Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 212556890 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 212565266 - 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>2011-03-21 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-21 17:00:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>212565266</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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Adding 3025/3024 extends to the 11-limit and gives <<38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning. | Adding 3025/3024 extends to the 11-limit and gives <<38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning. | ||
Commas: 2401/2400, 29360128/29296875 | |||
POTE generator: ~1024/875 = 271.107 | |||
Map: [<1 31 0 9|, <0 -38 3 -8|] | |||
EDOs: [[31edo|31]], [[177edo|177]], [[208edo|208]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]] | |||
Badness: 0.0358 | |||
==11-limit== | |||
Commas: 2401/2400, 3025/3024, 5632/5625 | |||
POTE generator: ~90/77 = 271.111 | |||
Map: [<1 31 0 9 53|, <0 -38 3 -8 -64|] | |||
EDOs: [[31edo|31]], [[208edo|208]], [[239edo|239]], [[270edo|270]] | |||
Badness: 0.0175 | |||
=Decoid= | =Decoid= | ||
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Badness: 0.0135</pre></div> | Badness: 0.0135</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:26:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><br /> | ||
Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | ||
<br /> | <br /> | ||
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Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.<br /> | Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id=" | Commas: 2401/2400, 29360128/29296875<br /> | ||
<br /> | |||
POTE generator: ~1024/875 = 271.107<br /> | |||
<br /> | |||
Map: [&lt;1 31 0 9|, &lt;0 -38 3 -8|]<br /> | |||
EDOs: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/177edo">177</a>, <a class="wiki_link" href="/208edo">208</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/270edo">270</a>, <a class="wiki_link" href="/571edo">571</a>, <a class="wiki_link" href="/841edo">841</a>, <a class="wiki_link" href="/1111edo">1111</a><br /> | |||
Badness: 0.0358<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Quasiorwell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> | |||
Commas: 2401/2400, 3025/3024, 5632/5625<br /> | |||
<br /> | |||
POTE generator: ~90/77 = 271.111<br /> | |||
<br /> | |||
Map: [&lt;1 31 0 9 53|, &lt;0 -38 3 -8 -64|]<br /> | |||
EDOs: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/208edo">208</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/270edo">270</a><br /> | |||
Badness: 0.0175<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Decoid"></a><!-- ws:end:WikiTextHeadingRule:20 -->Decoid</h1> | |||
Commas: 2401/2400, 67108864/66976875<br /> | Commas: 2401/2400, 67108864/66976875<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0339<br /> | Badness: 0.0339<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Decoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 2401/2400, 5832/5825, 9801/9800<br /> | Commas: 2401/2400, 5832/5825, 9801/9800<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0187<br /> | Badness: 0.0187<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Decoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | ||
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | ||
<br /> | <br /> | ||