Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 537227354 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 538718916 - 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>2015-01-13 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-01-27 13:47:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>538718916</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 9 7 12 11|, <0 -22 -43 -27 -55 -47|] | Map: [<1 5 9 7 12 11|, <0 -22 -43 -27 -55 -47|] | ||
EDOs: 58, 103, 161 | EDOs: 58, 103, 161 | ||
Badness: 0.0218</pre></div> | Badness: 0.0218 | ||
=Catafourth= | |||
Commas: 2400/2401, 78732/78125 | |||
POTE generator: ~250/189 = 489.235 | |||
Map: [<1 13 17 13|, <0 -28 -36 -25|] | |||
Wedgie: <<[28 36 25 -8 -39 -43|| | |||
EDOs: 27, 76, 103, 130 | |||
Badness: 0.0796 | |||
==11-limit== | |||
Commas: 243/242, 441/440, 78408/78125 | |||
POTE generator: ~250/189 = 489.252 | |||
Map: [<1 13 17 13 32|, <0 -28 -36 -25 -70|] | |||
EDOs: 103, 130, 233, 363, 493e, 856be | |||
Badness: 0.0368 | |||
==13-limit== | |||
Commas: 243/242, 351/350, 441/440, 10985/10976 | |||
POTE generator: ~65/49 = 489.256 | |||
Map: [<1 13 17 13 32 9|, <0 -28 -36 -25 -70 -13|] | |||
EDOs: 103, 130, 233, 363 | |||
Badness: 0.0217</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:98:&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:98 --><!-- ws:start:WikiTextTocRule:99: --><a href="#Hemififths">Hemififths</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: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#Semihemi">Semihemi</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- 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="#Hemitert">Hemitert</a><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --> | <a href="#Emmthird">Emmthird</a><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | <a href="#Quinmite">Quinmite</a><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --> | <a href="#Unthirds">Unthirds</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Newt">Newt</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --> | <a href="#Amicable">Amicable</a><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --> | <a href="#Septidiasemi">Septidiasemi</a><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Maviloid">Maviloid</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Subneutral">Subneutral</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Osiris">Osiris</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Gorgik">Gorgik</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <a href="#Fibo">Fibo</a><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --> | <a href="#Mintone">Mintone</a><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --> | <a href="#Catafourth">Catafourth</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><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 /> | ||
| Line 902: | Line 930: | ||
Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]<br /> | Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]<br /> | ||
EDOs: 58, 103, 161<br /> | EDOs: 58, 103, 161<br /> | ||
Badness: 0.0218</body></html></pre></div> | Badness: 0.0218<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Catafourth"></a><!-- ws:end:WikiTextHeadingRule:92 -->Catafourth</h1> | |||
Commas: 2400/2401, 78732/78125<br /> | |||
<br /> | |||
POTE generator: ~250/189 = 489.235<br /> | |||
<br /> | |||
Map: [&lt;1 13 17 13|, &lt;0 -28 -36 -25|]<br /> | |||
Wedgie: &lt;&lt;[28 36 25 -8 -39 -43||<br /> | |||
EDOs: 27, 76, 103, 130<br /> | |||
Badness: 0.0796<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Catafourth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> | |||
Commas: 243/242, 441/440, 78408/78125<br /> | |||
<br /> | |||
POTE generator: ~250/189 = 489.252<br /> | |||
<br /> | |||
Map: [&lt;1 13 17 13 32|, &lt;0 -28 -36 -25 -70|]<br /> | |||
EDOs: 103, 130, 233, 363, 493e, 856be<br /> | |||
Badness: 0.0368<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Catafourth-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2> | |||
Commas: 243/242, 351/350, 441/440, 10985/10976<br /> | |||
<br /> | |||
POTE generator: ~65/49 = 489.256<br /> | |||
<br /> | |||
Map: [&lt;1 13 17 13 32 9|, &lt;0 -28 -36 -25 -70 -13|]<br /> | |||
EDOs: 103, 130, 233, 363<br /> | |||
Badness: 0.0217</body></html></pre></div> | |||