Starling temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 204715270 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 205327850 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-26 22:09:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>205327850</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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Badness: 0.0256 | Badness: 0.0256 | ||
=== | ===Sensor=== | ||
Commas: 126/125, 245/243, 385/384 | Commas: 126/125, 245/243, 385/384 | ||
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Badness: 0.0379 | Badness: 0.0379 | ||
===13-limit=== | ====13-limit==== | ||
Commas: 91/90, 126/125, 169/168, 385/384 | Commas: 91/90, 126/125, 169/168, 385/384 | ||
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EDOs: 19, 27, 73, 100 | EDOs: 19, 27, 73, 100 | ||
Badness: 0.0200 | Badness: 0.0200 | ||
===Sensus=== | |||
Commas: 126/125, 176/175, 245/243 | |||
POTE generator: ~9/7 = 443.626 | |||
Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|] | |||
EDOs: 8, 19, 27, 46, 165 | |||
Badness: 0.0295 | |||
====13-limit==== | |||
Commas: 91/90, 126/125, 169/168, 352/351 | |||
POTE generator: ~9/7 = 443.559 | |||
Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|] | |||
EDOs: 8, 19, 27, 46, 303 | |||
Badness: 0.0208 | |||
==Valentine temperament== | ==Valentine temperament== | ||
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Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Sensi temperament- | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Sensi temperament-Sensor"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensor</h3> | ||
Commas: 126/125, 245/243, 385/384<br /> | Commas: 126/125, 245/243, 385/384<br /> | ||
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Badness: 0.0379<br /> | Badness: 0.0379<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt; | <!-- ws:start:WikiTextHeadingRule:10:&lt;h4&gt; --><h4 id="toc5"><a name="x-Sensi temperament-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h4> | ||
Commas: 91/90, 126/125, 169/168, 385/384<br /> | Commas: 91/90, 126/125, 169/168, 385/384<br /> | ||
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Badness: 0.0200<br /> | Badness: 0.0200<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Sensi temperament-Sensus"></a><!-- ws:end:WikiTextHeadingRule:16 -->Sensus</h3> | ||
Commas: 126/125, 176/175, 245/243<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 443.626<br /> | |||
<br /> | |||
Map: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]<br /> | |||
EDOs: 8, 19, 27, 46, 165<br /> | |||
Badness: 0.0295<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h4&gt; --><h4 id="toc9"><a name="x-Sensi temperament-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h4> | |||
Commas: 91/90, 126/125, 169/168, 352/351<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 443.559<br /> | |||
<br /> | |||
Map: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]<br /> | |||
EDOs: 8, 19, 27, 46, 303<br /> | |||
Badness: 0.0208<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Valentine temperament"></a><!-- ws:end:WikiTextHeadingRule:20 -->Valentine temperament</h2> | |||
Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3*7/5. In this respect it resembles miracle, with a generator of 3*5/7, and casablanca, with a generator of 5*7/3. These three generators are the simplest in terms of the relationship of tetrads in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice of 7-limit tetrads</a>. Valentine can also be described as the 31&amp;46 temperament, and <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/108edo">108edo</a> or <a class="wiki_link" href="/185edo">185edo</a> make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)^(1/9) as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as &lt;&lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).<br /> | Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3*7/5. In this respect it resembles miracle, with a generator of 3*5/7, and casablanca, with a generator of 5*7/3. These three generators are the simplest in terms of the relationship of tetrads in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice of 7-limit tetrads</a>. Valentine can also be described as the 31&amp;46 temperament, and <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/108edo">108edo</a> or <a class="wiki_link" href="/185edo">185edo</a> make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)^(1/9) as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as &lt;&lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).<br /> | ||
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Badness: 0.0311<br /> | Badness: 0.0311<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x-Valentine temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h3> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br /> | ||
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Badness: 0.0167<br /> | Badness: 0.0167<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Valentine temperament-Lupercalia"></a><!-- ws:end:WikiTextHeadingRule:24 -->Lupercalia</h3> | ||
Commas: 66/65, 105/104, 121/120, 126/125<br /> | Commas: 66/65, 105/104, 121/120, 126/125<br /> | ||
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Badness: 0.0213<br /> | Badness: 0.0213<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="x-Valentine temperament-Valentino"></a><!-- ws:end:WikiTextHeadingRule:26 -->Valentino</h3> | ||
Commas: 121/120, 126/125, 176/175, 196/195<br /> | Commas: 121/120, 126/125, 176/175, 196/195<br /> | ||
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Badness: 0.0207<br /> | Badness: 0.0207<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Casablanca temperament"></a><!-- ws:end:WikiTextHeadingRule:28 -->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 /> | ||
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Badness: 0.1012<br /> | Badness: 0.1012<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Casablanca temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h3> | ||
Commas: 126/125, 385/384, 2420/2401<br /> | Commas: 126/125, 385/384, 2420/2401<br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x-Nusecond temperament"></a><!-- ws:end:WikiTextHeadingRule:32 -->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 /> | ||
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Badness: 0.0504<br /> | Badness: 0.0504<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Nusecond temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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 /> | ||
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