;&amp;quot;, Paul Erlich, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; (at least the beginning part is in porcupine).&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;&amp;quot;, Gene Ward Smith and Modest Mussorgsky, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow"&gt;being a&lt;/a&gt;&amp;quot;, Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3" rel="nofollow"&gt;Playing Gently with Miller's Porcupine&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;, &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow"&gt;15 Porcupines in India&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;, Sarangi, Tambura and Sitar improvisation by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow"&gt;15 Quills&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt; piano solo by Chris Vaisvil&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3" rel="nofollow"&gt;Prickly Side of Love&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt; - rock band in Porcupine Temperament with vocals by Chris Vaisvil&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow"&gt;Porcupine Organ Composition&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3');"&gt;Among Other Things 2&lt;/a&gt;&lt;/em&gt; by Petr Pařízek&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3" rel="nofollow"&gt;Porcupine Comma Pump&lt;/a&gt;&lt;/em&gt;, by Jake Freivald&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Images"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Images&lt;/h2&gt;
+  &lt;ul&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow"&gt;Mizarian Porcupine Overture&lt;/a&gt;&amp;quot;, Herman Miller, 1999. (15edo, namesake of the temperament)&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow"&gt;Glassic&lt;/a&gt;&amp;quot;, Paul Erlich, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; (at least the beginning part is in porcupine).&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;&amp;quot;, Gene Ward Smith and Modest Mussorgsky, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow"&gt;being a&lt;/a&gt;&amp;quot;, Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3" rel="nofollow"&gt;Playing Gently with Miller's Porcupine&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;, &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow"&gt;15 Porcupines in India&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt;, Sarangi, Tambura and Sitar improvisation by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow"&gt;15 Quills&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt; piano solo by Chris Vaisvil&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3" rel="nofollow"&gt;Prickly Side of Love&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt; - rock band in Porcupine Temperament with vocals by Chris Vaisvil&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow"&gt;Porcupine Organ Composition&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3');"&gt;Among Other Things 2&lt;/a&gt;&lt;/em&gt; by Petr Pařízek&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3" rel="nofollow"&gt;Porcupine Comma Pump&lt;/a&gt;&lt;/em&gt;, by Jake Freivald&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Images"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Images&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextLocalImageRule:373:&amp;lt;img src=&amp;quot;/file/view/porcupine8.jpg/272051226/porcupine8.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine8.jpg/272051226/porcupine8.jpg" alt="porcupine8.jpg" title="porcupine8.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:373 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+  &lt;!-- ws:start:WikiTextLocalImageRule:557:&amp;lt;img src=&amp;quot;/file/view/porcupine8.jpg/272051226/porcupine8.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine8.jpg/272051226/porcupine8.jpg" alt="porcupine8.jpg" title="porcupine8.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:557 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>