Porcupine: Difference between revisions
Wikispaces>genewardsmith **Imported revision 270437742 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 270516226 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-11-01 00:27:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>270516226</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> | ||
| Line 13: | Line 13: | ||
|| 0 || 162.75 || 325.50 || 488.25 || 651.00 || 813.75 || 976.50 || 1139.25 || 102.00 || 264.75 || 427.50 || 590.25 || 753.00 || | || 0 || 162.75 || 325.50 || 488.25 || 651.00 || 813.75 || 976.50 || 1139.25 || 102.00 || 264.75 || 427.50 || 590.25 || 753.00 || | ||
|| 1/1 || 12/11~11/10~10/9 || 6/5~11/9 || 4/3 || 16/11 || 8/5 || 16/9~7/4 || 48/25~160/81 || 16/15 || 7/6 || 14/11 || 7/5 || 14/9 || | || 1/1 || 12/11~11/10~10/9 || 6/5~11/9 || 4/3 || 16/11 || 8/5 || 16/9~7/4 || 48/25~160/81 || 16/15 || 7/6 || 14/11 || 7/5 || 14/9 || | ||
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 cents ([[ | 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]]). | ||
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. | ||
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.</pre></div> | 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. | ||
==Musical examples== | |||
* "[[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music|Mizarian Porcupine Overture]]", Herman Miller, 1999. (15edo, namesake of the temperament) | |||
* "[[http://lumma.org/music/theory/tctmo/glassic.mp3|Glassic]]", Paul Erlich, 22edo (at least the beginning part is in porcupine).</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> 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> temperament, a 7-limit one, an 11-limit one, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. In the 2.3.5.11 subgroup it is one of the best temperaments, with a unique combination of efficiency and accuracy.<br /> | <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> 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> temperament, a 7-limit one, an 11-limit one, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. In the 2.3.5.11 subgroup it is one of the best temperaments, with a unique combination of efficiency and accuracy.<br /> | ||
| Line 84: | Line 88: | ||
</table> | </table> | ||
The specific tuning shown is the full 11-limit <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>, but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents (<a class="wiki_link" href="/15edo">15edo</a>) and as large as 165 cents (<a class="wiki_link" href="/ | The specific tuning shown is the full 11-limit <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>, but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents (<a class="wiki_link" href="/15edo">15edo</a>) and as large as 165.5 cents (<a class="wiki_link" href="/29edo">29edo</a>).<br /> | ||
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.<br /> | 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.<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 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.</body></html></pre></div> | 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 /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:2 -->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://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow">Glassic</a>&quot;, Paul Erlich, 22edo (at least the beginning part is in porcupine).</li></ul></body></html></pre></div> | |||