Dicot family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 387563378 - Original comment: ** |
Wikispaces>PiotrGrochowski **Imported revision 595544890 - 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: | : This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-10-16 12:11:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>595544890</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is |-3 -1 2>, and flipping that yields <<2 1 -3|| for the [[wedgie]]. 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 [[7edo]], [[24edo]] using the val <24 38 55| and [[31edo]] using the val <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. | The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is |-3 -1 2>, and flipping that yields <<2 1 -3|| for the [[wedgie]]. 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 [[7edo]], [[24edo]] using the val <24 38 55| and [[31edo]] using the val <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. | ||
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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]] | 3 4 6 7 10 13 17 20 | ||
EDOs: [[3edo|3]], [[4edo|4]], [[6edo|6]], [[7edo|7]], [[10edo|10]], [[13edo|13]], [[14edo|14c]], [[17edo|17]], [[20edo|20]], [[24edo|24c]], [[31edo|31c]] | |||
Badness: 0.0130 | Badness: 0.0130 | ||
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Badness: 0.0307 | Badness: 0.0307 | ||
==Dichosis== | ==Dichosis== | ||
Commas: 25/24, 35/33, 64/63 | Commas: 25/24, 35/33, 64/63 | ||
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EDOs: 7, [[14edo|14c]] | EDOs: 7, [[14edo|14c]] | ||
==11-limit== | ==11-limit== | ||
11-limit jamesbond is called "septimal" on the Regular Temperament Finder. | 11-limit jamesbond is called "septimal" on the Regular Temperament Finder. | ||
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Badness: 0.0235 | Badness: 0.0235 | ||
==13-limit== | ==13-limit== | ||
Commas: 25/24 27/26 33/32 45/44 | Commas: 25/24 27/26 33/32 45/44 | ||
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Badness: 0.0230 | Badness: 0.0230 | ||
==Septimal== | ==Septimal== | ||
Commas: 25/24, 33/32, 45/44, 65/63 | Commas: 25/24, 33/32, 45/44, 65/63 | ||
POTE generator: ~8/7 = 247.447 | POTE generator: ~8/7 = 247.447 | ||
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<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:44:&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:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Dicot">Dicot</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- 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="#Flat">Flat</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Decimal">Decimal</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: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Sidi">Sidi</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Quad">Quad</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <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:44:&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:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Dicot">Dicot</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- 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="#Flat">Flat</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Decimal">Decimal</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: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Sidi">Sidi</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Quad">Quad</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | ||
<!-- ws:end:WikiTextTocRule:67 --> | <!-- ws:end:WikiTextTocRule:67 -->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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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 /> | 3 4 6 7 10 13 17 20<br /> | ||
EDOs: <a class="wiki_link" href="/3edo">3</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/13edo">13</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/20edo">20</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/31edo">31c</a><br /> | |||
Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Dichotic-Dichosis"></a><!-- ws:end:WikiTextHeadingRule:28 -->Dichosis</h2> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Dichotic-Dichosis"></a><!-- ws:end:WikiTextHeadingRule:28 -->Dichosis</h2> | ||
Commas: 25/24, 35/33, 64/63<br /> | Commas: 25/24, 35/33, 64/63<br /> | ||
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POTE generator: ~5/4 = 360.659<br /> | POTE generator: ~5/4 = 360.659<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Jamesbond-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Jamesbond-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
11-limit jamesbond is called &quot;septimal&quot; on the Regular Temperament Finder.<br /> | 11-limit jamesbond is called &quot;septimal&quot; on the Regular Temperament Finder.<br /> | ||
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Commas: 25/24, 33/32, 45/44<br /> | Commas: 25/24, 33/32, 45/44<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Jamesbond-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Jamesbond-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 25/24 27/26 33/32 45/44<br /> | Commas: 25/24 27/26 33/32 45/44<br /> | ||
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POTE generator: ~8/7 = 250.764<br /> | POTE generator: ~8/7 = 250.764<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Jamesbond-Septimal"></a><!-- ws:end:WikiTextHeadingRule:36 -->Septimal</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Jamesbond-Septimal"></a><!-- ws:end:WikiTextHeadingRule:36 -->Septimal</h2> | ||
Commas: 25/24, 33/32, 45/44, 65/63 <br /> | Commas: 25/24, 33/32, 45/44, 65/63<br /> | ||
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POTE generator: ~8/7 = 247.447<br /> | POTE generator: ~8/7 = 247.447<br /> | ||