Porcupine: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 288421958 - Original comment: ** |
Wikispaces>vaisvil **Imported revision 288948781 - 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:vaisvil|vaisvil]] and made on <tt>2011-12-31 23:43:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288948781</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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The 11/9 interval, usually considered a "neutral third", is in porcupine identical to the 6/5 "minor third". This means that the 27/20 "wolf fifth" of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone). | The 11/9 interval, usually considered a "neutral third", is in porcupine identical to the 6/5 "minor third". This means that the 27/20 "wolf fifth" of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone). | ||
The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from <50 to 80 cents in general, represents both 25/24 and 81/80. | The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from <50 to 80 cents in general, represents both 25/24 and 81/80. | ||
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==History== | ==History== | ||
<span class="commentBody">Porcupine temperament/scales were discovered by [[Dave Keenan]], but didn't have a name until [[Herman Miller]] mentioned that his Mizarian Porcupine Overture in 15-tET had a section where it "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.</span> | <span class="commentBody">Porcupine temperament/scales were discovered by [[Dave Keenan]], but didn't have a name until [[Herman Miller]] mentioned that his Mizarian Porcupine Overture in 15-tET had a section where it "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.</span> | ||
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* "[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]", Gene Ward Smith and Modest Mussorgsky, [[22edo]]. | * "[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]", 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]. | ||
* [[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3|Playing Gently with Miller's Porcupine]], [[Chris Vaisvil]] | |||
* [[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3|15 Porcupines in India]], Sarangi, Tambura and Sitar improvisation by [[Chris Vaisvil]] | |||
* [[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3|15 Quills]] piano solo by Chris Vaisvil | |||
* [[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3|Prickly Side of Love]] - rock band in Porcupine Temperament with vocals by Chris Vaisvil | |||
==Images== | ==Images== | ||
[[image:porcupine8.jpg]]</pre></div> | [[image:porcupine8.jpg]]</pre></div> | ||
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The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two &quot;perfect fourths&quot; equals three &quot;minor thirds&quot;. As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to <a class="wiki_link" href="/12edo">12edo</a>, and to meantone in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The &quot;equal tetrachord&quot; formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.<br /> | The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two &quot;perfect fourths&quot; equals three &quot;minor thirds&quot;. As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to <a class="wiki_link" href="/12edo">12edo</a>, and to meantone in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The &quot;equal tetrachord&quot; formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:1 -->Interval chain</h2> | ||
Main article: <a class="wiki_link" href="/Porcupine%20intervals">Porcupine intervals</a><br /> | Main article: <a class="wiki_link" href="/Porcupine%20intervals">Porcupine intervals</a><br /> | ||
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The 11/9 interval, usually considered a &quot;neutral third&quot;, is in porcupine identical to the 6/5 &quot;minor third&quot;. This means that the 27/20 &quot;wolf fifth&quot; of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone).<br /> | The 11/9 interval, usually considered a &quot;neutral third&quot;, is in porcupine identical to the 6/5 &quot;minor third&quot;. This means that the 27/20 &quot;wolf fifth&quot; of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone).<br /> | ||
The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from &lt;50 to 80 cents in general, represents both 25/24 and 81/80.<br /> | The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from &lt;50 to 80 cents in general, represents both 25/24 and 81/80.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x-History"></a><!-- ws:end:WikiTextHeadingRule:3 -->History</h2> | |||
<span class="commentBody">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 where it &quot;pumps&quot; the 250:243 &quot;comma.&quot; 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.</span><br /> | <span class="commentBody">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 where it &quot;pumps&quot; the 250:243 &quot;comma.&quot; 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.</span><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:5 -->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></ul><!-- ws:start:WikiTextHeadingRule: | <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></ul><!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:7 -->Images</h2> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:85:&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:85 --></body></html></pre></div> | ||