Dicot family: Difference between revisions

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**Imported revision 190199590 - Original comment: **
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**Imported revision 237583745 - 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>2010-12-29 11:17:12 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-19 16:17:26 UTC</tt>.<br>
: The original revision id was <tt>190199590</tt>.<br>
: The original revision id was <tt>237583745</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">The 5-limit parent comma for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is |-3 -1 2&gt;, and flipping that yields &lt;&lt;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 &lt;24 38 55| and [[31edo]] 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.
<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">The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is |-3 -1 2&gt;, and flipping that yields &lt;&lt;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 &lt;24 38 55| and [[31edo]] 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.




==Seven limit children==
==Seven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit 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, both 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.
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] 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, both 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.


[[POTE tuning|POTE generator]]: 348.594
[[POTE tuning|POTE generator]]: 348.594


Map: [&lt;1 1 2|, &lt;0 2 1|]
Map: [&lt;1 1 2|, &lt;0 2 1|]
EDOs: 7, 17, 24, 31
EDOs: [[7edo|7]], [[17edo|17]], [[24edo|24]], [[31edo|31]]


===Septimal dicot===
===Septimal dicot===
Commas: 15/14, 25/24
[[Comma]]s: 15/14, 25/24


[[POTE tuning|POTE generator]]: 336.381
[[POTE tuning|POTE generator]]: 336.381
Line 31: Line 31:


Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]
Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]
EDOs: 7, 10, 57
EDOs: 7, [[10edo|10]], [[57edo|57]]


===Decimal===
===Decimal===
Line 39: Line 39:


Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]
Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]
EDOs: 4, 10, 14, 24, 62
EDOs: [[4edo|4]], 10, [[14edo|14]], 24, [[62edo|62]]


===Jamesbond===
===Jamesbond===
Line 47: Line 47:


Map: [&lt;7 11 16 20|, &lt;0 0 0 -1|]
Map: [&lt;7 11 16 20|, &lt;0 0 0 -1|]
EDOs: 7, 14, 595, 609
EDOs: 7, 14, [[595edo|595]], [[609edo|609]]


===Sidi===
===Sidi===
Line 55: Line 55:


Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
EDOs: 14, 59
EDOs: 14, [[59edo|59]]
 
 
 


</pre></div>
</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dicot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma 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;
<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;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;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. Septimal dicot, with wedgie &amp;lt;&amp;lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &amp;lt;&amp;lt;2 1 6 -3 4 11|| adds 28/27, both retaining the same period and generator. Decimal with wedgie &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &amp;lt;&amp;lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &amp;lt;&amp;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.&lt;br /&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. Septimal dicot, with wedgie &amp;lt;&amp;lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &amp;lt;&amp;lt;2 1 6 -3 4 11|| adds 28/27, both retaining the same period and generator. Decimal with wedgie &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &amp;lt;&amp;lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &amp;lt;&amp;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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 348.594&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 348.594&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 1|]&lt;br /&gt;
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 1|]&lt;br /&gt;
EDOs: 7, 17, 24, 31&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Septimal dicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal dicot&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Septimal dicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal dicot&lt;/h3&gt;
Commas: 15/14, 25/24&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15/14, 25/24&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 336.381&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 336.381&lt;br /&gt;
Line 87: Line 84:
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 1|, &amp;lt;0 2 1 6|]&lt;br /&gt;
Map: [&amp;lt;1 1 2 1|, &amp;lt;0 2 1 6|]&lt;br /&gt;
EDOs: 7, 10, 57&lt;br /&gt;
EDOs: 7, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Seven limit children-Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Decimal&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Seven limit children-Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Decimal&lt;/h3&gt;
Line 95: Line 92:
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 3 4|, &amp;lt;0 2 1 1|]&lt;br /&gt;
Map: [&amp;lt;2 0 3 4|, &amp;lt;0 2 1 1|]&lt;br /&gt;
EDOs: 4, 10, 14, 24, 62&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, 10, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, 24, &lt;a class="wiki_link" href="/62edo"&gt;62&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Seven limit children-Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Jamesbond&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Seven limit children-Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Jamesbond&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 11 16 20|, &amp;lt;0 0 0 -1|]&lt;br /&gt;
Map: [&amp;lt;7 11 16 20|, &amp;lt;0 0 0 -1|]&lt;br /&gt;
EDOs: 7, 14, 595, 609&lt;br /&gt;
EDOs: 7, 14, &lt;a class="wiki_link" href="/595edo"&gt;595&lt;/a&gt;, &lt;a class="wiki_link" href="/609edo"&gt;609&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Seven limit children-Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Sidi&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Seven limit children-Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Sidi&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 3 6|, &amp;lt;0 -4 -2 -9|]&lt;br /&gt;
Map: [&amp;lt;1 3 3 6|, &amp;lt;0 -4 -2 -9|]&lt;br /&gt;
EDOs: 14, 59&lt;/body&gt;&lt;/html&gt;</pre></div>
EDOs: 14, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 16:17, 19 June 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenwolf and made on 2011-06-19 16:17:26 UTC.
The original revision id was 237583745.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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.


==Seven limit children==
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, both 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.

[[POTE tuning|POTE generator]]: 348.594

Map: [<1 1 2|, <0 2 1|]
EDOs: [[7edo|7]], [[17edo|17]], [[24edo|24]], [[31edo|31]]

===Septimal dicot===
[[Comma]]s: 15/14, 25/24

[[POTE tuning|POTE generator]]: 336.381

Map: [<1 1 2 3|, <0 2 1 3|]
EDOs: 4, 7, 25

===Sharp===
Commas: 25/24, 28/27

[[POTE tuning|POTE generator]]: 357.938

Map: [<1 1 2 1|, <0 2 1 6|]
EDOs: 7, [[10edo|10]], [[57edo|57]]

===Decimal===
Commas: 25/24, 49/48

[[POTE tuning|POTE generator]]: 251.557

Map: [<2 0 3 4|, <0 2 1 1|]
EDOs: [[4edo|4]], 10, [[14edo|14]], 24, [[62edo|62]]

===Jamesbond===
Commas: 25/24, 81/80

[[POTE tuning|POTE generator]]: 86.710

Map: [<7 11 16 20|, <0 0 0 -1|]
EDOs: 7, 14, [[595edo|595]], [[609edo|609]]

===Sidi===
Commas: 25/24, 245/243

[[POTE tuning|POTE generator]]: 427.208

Map: [<1 3 3 6|, <0 -4 -2 -9|]
EDOs: 14, [[59edo|59]]

Original HTML content:

<html><head><title>Dicot family</title></head><body>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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
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, both 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 />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 348.594<br />
<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="/17edo">17</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/31edo">31</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Septimal dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal dicot</h3>
<a class="wiki_link" href="/Comma">Comma</a>s: 15/14, 25/24<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 336.381<br />
<br />
Map: [&lt;1 1 2 3|, &lt;0 2 1 3|]<br />
EDOs: 4, 7, 25<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Sharp"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sharp</h3>
Commas: 25/24, 28/27<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 357.938<br />
<br />
Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]<br />
EDOs: 7, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/57edo">57</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Decimal"></a><!-- ws:end:WikiTextHeadingRule:6 -->Decimal</h3>
Commas: 25/24, 49/48<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 251.557<br />
<br />
Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]<br />
EDOs: <a class="wiki_link" href="/4edo">4</a>, 10, <a class="wiki_link" href="/14edo">14</a>, 24, <a class="wiki_link" href="/62edo">62</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Seven limit children-Jamesbond"></a><!-- ws:end:WikiTextHeadingRule:8 -->Jamesbond</h3>
Commas: 25/24, 81/80<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 86.710<br />
<br />
Map: [&lt;7 11 16 20|, &lt;0 0 0 -1|]<br />
EDOs: 7, 14, <a class="wiki_link" href="/595edo">595</a>, <a class="wiki_link" href="/609edo">609</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Seven limit children-Sidi"></a><!-- ws:end:WikiTextHeadingRule:10 -->Sidi</h3>
Commas: 25/24, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 427.208<br />
<br />
Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]<br />
EDOs: 14, <a class="wiki_link" href="/59edo">59</a></body></html>