Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 202576870 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 202648560 - 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>2011-02-17 04:47:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>202648560</tt>.<br> | ||
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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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=Nearly Micro= | =Nearly Micro= | ||
==Octoid== | |||
Commas: 4375/4374, 16875/16807 | |||
===11-limit=== | |||
Commas: 540/539, 1375/1372, 4000/3993 | |||
===13-limit=== | |||
Commas: 540/539, 1375/1372, 4000/3993, 625/624 | |||
==Amity== | ==Amity== | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule:20 -->Nearly Micro</h1> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule:20 -->Nearly Micro</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Nearly Micro-Amity"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Nearly Micro-Octoid"></a><!-- ws:end:WikiTextHeadingRule:22 -->Octoid</h2> | ||
Commas: 4375/4374, 16875/16807<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Nearly Micro-Octoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h3> | |||
Commas: 540/539, 1375/1372, 4000/3993<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Nearly Micro-Octoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h3> | |||
Commas: 540/539, 1375/1372, 4000/3993, 625/624<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Nearly Micro-Amity"></a><!-- ws:end:WikiTextHeadingRule:28 -->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 /> | 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:30:&lt;h2&gt; --><h2 id="toc15"><a name="Nearly Micro-Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->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> | ||