Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 513247506 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 513249110 - 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>2014-06-08 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-08 14:00:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>513249110</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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Map: [<1 5 1 3|, <0 -18 7 -1|] | Map: [<1 5 1 3|, <0 -18 7 -1|] | ||
Wedgie: <<18 -7 1 -53 -49 22|| | Wedgie: <<18 -7 1 -53 -49 22|| | ||
EDOs: 21, 37, 58 | EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd | ||
Badness: 0.1584 | |||
==11-limit== | |||
Commas: 176/175, 2401/2400, 2560/2541 | |||
POTE generator: ~8/7 = 227.500 | |||
Map: [<1 5 1 3 1|, <0 -18 7 -1 13|] | |||
EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde | |||
Badness: 0.059 | |||
==13-limit== | |||
Commas: 176/175, 196/195, 364/363, 512/507 | |||
POTE generator: ~8/7 = 227.493 | |||
Map: [<1 5 1 3 1 2|, <0 -18 7 -1 13 9|] | |||
EDOs: 21, 37, 58, 153bcef, 211bcdef | |||
Badness: 0.0322 | |||
</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:80:&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:80 --><!-- ws:start:WikiTextTocRule:81: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --> | <a href="#Semihemi">Semihemi</a><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --> | <a href="#Hemitert">Hemitert</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --> | <a href="#Emmthird">Emmthird</a><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Quinmite">Quinmite</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --> | <a href="#Unthirds">Unthirds</a><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --> | <a href="#Newt">Newt</a><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --> | <a href="#Amicable">Amicable</a><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#Septidiasemi">Septidiasemi</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --> | <a href="#Maviloid">Maviloid</a><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --> | <a href="#Subneutral">Subneutral</a><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Osiris">Osiris</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --> | <a href="#Gorgik">Gorgik</a><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><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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Map: [&lt;1 5 1 3|, &lt;0 -18 7 -1|]<br /> | Map: [&lt;1 5 1 3|, &lt;0 -18 7 -1|]<br /> | ||
Wedgie: &lt;&lt;18 -7 1 -53 -49 22||<br /> | Wedgie: &lt;&lt;18 -7 1 -53 -49 22||<br /> | ||
EDOs: 21, 37, 58 | EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd<br /> | ||
Badness: 0.1584<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Gorgik-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2> | |||
Commas: 176/175, 2401/2400, 2560/2541<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 227.500<br /> | |||
<br /> | |||
Map: [&lt;1 5 1 3 1|, &lt;0 -18 7 -1 13|]<br /> | |||
EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde<br /> | |||
Badness: 0.059<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Gorgik-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2> | |||
Commas: 176/175, 196/195, 364/363, 512/507<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 227.493<br /> | |||
<br /> | |||
Map: [&lt;1 5 1 3 1 2|, &lt;0 -18 7 -1 13 9|]<br /> | |||
EDOs: 21, 37, 58, 153bcef, 211bcdef<br /> | |||
Badness: 0.0322</body></html></pre></div> | |||