Porcupine: Difference between revisions
Wikispaces>phylingual **Imported revision 356216740 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 359393613 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-08-23 04:11:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>359393613</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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==Interval chain== | ==Interval chain== | ||
Main article: [[Porcupine intervals]] | Main article: [[Porcupine intervals]] | ||
||~ Generators ||~ Cents ||~ Ratios || | ||~ Generators ||~ Cents ||~ Ratios ||~ Octave inverse ||~ Ratios || | ||
|| 0 ||> 0.00 ||= 1/1 || | || 0 ||> 0.00 ||= 1/1 ||> 1200.00 ||= 2/1 || | ||
|| 1 ||> 162.75 ||= 12/11~11/10~10/9 || | || 1 ||> 162.75 ||= 12/11~11/10~10/9 ||> 1037.25 ||= 9/5~20/11~11/6 || | ||
|| 2 ||> 325.50 ||= 6/5~11/9 || | || 2 ||> 325.50 ||= 6/5~11/9 ||> 874.50 ||= 18/11~5/3 || | ||
|| 3 ||> 488.25 ||= 4/3 || | || 3 ||> 488.25 ||= 4/3 ||> 711.75 ||= 3/2 || | ||
|| 4 ||> 651.00 ||= 16/11~22/15 || | || 4 ||> 651.00 ||= 16/11~22/15 ||> 549.00 ||= 15/11~11/8 || | ||
|| 5 ||> 813.75 ||= 8/5 || | || 5 ||> 813.75 ||= 8/5 ||> 386.25 ||= 5/4 || | ||
|| 6 ||> 976.50 ||= 7/4~16/9 || | || 6 ||> 976.50 ||= 7/4~16/9 ||> 223.50 ||= 9/8~8/7 || | ||
|| 7 ||> 1139.25 ||= 48/25~160/81 || | || 7 ||> 1139.25 ||= 48/25~160/81 ||> 60.75 ||= 81/80~25/24 || | ||
|| 8 ||> 102.00 ||= 16/15~21/20 || | || 8 ||> 102.00 ||= 16/15~21/20 ||> 1008.00 ||= 40/21~15/8 || | ||
|| 9 ||> 264.75 ||= 7/6 || | || 9 ||> 264.75 ||= 7/6 ||> 935.25 ||= 12/7 || | ||
|| 10 ||> 427.50 ||= 14/11 || | || 10 ||> 427.50 ||= 14/11 ||> 772.50 ||= 11/7 || | ||
|| 11 ||> 590.25 ||= 7/5 || | || 11 ||> 590.25 ||= 7/5 ||> 609.75 ||= 10/7 || | ||
|| 12 ||> 753.00 ||= 14/9 || | || 12 ||> 753.00 ||= 14/9 ||> 446.00 ||= 9/7 || | ||
The specific tuning shown is the full 11-limit [[POTE tuning]], but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.) | The specific tuning shown is the full 11-limit [[POTE tuning]], but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.) | ||
12/11, 11/10, and 10/9 are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find. | 12/11, 11/10, and 10/9 are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find. | ||
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* "[[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music|Mizarian Porcupine Overture]]", Herman Miller, 1999. (15edo, namesake of the temperament) | * "[[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music|Mizarian Porcupine Overture]]", Herman Miller, 1999. (15edo, namesake of the temperament) | ||
* "[[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095|Glassic]]", Paul Erlich, [[22edo]] (at least the beginning part is in porcupine). | * "[[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095|Glassic]]", Paul Erlich, [[22edo]] (at least the beginning part is in porcupine). | ||
* "<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * "<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]</span></span>", Gene Ward Smith and Modest Mussorgsky, [[22edo]]. | ||
* "[[http://soundclick.com/share.cfm?id=8839060|being a]]", Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8]. | * "[[http://soundclick.com/share.cfm?id=8839060|being a]]", Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8]. | ||
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3|Playing Gently with Miller's Porcupine]]</span></span>, [[Chris Vaisvil]] | ||
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3|15 Porcupines in India]]</span></span>, Sarangi, Tambura and Sitar improvisation by [[Chris Vaisvil]] | ||
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3|15 Quills]]</span></span> piano solo by Chris Vaisvil | ||
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3|Prickly Side of Love]]</span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil | ||
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"> | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3|Porcupine Organ Composition]]</span> by [[Chris Vaisvil]] | ||
* | * [[file:xenharmonic/AmongOtherThings2.mp3|Among Other Things 2]] by Petr Pařízek | ||
==Images== | ==Images== | ||
[[image:porcupine8.jpg]]</pre></div> | [[image:porcupine8.jpg]]</pre></div> | ||
| Line 64: | Line 64: | ||
</th> | </th> | ||
<th>Cents<br /> | <th>Cents<br /> | ||
</th> | |||
<th>Ratios<br /> | |||
</th> | |||
<th>Octave inverse<br /> | |||
</th> | </th> | ||
<th>Ratios<br /> | <th>Ratios<br /> | ||
| Line 74: | Line 78: | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
</td> | |||
<td style="text-align: right;">1200.00<br /> | |||
</td> | |||
<td style="text-align: center;">2/1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 82: | Line 90: | ||
</td> | </td> | ||
<td style="text-align: center;">12/11~11/10~10/9<br /> | <td style="text-align: center;">12/11~11/10~10/9<br /> | ||
</td> | |||
<td style="text-align: right;">1037.25<br /> | |||
</td> | |||
<td style="text-align: center;">9/5~20/11~11/6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 90: | Line 102: | ||
</td> | </td> | ||
<td style="text-align: center;">6/5~11/9<br /> | <td style="text-align: center;">6/5~11/9<br /> | ||
</td> | |||
<td style="text-align: right;">874.50<br /> | |||
</td> | |||
<td style="text-align: center;">18/11~5/3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 98: | Line 114: | ||
</td> | </td> | ||
<td style="text-align: center;">4/3<br /> | <td style="text-align: center;">4/3<br /> | ||
</td> | |||
<td style="text-align: right;">711.75<br /> | |||
</td> | |||
<td style="text-align: center;">3/2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 106: | Line 126: | ||
</td> | </td> | ||
<td style="text-align: center;">16/11~22/15<br /> | <td style="text-align: center;">16/11~22/15<br /> | ||
</td> | |||
<td style="text-align: right;">549.00<br /> | |||
</td> | |||
<td style="text-align: center;">15/11~11/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 114: | Line 138: | ||
</td> | </td> | ||
<td style="text-align: center;">8/5<br /> | <td style="text-align: center;">8/5<br /> | ||
</td> | |||
<td style="text-align: right;">386.25<br /> | |||
</td> | |||
<td style="text-align: center;">5/4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 122: | Line 150: | ||
</td> | </td> | ||
<td style="text-align: center;">7/4~16/9<br /> | <td style="text-align: center;">7/4~16/9<br /> | ||
</td> | |||
<td style="text-align: right;">223.50<br /> | |||
</td> | |||
<td style="text-align: center;">9/8~8/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 130: | Line 162: | ||
</td> | </td> | ||
<td style="text-align: center;">48/25~160/81<br /> | <td style="text-align: center;">48/25~160/81<br /> | ||
</td> | |||
<td style="text-align: right;">60.75<br /> | |||
</td> | |||
<td style="text-align: center;">81/80~25/24<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 138: | Line 174: | ||
</td> | </td> | ||
<td style="text-align: center;">16/15~21/20<br /> | <td style="text-align: center;">16/15~21/20<br /> | ||
</td> | |||
<td style="text-align: right;">1008.00<br /> | |||
</td> | |||
<td style="text-align: center;">40/21~15/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 146: | Line 186: | ||
</td> | </td> | ||
<td style="text-align: center;">7/6<br /> | <td style="text-align: center;">7/6<br /> | ||
</td> | |||
<td style="text-align: right;">935.25<br /> | |||
</td> | |||
<td style="text-align: center;">12/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 154: | Line 198: | ||
</td> | </td> | ||
<td style="text-align: center;">14/11<br /> | <td style="text-align: center;">14/11<br /> | ||
</td> | |||
<td style="text-align: right;">772.50<br /> | |||
</td> | |||
<td style="text-align: center;">11/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 162: | Line 210: | ||
</td> | </td> | ||
<td style="text-align: center;">7/5<br /> | <td style="text-align: center;">7/5<br /> | ||
</td> | |||
<td style="text-align: right;">609.75<br /> | |||
</td> | |||
<td style="text-align: center;">10/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 170: | Line 222: | ||
</td> | </td> | ||
<td style="text-align: center;">14/9<br /> | <td style="text-align: center;">14/9<br /> | ||
</td> | |||
<td style="text-align: right;">446.00<br /> | |||
</td> | |||
<td style="text-align: center;">9/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 188: | Line 244: | ||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:7 -->Musical examples</h2> | <!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:7 -->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;<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a></span></span>&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><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span>, <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow">15 Porcupines in India</a></span></span>, Sarangi, Tambura and Sitar improvisation by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow">15 Quills</a></span></span> piano solo by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow">Porcupine Organ Composition</a></span> 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></ul><!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:9 -->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;<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a></span></span>&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><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span>, <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow">15 Porcupines in India</a></span></span>, Sarangi, Tambura and Sitar improvisation by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow">15 Quills</a></span></span> piano solo by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow">Porcupine Organ Composition</a></span> 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></ul><!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:9 -->Images</h2> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:203:&lt;img src=&quot;/file/view/porcupine8.jpg/272051226/porcupine8.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/porcupine8.jpg/272051226/porcupine8.jpg" alt="porcupine8.jpg" title="porcupine8.jpg" /><!-- ws:end:WikiTextLocalImageRule:203 --></body></html></pre></div> | ||