Porcupine: Difference between revisions
Wikispaces>guest **Imported revision 314154482 - Original comment: ** |
Wikispaces>Ninly **Imported revision 317339578 - Original comment: Basic cleanup** |
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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:Ninly|Ninly]] and made on <tt>2012-04-03 14:00:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>317339578</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Basic cleanup</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> | ||
<h4>Original Wikitext content:</h4> | <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">**Porcupine** is a [[Regular Temperaments|linear temperament]] in the [[porcupine family]] that tempers out 250/243, the porcupine [[Comma|comma]], and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-[[Harmonic Limit|limit]] | <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">**Porcupine** is a [[Regular Temperaments|linear temperament]] in the [[porcupine family]] that tempers out 250/243, the porcupine [[Comma|comma]], and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-[[Harmonic Limit|limit]], 7-limit, or 11-limit temperament, or a 2.3.5.11 [[Subgroup temperaments|subgroup temperament]]. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy. | ||
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 "perfect fourths" equals three "minor thirds". 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 [[12edo]], and to meantone in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales. | 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 "perfect fourths" equals three "minor thirds". 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 [[12edo]], and to meantone in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales. | ||
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* <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"><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">[[http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3|Porcupine Organ Composition]]</span> by [[Chris Vaisvil]] | * <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]] | ||
* [[http://dl.dropbox.com/u/8497979/AmongOtherThings2.mp3|Among Other Things 2]] by Petr Parížek | * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://dl.dropbox.com/u/8497979/AmongOtherThings2.mp3|Among Other Things 2]]</span> by Petr Parížek | ||
==Images== | ==Images== | ||
[[image:porcupine8.jpg]]</pre></div> | [[image:porcupine8.jpg]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Porcupine</title></head><body><strong>Porcupine</strong> is a <a class="wiki_link" href="/Regular%20Temperaments">linear temperament</a> in the <a class="wiki_link" href="/porcupine%20family">porcupine family</a> that tempers out 250/243, the porcupine <a class="wiki_link" href="/Comma">comma</a>, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-<a class="wiki_link" href="/Harmonic%20Limit">limit</a> | <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>Porcupine</title></head><body><strong>Porcupine</strong> is a <a class="wiki_link" href="/Regular%20Temperaments">linear temperament</a> in the <a class="wiki_link" href="/porcupine%20family">porcupine family</a> that tempers out 250/243, the porcupine <a class="wiki_link" href="/Comma">comma</a>, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-<a class="wiki_link" href="/Harmonic%20Limit">limit</a>, 7-limit, or 11-limit temperament, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.<br /> | ||
<br /> | <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 /> | 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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:5 -->Musical examples</h2> | <!-- 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;<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 class="wiki_link_ext" href="http://dl.dropbox.com/u/8497979/AmongOtherThings2.mp3" rel="nofollow">Among Other Things 2</a> by Petr Parížek</li></ul><!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:7 -->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><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://dl.dropbox.com/u/8497979/AmongOtherThings2.mp3" rel="nofollow">Among Other Things 2</a></span> by Petr Parížek</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:89:&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:89 --></body></html></pre></div> | <!-- ws:start:WikiTextLocalImageRule:89:&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:89 --></body></html></pre></div> | ||