Dicot family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 323644050 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 323717118 - 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>2012-04-21 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-21 17:25:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>323717118</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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Commas: 25/24, 81/80 | Commas: 25/24, 81/80 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: ~8/7 = 258.139 | ||
Map: [<7 11 16 | Map: [<7 11 16 0|, <0 0 0 1|] | ||
EDOs: 7, [[14edo|14c]] | EDOs: 7, [[14edo|14c]] | ||
==11-limit== | ==11-limit== | ||
11-limit jamesbond is | 11-limit jamesbond is called "septimal" on the Regular Temperament Finder. | ||
Commas: 25/24, 33/32, 45/44 | Commas: 25/24, 33/32, 45/44 | ||
POTE generator: ~8/7 = 258.910 | |||
Map: [<7 11 16 0 24|, <0 0 0 1 0|] | Map: [<7 11 16 0 24|, <0 0 0 1 0|] | ||
EDOs: 7, 14c | EDOs: 7, 14c | ||
Badness: 0.0235 | Badness: 0.0235 | ||
==13-limit== | |||
Commas: 25/24 27/26 33/32 45/44 | |||
POTE generator: ~8/7 = 250.764 | |||
Map: [<7 11 16 0 24 26|, <0 0 0 1 0 0|] | |||
EDOs: 7, 14c | |||
Badness: 0.0230 | |||
=Sidi= | =Sidi= | ||
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Badness: 0.0460</pre></div> | Badness: 0.0460</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>Dicot family</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>Dicot family</title></head><body><!-- ws:start:WikiTextTocRule:40:&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:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Dicot">Dicot</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Flat">Flat</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Decimal">Decimal</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- 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="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Sidi">Sidi</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Quad">Quad</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:61 -->The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/comma">comma</a> for the dicot family is 25/24, the <a class="wiki_link" href="/chromatic%20semitone">chromatic semitone</a>. Its <a class="wiki_link" href="/monzo">monzo</a> is |-3 -1 2&gt;, and flipping that yields &lt;&lt;2 1 -3|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are <a class="wiki_link" href="/7edo">7edo</a>, <a class="wiki_link" href="/24edo">24edo</a> using the val &lt;24 38 55| and <a class="wiki_link" href="/31edo">31edo</a> using the val &lt;31 49 71|. In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all.<br /> | ||
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Commas: 25/24, 81/80<br /> | Commas: 25/24, 81/80<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 258.139<br /> | ||
<br /> | <br /> | ||
Map: [&lt;7 11 16 | Map: [&lt;7 11 16 0|, &lt;0 0 0 1|]<br /> | ||
EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br /> | EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Jamesbond-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Jamesbond-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
11-limit jamesbond is | 11-limit jamesbond is called &quot;septimal&quot; on the Regular Temperament Finder.<br /> | ||
<br /> | <br /> | ||
Commas: 25/24, 33/32, 45/44<br /> | Commas: 25/24, 33/32, 45/44<br /> | ||
<br /> | |||
POTE generator: ~8/7 = 258.910<br /> | |||
<br /> | <br /> | ||
Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]<br /> | Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]<br /> | ||
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Badness: 0.0235<br /> | Badness: 0.0235<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Jamesbond-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 25/24 27/26 33/32 45/44<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 250.764<br /> | |||
<br /> | |||
Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|]<br /> | |||
EDOs: 7, 14c<br /> | |||
Badness: 0.0230<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Sidi"></a><!-- ws:end:WikiTextHeadingRule:34 -->Sidi</h1> | |||
Commas: 25/24, 245/243<br /> | Commas: 25/24, 245/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Sidi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 25/24, 45/44, 99/98<br /> | Commas: 25/24, 45/44, 99/98<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0330<br /> | Badness: 0.0330<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Quad"></a><!-- ws:end:WikiTextHeadingRule:38 -->Quad</h1> | ||
Commas: 9/8, 25/24<br /> | Commas: 9/8, 25/24<br /> | ||
<br /> | <br /> | ||