Dicot family: Difference between revisions

Revision as of 17:39, 19 November 2011

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This revision was by author genewardsmith and made on 2011-11-19 17:39:59 UTC.

The original revision id was 277267812.

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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]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]]

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

[[POTE tuning|POTE generator]]: 336.381

Map: [<1 1 2 3|, <0 2 1 3|]
EDOs: [[11edo|11c]], [[14edo|14cd]], [[18edo|18bc]], [[25edo|25bcd]]

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

[[POTE tuning|POTE generator]]: 357.938

Map: [<1 1 2 1|, <0 2 1 6|]
EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]

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

[[POTE tuning|POTE generator]]: 251.557

Map: [<2 0 3 4|, <0 2 1 1|]
EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]

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

[[POTE tuning|POTE generator]]: 86.710

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

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

[[POTE tuning|POTE generator]]: 427.208

Map: [<1 3 3 6|, <0 -4 -2 -9|]
EDOs: [[14edo|14c]], [[45edo|45c]], <59 93 135 165|

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="/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 />
<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: <a class="wiki_link" href="/11edo">11c</a>, <a class="wiki_link" href="/14edo">14cd</a>, <a class="wiki_link" href="/18edo">18bc</a>, <a class="wiki_link" href="/25edo">25bcd</a><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: <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 />
<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="/10edo">10</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/38edo">38cd</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, <a class="wiki_link" href="/14edo">14c</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: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/45edo">45c</a>, &lt;59 93 135 165|</body></html>

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-06-19 16:17:58 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-19 17:39:59 UTC</tt>.<br>
-: The original revision id was <tt>237583799</tt>.<br>
+: The original revision id was <tt>277267812</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 15: / Line 15: @@
 Map: [&lt;1 1 2|, &lt;0 2 1|]
-EDOs: [[7edo|7]], [[17edo|17]], [[24edo|24]], [[31edo|31]]
+EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]]
 ===Septimal dicot===
@@ Line 23: / Line 23: @@
 Map: [&lt;1 1 2 3|, &lt;0 2 1 3|]
-EDOs: 4, 7, [[25edo|25]]
+EDOs: [[11edo|11c]], [[14edo|14cd]], [[18edo|18bc]], [[25edo|25bcd]]
 ===Sharp===
@@ Line 31: / Line 31: @@
 Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]
-EDOs: 7, [[10edo|10]], [[57edo|57]]
+EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]
 ===Decimal===
@@ Line 39: / Line 39: @@
 Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]
-EDOs: [[4edo|4]], 10, [[14edo|14]], 24, [[62edo|62]]
+EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]
 ===Jamesbond===
@@ Line 47: / Line 47: @@
 Map: [&lt;7 11 16 20|, &lt;0 0 0 -1|]
-EDOs: 7, 14, [[595edo|595]], [[609edo|609]]
+EDOs: 7, [[14edo|14c]]
 ===Sidi===
@@ Line 55: / Line 55: @@
 Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
-EDOs: 14, [[59edo|59]]
+EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
 </pre></div>
@@ Line 68: / Line 68: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2|, &amp;lt;0 2 1|]&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;
+EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24c&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31c&lt;/a&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;
@@ Line 76: / Line 76: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 3|, &amp;lt;0 2 1 3|]&lt;br /&gt;
-EDOs: 4, 7, &lt;a class="wiki_link" href="/25edo"&gt;25&lt;/a&gt;&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/11edo"&gt;11c&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14cd&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18bc&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25bcd&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Seven limit children-Sharp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Sharp&lt;/h3&gt;
@@ Line 84: / Line 84: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 1|, &amp;lt;0 2 1 6|]&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;
+EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37cd&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57bcd&lt;/a&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;
@@ Line 92: / Line 92: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 0 3 4|, &amp;lt;0 2 1 1|]&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;
+EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24c&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38cd&lt;/a&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;
@@ Line 100: / Line 100: @@
 &lt;br /&gt;
 Map: [&amp;lt;7 11 16 20|, &amp;lt;0 0 0 -1|]&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;
+EDOs: 7, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&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;
@@ Line 108: / Line 108: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 3 3 6|, &amp;lt;0 -4 -2 -9|]&lt;br /&gt;
-EDOs: 14, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&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;/body&gt;&lt;/html&gt;</pre></div>

Dicot family: Difference between revisions

Revision as of 17:39, 19 November 2011

IMPORTED REVISION FROM WIKISPACES

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