Dicot family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 289404311 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289404847 - 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>2012-01-03 21: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-03 21:09:19 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289404847</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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The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie <<2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie <<2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie <<2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie <<4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie <<4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie <<0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator. | The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie <<2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie <<2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie <<2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie <<4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie <<4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie <<0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator. | ||
=Dicot= | |||
Comma: 25/24 | |||
POTE generator: ~5/4 = 348.594 | |||
Map: [<1 1 2|, <0 2 1|] | Map: [<1 1 2|, <0 2 1|] | ||
EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]] | EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]] | ||
Badness: 0.0130 | |||
=7-limit | ==7-limit== | ||
[[Comma]]s: 15/14, 25/24 | [[Comma]]s: 15/14, 25/24 | ||
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Badness: 0.0330</pre></div> | Badness: 0.0330</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: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: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Dicot">Dicot</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Decimal">Decimal</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="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Sidi">Sidi</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><br /> | ||
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 /> | 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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The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. Septimal dicot, with wedgie &lt;&lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &lt;&lt;2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie &lt;&lt;2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie &lt;&lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &lt;&lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &lt;&lt;0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. Septimal dicot, with wedgie &lt;&lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &lt;&lt;2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie &lt;&lt;2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie &lt;&lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &lt;&lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &lt;&lt;0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.<br /> | ||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Dicot</h1> | ||
Comma: 25/24<br /> | |||
<br /> | |||
POTE generator: ~5/4 = 348.594<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 2|, &lt;0 2 1|]<br /> | Map: [&lt;1 1 2|, &lt;0 2 1|]<br /> | ||
EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/31edo">31c</a><br /> | EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/31edo">31c</a><br /> | ||
Badness: 0.0130<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Dicot-7-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->7-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15/14, 25/24<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 15/14, 25/24<br /> | ||
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Badness: 0.0199<br /> | Badness: 0.0199<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Dicot-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
Commas: 15/14, 22/21, 25/24<br /> | Commas: 15/14, 22/21, 25/24<br /> | ||
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Badness: 0.0199<br /> | Badness: 0.0199<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Sharp"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sharp</h1> | ||
Commas: 25/24, 28/27<br /> | Commas: 25/24, 28/27<br /> | ||
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EDOs: <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/37edo">37cd</a>, <a class="wiki_link" href="/57edo">57bcd</a><br /> | EDOs: <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/37edo">37cd</a>, <a class="wiki_link" href="/57edo">57bcd</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Decimal"></a><!-- ws:end:WikiTextHeadingRule:10 -->Decimal</h1> | ||
Commas: 25/24, 49/48<br /> | Commas: 25/24, 49/48<br /> | ||
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Badness: 0.0283<br /> | Badness: 0.0283<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Decimal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | ||
Commas: 25/24, 45/44, 49/48<br /> | Commas: 25/24, 45/44, 49/48<br /> | ||
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Badness: 0.0267<br /> | Badness: 0.0267<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Decimal-Decimated"></a><!-- ws:end:WikiTextHeadingRule:14 -->Decimated</h2> | ||
Commas: 25/24, 33/32, 49/48<br /> | Commas: 25/24, 33/32, 49/48<br /> | ||
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Badness: 0.0315<br /> | Badness: 0.0315<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Dichotic"></a><!-- ws:end:WikiTextHeadingRule:16 -->Dichotic</h1> | ||
Commas: 25/24, 64/63<br /> | Commas: 25/24, 64/63<br /> | ||
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Badness: 0.0376<br /> | Badness: 0.0376<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Dichotic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> | ||
Commas: 25/24, 45/44, 64/63<br /> | Commas: 25/24, 45/44, 64/63<br /> | ||
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Badness: 0.0307<br /> | Badness: 0.0307<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Jamesbond"></a><!-- ws:end:WikiTextHeadingRule:20 -->Jamesbond</h1> | ||
Commas: 25/24, 81/80<br /> | Commas: 25/24, 81/80<br /> | ||
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EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br /> | EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Sidi"></a><!-- ws:end:WikiTextHeadingRule:22 -->Sidi</h1> | ||
Commas: 25/24, 245/243<br /> | Commas: 25/24, 245/243<br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Sidi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
Commas: 25/24, 45/44, 99/98<br /> | Commas: 25/24, 45/44, 99/98<br /> | ||
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