Dicot family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2012-01-02 14:49:38 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 15:03:05 UTC</tt>.<br>

: The original revision id was <tt>~~289104701~~</tt>.<br>

: The original revision id was <tt>289106913</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>

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EDOs: 7, [[14edo|14c]]

===Sidi===

=Sidi=

Commas: 25/24, 245/243

[[POTE tuning|POTE generator]]: 427.208

[[POTE tuning|POTE generator]]: ~9/7 = 427.208

Map: [<1 3 3 6|, <0 -4 -2 -9|]

EDOs: [[14edo|14c]], [[45edo|45c]], <59 93 135 165|

Badness: 0.0566

</pre></div>

==11-limit==

Commas: 25/24, 45/44, 99/98

POTE generator: ~9/7 = 427.273

Map: [<1 3 3 6 7|, <0 -4 -2 -9 -10|]

EDOs: 14c, 17, 45ce, 59bccde

Badness: 0.0330</pre></div>

<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> | <a href="#Septimal dicot">Septimal dicot</a> | <a href="#Sharp">Sharp</a> | <a href="#Decimal">Decimal</a> | <a href="#Dichotic">Dichotic</a> | <a href="#Jamesbond">Jamesbond</a>

<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> | <a href="#Septimal dicot">Septimal dicot</a> | <a href="#Sharp">Sharp</a> | <a href="#Decimal">Decimal</a> | <a href="#Dichotic">Dichotic</a> | <a href="#Jamesbond">Jamesbond</a> | <a href="#Sidi">Sidi</a>

<br />

<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 />

<br />

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EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br />

<br />

<h3 id="toc9"><a name="~~Jamesbond--~~Sidi"></a>Sidi</h3>

<h1 id="toc9"><a name="Sidi"></a>Sidi</h1>

Commas: 25/24, 245/243<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 427.208<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 427.208<br />

<br />

Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]<br />

EDOs: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/45edo">45c</a>, &lt;59 93 135 165|</body></html></pre></div>

EDOs: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/45edo">45c</a>, &lt;59 93 135 165|<br />

Badness: 0.0566<br />

<br />

<h2 id="toc10"><a name="Sidi-11-limit"></a>11-limit</h2>

Commas: 25/24, 45/44, 99/98<br />

<br />

POTE generator: ~9/7 = 427.273<br />

<br />

Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]<br />

EDOs: 14c, 17, 45ce, 59bccde<br />

Badness: 0.0330</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-01-02 14:49:38 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 15:03:05 UTC</tt>.<br>
-: The original revision id was <tt>289104701</tt>.<br>
+: The original revision id was <tt>289106913</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>
@@ Line 90: / Line 90: @@
 EDOs: 7, [[14edo|14c]]
-===Sidi===
+=Sidi=
 Commas: 25/24, 245/243
-[[POTE tuning|POTE generator]]: 427.208
+[[POTE tuning|POTE generator]]: ~9/7 = 427.208
 Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
 EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
+Badness: 0.0566
-</pre></div>
+==11-limit==
+Commas: 25/24, 45/44, 99/98
+POTE generator: ~9/7 = 427.273
+Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]
+EDOs: 14c, 17, 45ce, 59bccde
+Badness: 0.0330</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dicot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Septimal dicot"&gt;Septimal dicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Decimal"&gt;Decimal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dicot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:22:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Septimal dicot"&gt;Septimal dicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Decimal"&gt;Decimal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Sidi"&gt;Sidi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;br /&gt;
 The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; for the dicot family is 25/24, the &lt;a class="wiki_link" href="/chromatic%20semitone"&gt;chromatic semitone&lt;/a&gt;. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |-3 -1 2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 1 -3|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; using the val &amp;lt;24 38 55| and &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; using the val &amp;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.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 184: / Line 192: @@
 EDOs: 7, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Jamesbond--Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Sidi&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Sidi&lt;/h1&gt;
 Commas: 25/24, 245/243&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 427.208&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 427.208&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 3 3 6|, &amp;lt;0 -4 -2 -9|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45c&lt;/a&gt;, &amp;lt;59 93 135 165|&lt;/body&gt;&lt;/html&gt;</pre></div>
+EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45c&lt;/a&gt;, &amp;lt;59 93 135 165|&lt;br /&gt;
+Badness: 0.0566&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Sidi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
+Commas: 25/24, 45/44, 99/98&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~9/7 = 427.273&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 3 3 6 7|, &amp;lt;0 -4 -2 -9 -10|]&lt;br /&gt;
+EDOs: 14c, 17, 45ce, 59bccde&lt;br /&gt;
+Badness: 0.0330&lt;/body&gt;&lt;/html&gt;</pre></div>

Dicot family: Difference between revisions

Wikispaces>genewardsmith