Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 191311358 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 191311496 - 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>2011-01-06 01: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-06 01:41:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>191311496</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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[[POTE tuning|POTE generator]]: 208.899 | [[POTE tuning|POTE generator]]: 208.899 | ||
Map: | Map: [<2 7 13 -1|, <0 -11 -24 19|] | ||
Wedgie: <<22 48 -38 25 -122 -223|| | Wedgie: <<22 48 -38 25 -122 -223|| | ||
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798 | EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798 | ||
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[[POTE tuning|POTE generator]]: 208.901 | [[POTE tuning|POTE generator]]: 208.901 | ||
Map: | Map: [<2 7 13 -1 1|, <0 -11 -24 19 17|] | ||
EDOs: 46, 132, 178, 224, 270, 494, 764 | EDOs: 46, 132, 178, 224, 270, 494, 764 | ||
Badness: 0.0129 | Badness: 0.0129 | ||
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[[POTE tuning|POTE generator]]: 208.903 | [[POTE tuning|POTE generator]]: 208.903 | ||
Map: | Map: [<2 7 13 -1 1 -2|, <0 -11 -24 19 17 27|] | ||
EDOs: 46, 178, 224, 270, 494, 764, 1258 | EDOs: 46, 178, 224, 270, 494, 764, 1258 | ||
Badness: 0.00886 | Badness: 0.00886 | ||
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.899<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.899<br /> | ||
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Map: < | Map: [&lt;2 7 13 -1|, &lt;0 -11 -24 19|]<br /> | ||
Wedgie: &lt;&lt;22 48 -38 25 -122 -223||<br /> | |||
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798<br /> | |||
Badness: 0.0370<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Abigail-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h3> | |||
Comma: 3025/3024, 4375/4374, 20614528/20588575<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.901<br /> | |||
<br /> | |||
Map: [&lt;2 7 13 -1 1|, &lt;0 -11 -24 19 17|]<br /> | |||
EDOs: 46, 132, 178, 224, 270, 494, 764<br /> | |||
Badness: 0.0129<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Abigail-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h3> | |||
Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.903<br /> | |||
<br /> | |||
Map: [&lt;2 7 13 -1 1 -2|, &lt;0 -11 -24 19 17 27|]<br /> | |||
EDOs: 46, 178, 224, 270, 494, 764, 1258<br /> | |||
Badness: 0.00886<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule:14 -->Nearly Micro</h1> | |||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Nearly Micro-Amity"></a><!-- ws:end:WikiTextHeadingRule:16 -->Amity</h2> | |||
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. <a class="wiki_link" href="/99edo">99edo</a> is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.<br /> | |||
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In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.<br /> | In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Nearly Micro-Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:18 -->Parakleismic</h2> | ||
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.</body></html></pre></div> | In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.</body></html></pre></div> | ||