Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 202648560 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 202886120 - 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>2011-02-17 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-17 16:22:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>202886120</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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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. | 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. | ||
===5-limit=== | |||
Comma: 1600000/1594323 | |||
POTE generator: ~243/200 = 339.519 | |||
Map: [<1 3 6|, <0 -5 -13|] | |||
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873 | |||
Badness: 0.0220 | |||
===7-limit=== | |||
Commas: 4375/4374, 5120/5103 | |||
POTE generator: ~243/200 = 339.432 | |||
Map: [<1 3 6 -2|, <0 -5 -13 17|] | |||
EDOs: 7, 39, 46, 53, 99, 251, 350 | |||
Badness: 0.0236 | |||
===Hemiamity=== | |||
Commas: 4375/4374, 5120/5103, 3025/3024 | |||
POTE generator: ~ 243/200 = 339.493 | |||
Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|] | |||
EDOs: 14, 46, 106, 152, 350 | |||
==Parakleismic== | ==Parakleismic== | ||
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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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Nearly Micro-Amity-5-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->5-limit</h3> | ||
Comma: 1600000/1594323<br /> | |||
<br /> | |||
POTE generator: ~243/200 = 339.519<br /> | |||
<br /> | |||
Map: [&lt;1 3 6|, &lt;0 -5 -13|]<br /> | |||
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873<br /> | |||
Badness: 0.0220<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Nearly Micro-Amity-7-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->7-limit</h3> | |||
Commas: 4375/4374, 5120/5103<br /> | |||
<br /> | |||
POTE generator: ~243/200 = 339.432<br /> | |||
<br /> | |||
Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]<br /> | |||
EDOs: 7, 39, 46, 53, 99, 251, 350<br /> | |||
Badness: 0.0236<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Nearly Micro-Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule:34 -->Hemiamity</h3> | |||
Commas: 4375/4374, 5120/5103, 3025/3024<br /> | |||
<br /> | |||
POTE generator: ~ 243/200 = 339.493<br /> | |||
<br /> | |||
Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]<br /> | |||
EDOs: 14, 46, 106, 152, 350<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Nearly Micro-Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:36 -->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> | ||