Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 290271047 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 293077668 - 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>2012-01- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-17 21:54:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>293077668</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: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c | EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c | ||
Badness: 0.0373 | Badness: 0.0373 | ||
=Unthirds= | |||
Commas: 2401/2400, 68359375/68024448 | |||
POTE generator: ~3969/3125 = 416.717 | |||
Map: [<1 29 33 25|, <0 -42 -47 -34|] | |||
Wedgie: <<42 47 34 -23 -64 -53|| | |||
EDOs: 72, 167, 239, 311, 694, 1005c | |||
Badness: 0.0753 | |||
==11-limit== | |||
Commas: 2401/2400, 3025/3024, 4000/3993 | |||
POTE generator: ~14/11 = 416.718 | |||
Map: [<1 29 33 25 25|, <0 -42 -47 -34 -33|] | |||
EDOs: 72, 167, 239, 311, 1316c | |||
Badness: 0.0229 | |||
==13-limit== | |||
Commas: 625/624, 1575/1573, 2080/2079, 2401/2400 | |||
POTE generator: ~14/11 = 416.716 | |||
Map: [<1 29 33 25 25 99|, <0 -42 -47 -34 -33 -146|] | |||
EDOs: 72, 311, 694, 1005c, 1699cd | |||
Badness: 0.0209 | |||
</pre></div> | </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:46:&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:46 --><!-- ws:start:WikiTextTocRule:47: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Emmthird">Emmthird</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Quinmite">Quinmite</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Unthirds">Unthirds</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:70 --><br /> | ||
<br /> | <br /> | ||
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 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, |-5 -1 -2 4&gt; = 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 /> | ||
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Wedgie: &lt;&lt;34 29 23 -33 -59 -28||<br /> | Wedgie: &lt;&lt;34 29 23 -33 -59 -28||<br /> | ||
EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c<br /> | EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c<br /> | ||
Badness: 0.0373</body></html></pre></div> | Badness: 0.0373<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Unthirds"></a><!-- ws:end:WikiTextHeadingRule:40 -->Unthirds</h1> | |||
Commas: 2401/2400, 68359375/68024448<br /> | |||
<br /> | |||
POTE generator: ~3969/3125 = 416.717<br /> | |||
<br /> | |||
Map: [&lt;1 29 33 25|, &lt;0 -42 -47 -34|]<br /> | |||
Wedgie: &lt;&lt;42 47 34 -23 -64 -53||<br /> | |||
EDOs: 72, 167, 239, 311, 694, 1005c<br /> | |||
Badness: 0.0753<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Unthirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | |||
Commas: 2401/2400, 3025/3024, 4000/3993<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 416.718<br /> | |||
<br /> | |||
Map: [&lt;1 29 33 25 25|, &lt;0 -42 -47 -34 -33|]<br /> | |||
EDOs: 72, 167, 239, 311, 1316c<br /> | |||
Badness: 0.0229<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Unthirds-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | |||
Commas: 625/624, 1575/1573, 2080/2079, 2401/2400<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 416.716<br /> | |||
<br /> | |||
Map: [&lt;1 29 33 25 25 99|, &lt;0 -42 -47 -34 -33 -146|]<br /> | |||
EDOs: 72, 311, 694, 1005c, 1699cd<br /> | |||
Badness: 0.0209</body></html></pre></div> | |||