Starling temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 204580816 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 204715270 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-02-24 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-24 12:27:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>204715270</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 141: | Line 141: | ||
[[Edo|Edos]]: [[15edo|15]], [[31edo|31]], [[46edo|46]], [[77edo|77]], [[108edo|108]], [[185edo|185]] | [[Edo|Edos]]: [[15edo|15]], [[31edo|31]], [[46edo|46]], [[77edo|77]], [[108edo|108]], [[185edo|185]] | ||
Badness: 0.0167 | Badness: 0.0167 | ||
===Lupercalia=== | |||
Commas: 66/65, 105/104, 121/120, 126/125 | |||
POTE generator: ~22/21 = 77.709 | |||
Map: [<1 1 2 3 3 3|, <0 9 5 -3 7 11|] | |||
EDOs: 15, 31, 108, 139 | |||
Badness: 0.0213 | |||
===Valentino=== | |||
Commas: 121/120, 126/125, 176/175, 196/195 | |||
POTE generator: ~22/21 = 77.958 | |||
Map: [<1 1 2 3 3 5|, <0 9 5 -3 7 -20|] | |||
EDOs: 15, 31, 46, 77, 431 | |||
Badness: 0.0207 | |||
==Casablanca temperament== | ==Casablanca temperament== | ||
| Line 335: | Line 353: | ||
Badness: 0.0167<br /> | Badness: 0.0167<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Valentine temperament-Lupercalia"></a><!-- ws:end:WikiTextHeadingRule:20 -->Lupercalia</h3> | ||
Commas: 66/65, 105/104, 121/120, 126/125<br /> | |||
<br /> | |||
POTE generator: ~22/21 = 77.709<br /> | |||
<br /> | |||
Map: [&lt;1 1 2 3 3 3|, &lt;0 9 5 -3 7 11|]<br /> | |||
EDOs: 15, 31, 108, 139<br /> | |||
Badness: 0.0213<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x-Valentine temperament-Valentino"></a><!-- ws:end:WikiTextHeadingRule:22 -->Valentino</h3> | |||
Commas: 121/120, 126/125, 176/175, 196/195<br /> | |||
<br /> | |||
POTE generator: ~22/21 = 77.958<br /> | |||
<br /> | |||
Map: [&lt;1 1 2 3 3 5|, &lt;0 9 5 -3 7 -20|]<br /> | |||
EDOs: 15, 31, 46, 77, 431<br /> | |||
Badness: 0.0207<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x-Casablanca temperament"></a><!-- ws:end:WikiTextHeadingRule:24 -->Casablanca temperament</h2> | |||
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &lt;&lt;19 14 4 -22 -47 -30||, or as 31&amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.<br /> | Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &lt;&lt;19 14 4 -22 -47 -30||, or as 31&amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.<br /> | ||
<br /> | <br /> | ||
| Line 348: | Line 384: | ||
Badness: 0.1012<br /> | Badness: 0.1012<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="x-Casablanca temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h3> | ||
Commas: 126/125, 385/384, 2420/2401<br /> | Commas: 126/125, 385/384, 2420/2401<br /> | ||
<br /> | <br /> | ||
| Line 355: | Line 391: | ||
Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Nusecond temperament"></a><!-- ws:end:WikiTextHeadingRule:28 -->Nusecond temperament</h2> | ||
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70, or in terms of its wedgie as &lt;&lt;11 13 17 -5 -4 3||. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. <a class="wiki_link" href="/31edo">31edo</a> can be used as a tuning, or <a class="wiki_link" href="/132edo">132edo</a> with a val which is the sum of the <a class="wiki_link" href="/Patent%20val">patent vals</a> for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.<br /> | Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70, or in terms of its wedgie as &lt;&lt;11 13 17 -5 -4 3||. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. <a class="wiki_link" href="/31edo">31edo</a> can be used as a tuning, or <a class="wiki_link" href="/132edo">132edo</a> with a val which is the sum of the <a class="wiki_link" href="/Patent%20val">patent vals</a> for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.<br /> | ||
<br /> | <br /> | ||
| Line 375: | Line 411: | ||
Badness: 0.0504<br /> | Badness: 0.0504<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Nusecond temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h3> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br /> | ||
<br /> | <br /> | ||