Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 209868590 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213134168 - 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>2011-03- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 07:36:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213134168</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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EDOs: 7, 39, 46, 53, 99, 251, 350 | EDOs: 7, 39, 46, 53, 99, 251, 350 | ||
Badness: 0.0236 | Badness: 0.0236 | ||
===Hitchcock=== | |||
Commas: 121/120, 176/175, 2200/2187 | |||
POTE generator: ~11/9 = 339.340 | |||
Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|] | |||
EDOs: 7, 39, 46, 53, 99 | |||
Badness: 0.0352 | |||
===Hemiamity=== | ===Hemiamity=== | ||
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Badness: 0.0236<br /> | Badness: 0.0236<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Nearly Micro-Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Nearly Micro-Amity-Hitchcock"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hitchcock</h3> | ||
Commas: 121/120, 176/175, 2200/2187<br /> | |||
<br /> | |||
POTE generator: ~11/9 = 339.340<br /> | |||
<br /> | |||
Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]<br /> | |||
EDOs: 7, 39, 46, 53, 99<br /> | |||
Badness: 0.0352<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 /> | Commas: 4375/4374, 5120/5103, 3025/3024<br /> | ||
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EDOs: 14, 46, 106, 152, 350<br /> | EDOs: 14, 46, 106, 152, 350<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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. <br /> | 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. <br /> | ||
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Badness: 0.0433<br /> | Badness: 0.0433<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Nearly Micro-Parakleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->7-limit</h3> | ||
Commas: 3136/3125, 5475/4374<br /> | Commas: 3136/3125, 5475/4374<br /> | ||
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Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h3&gt; --><h3 id="toc20"><a name="Nearly Micro-Parakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h3> | ||
Commas: 385/384, 3136/3125, 4375/4374<br /> | Commas: 385/384, 3136/3125, 4375/4374<br /> | ||
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