Dicot family: Difference between revisions

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>2012-03-~~10 20~~:11:12 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-12 19:26:03 UTC</tt>.<br>

: The original revision id was <tt>~~309709578~~</tt>.<br>

: The original revision id was <tt>320008890</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>

<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]]

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.

==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, 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

Line 23:

Line 22:

Badness: 0.0130

==7-limit==

[[Comma]]s: 15/14, 25/24

Line 33:

Line 32:

Badness: 0.0199

==11-limit==

Commas: 15/14, 22/21, 25/24

Line 42:

Line 41:

Badness: 0.0199

==Eudicot==

Commas: 15/14, 25/24, 33/32

Line 50:

Line 49:

EDOs: 4, 7, 18bc, 25bcd

=Flat=

Commas: 21/20, 25/24

Line 60:

Line 59:

Badness: 0.0254

=Sharp=

Commas: 25/24, 28/27

Line 68:

Line 67:

EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]

==11-limit==

Commas: 25/24, 28/27, 35/33

Line 77:

Line 76:

Badness: 0.0224

=Decimal=

Commas: 25/24, 49/48

Line 87:

Line 86:

Badness: 0.0283

==11-limit==

Commas: 25/24, 45/44, 49/48

Line 96:

Line 95:

Badness: 0.0267

==Decimated==

Commas: 25/24, 33/32, 49/48

Line 105:

Line 104:

Badness: 0.0315

==Decibel==

Commas: 25/24, 35/33, 49/48

Line 114:

Line 113:

Badness: 0.0324

=Dichotic=

Commas: 25/24, 64/63

Line 124:

Line 123:

Badness: 0.0376

==11-limit==

Commas: 25/24, 45/44, 64/63

Line 133:

Line 132:

Badness: 0.0307

=Jamesbond=

Commas: 25/24, 81/80

Line 141:

Line 140:

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

=Sidi=

Commas: 25/24, 245/243

Line 150:

Line 149:

Badness: 0.0566

==11-limit==

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

Line 159:

Line 158:

Badness: 0.0330

=Quad=

Commas: 9/8, 25/24

Line 170:

Line 169:

<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="#Dicot">Dicot</a> | <a href="#Flat">Flat</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> | <a href="#Quad">Quad</a>

~~<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 />

<br />

<h2 id="toc0"><a name="x-Seven limit children"></a>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, 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 />

<h1 id="toc1"><a name="Dicot"></a>Dicot</h1>

Comma: 25/24<br />

<br />

POTE generator: ~5/4 = 348.594<br />

Line 187:

Line 185:

<br />

<h2 id="toc2"><a name="Dicot-7-limit"></a>7-limit</h2>

<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>: ~5/4 = 336.381<br />

Line 197:

Line 195:

<br />

<h2 id="toc3"><a name="Dicot-11-limit"></a>11-limit</h2>

Commas: 15/14, 22/21, 25/24<br />

<br />

POTE generator: ~5/4 = 342.125<br />

Line 206:

Line 204:

<br />

<h2 id="toc4"><a name="Dicot-Eudicot"></a>Eudicot</h2>

Commas: 15/14, 25/24, 33/32<br />

<br />

POTE generator: ~5/4 = 336.051<br />

Line 214:

Line 212:

<br />

<h1 id="toc5"><a name="Flat"></a>Flat</h1>

Commas: 21/20, 25/24<br />

<br />

POTE generator: ~5/4 = 331.916<br />

Line 224:

Line 222:

<br />

<h1 id="toc6"><a name="Sharp"></a>Sharp</h1>

Commas: 25/24, 28/27<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 357.938<br />

Line 232:

Line 230:

<br />

<h2 id="toc7"><a name="Sharp-11-limit"></a>11-limit</h2>

Commas: 25/24, 28/27, 35/33<br />

<br />

POTE generator: ~5/4 = 356.106<br />

Line 241:

Line 239:

<br />

<h1 id="toc8"><a name="Decimal"></a>Decimal</h1>

Commas: 25/24, 49/48<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 251.557<br />

Line 251:

Line 249:

<br />

<h2 id="toc9"><a name="Decimal-11-limit"></a>11-limit</h2>

Commas: 25/24, 45/44, 49/48<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 253.493<br />

Line 260:

Line 258:

<br />

<h2 id="toc10"><a name="Decimal-Decimated"></a>Decimated</h2>

Commas: 25/24, 33/32, 49/48<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 255.066<br />

Line 269:

Line 267:

<br />

<h2 id="toc11"><a name="Decimal-Decibel"></a>Decibel</h2>

Commas: 25/24, 35/33, 49/48<br />

<br />

POTE generator: ~8/7 = 243.493<br />

Line 278:

Line 276:

<br />

<h1 id="toc12"><a name="Dichotic"></a>Dichotic</h1>

Commas: 25/24, 64/63<br />

<br />

POTE generator: ~5/4 = 356.264<br />

Line 288:

Line 286:

<br />

<h2 id="toc13"><a name="Dichotic-11-limit"></a>11-limit</h2>

Commas: 25/24, 45/44, 64/63<br />

<br />

POTE generator: ~5/4 = 354.262<br />

Line 297:

Line 295:

<br />

<h1 id="toc14"><a name="Jamesbond"></a>Jamesbond</h1>

Commas: 25/24, 81/80<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 86.710<br />

Line 305:

Line 303:

<br />

<h1 id="toc15"><a name="Sidi"></a>Sidi</h1>

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

<br />

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

Line 314:

Line 312:

<br />

<h2 id="toc16"><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 />

Line 323:

Line 321:

<br />

<h1 id="toc17"><a name="Quad"></a>Quad</h1>

Commas: 9/8, 25/24<br />

<br />

POTE generator: ~5/4 = 324.482<br />

@@ 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>2012-03-10 20:11:12 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-12 19:26:03 UTC</tt>.<br>
-: The original revision id was <tt>309709578</tt>.<br>
+: The original revision id was <tt>320008890</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>
 <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]]
+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.
-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, 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.
 =Dicot=
 Comma: 25/24
@@ Line 23: / Line 22: @@
 Badness: 0.0130
 ==7-limit==
 [[Comma]]s: 15/14, 25/24
@@ Line 33: / Line 32: @@
 Badness: 0.0199
 ==11-limit==
 Commas: 15/14, 22/21, 25/24
@@ Line 42: / Line 41: @@
 Badness: 0.0199
 ==Eudicot==
 Commas: 15/14, 25/24, 33/32
@@ Line 50: / Line 49: @@
 EDOs: 4, 7, 18bc, 25bcd
 =Flat=
 Commas: 21/20, 25/24
@@ Line 60: / Line 59: @@
 Badness: 0.0254
 =Sharp=
 Commas: 25/24, 28/27
@@ Line 68: / Line 67: @@
 EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]
 ==11-limit==
 Commas: 25/24, 28/27, 35/33
@@ Line 77: / Line 76: @@
 Badness: 0.0224
 =Decimal=
 Commas: 25/24, 49/48
@@ Line 87: / Line 86: @@
 Badness: 0.0283
 ==11-limit==
 Commas: 25/24, 45/44, 49/48
@@ Line 96: / Line 95: @@
 Badness: 0.0267
 ==Decimated==
 Commas: 25/24, 33/32, 49/48
@@ Line 105: / Line 104: @@
 Badness: 0.0315
 ==Decibel==
 Commas: 25/24, 35/33, 49/48
@@ Line 114: / Line 113: @@
 Badness: 0.0324
 =Dichotic=
 Commas: 25/24, 64/63
@@ Line 124: / Line 123: @@
 Badness: 0.0376
 ==11-limit==
 Commas: 25/24, 45/44, 64/63
@@ Line 133: / Line 132: @@
 Badness: 0.0307
 =Jamesbond=
 Commas: 25/24, 81/80
@@ Line 141: / Line 140: @@
 EDOs: 7, [[14edo|14c]]
 =Sidi=
 Commas: 25/24, 245/243
@@ Line 150: / Line 149: @@
 Badness: 0.0566
 ==11-limit==
 Commas: 25/24, 45/44, 99/98
@@ Line 159: / Line 158: @@
 Badness: 0.0330
 =Quad=
 Commas: 9/8, 25/24
@@ Line 170: / Line 169: @@
 <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:36:&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:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Dicot"&gt;Dicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Flat"&gt;Flat&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt; | &lt;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Decimal"&gt;Decimal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Sidi"&gt;Sidi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Quad"&gt;Quad&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:55 --&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;
-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;!-- 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 &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, and dichotic with wedgie &amp;lt;&amp;lt;2 1 -4 -3 -12 -12|| ads 64/63, all 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, and dichotic with wedgie &amp;lt;&amp;lt;2 1 -4 -3 -12 -12|| ads 64/63, all 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;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Dicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Dicot&lt;/h1&gt;
-Comma: 25/24&lt;br /&gt;
+ Comma: 25/24&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 348.594&lt;br /&gt;
@@ Line 187: / Line 185: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Dicot-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 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;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 336.381&lt;br /&gt;
@@ Line 197: / Line 195: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Dicot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h2&gt;
-Commas: 15/14, 22/21, 25/24&lt;br /&gt;
+ Commas: 15/14, 22/21, 25/24&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 342.125&lt;br /&gt;
@@ Line 206: / Line 204: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Dicot-Eudicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Eudicot&lt;/h2&gt;
-Commas: 15/14, 25/24, 33/32&lt;br /&gt;
+ Commas: 15/14, 25/24, 33/32&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 336.051&lt;br /&gt;
@@ Line 214: / Line 212: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Flat"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Flat&lt;/h1&gt;
-Commas: 21/20, 25/24&lt;br /&gt;
+ Commas: 21/20, 25/24&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 331.916&lt;br /&gt;
@@ Line 224: / Line 222: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Sharp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sharp&lt;/h1&gt;
-Commas: 25/24, 28/27&lt;br /&gt;
+ Commas: 25/24, 28/27&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 357.938&lt;br /&gt;
@@ Line 232: / Line 230: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Sharp-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
-Commas: 25/24, 28/27, 35/33&lt;br /&gt;
+ Commas: 25/24, 28/27, 35/33&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 356.106&lt;br /&gt;
@@ Line 241: / Line 239: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Decimal&lt;/h1&gt;
-Commas: 25/24, 49/48&lt;br /&gt;
+ Commas: 25/24, 49/48&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 251.557&lt;br /&gt;
@@ Line 251: / Line 249: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Decimal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
-Commas: 25/24, 45/44, 49/48&lt;br /&gt;
+ Commas: 25/24, 45/44, 49/48&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 253.493&lt;br /&gt;
@@ Line 260: / Line 258: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Decimal-Decimated"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Decimated&lt;/h2&gt;
-Commas: 25/24, 33/32, 49/48&lt;br /&gt;
+ Commas: 25/24, 33/32, 49/48&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 255.066&lt;br /&gt;
@@ Line 269: / Line 267: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Decimal-Decibel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Decibel&lt;/h2&gt;
-Commas: 25/24, 35/33, 49/48&lt;br /&gt;
+ Commas: 25/24, 35/33, 49/48&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~8/7 = 243.493&lt;br /&gt;
@@ Line 278: / Line 276: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Dichotic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Dichotic&lt;/h1&gt;
-Commas: 25/24, 64/63&lt;br /&gt;
+ Commas: 25/24, 64/63&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 356.264&lt;br /&gt;
@@ Line 288: / Line 286: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Dichotic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
-Commas: 25/24, 45/44, 64/63&lt;br /&gt;
+ Commas: 25/24, 45/44, 64/63&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 354.262&lt;br /&gt;
@@ Line 297: / Line 295: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Jamesbond&lt;/h1&gt;
-Commas: 25/24, 81/80&lt;br /&gt;
+ Commas: 25/24, 81/80&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 86.710&lt;br /&gt;
@@ Line 305: / Line 303: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Sidi&lt;/h1&gt;
-Commas: 25/24, 245/243&lt;br /&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;: ~9/7 = 427.208&lt;br /&gt;
@@ Line 314: / Line 312: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Sidi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
-Commas: 25/24, 45/44, 99/98&lt;br /&gt;
+ Commas: 25/24, 45/44, 99/98&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~9/7 = 427.273&lt;br /&gt;
@@ Line 323: / Line 321: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Quad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Quad&lt;/h1&gt;
-Commas: 9/8, 25/24&lt;br /&gt;
+ Commas: 9/8, 25/24&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 324.482&lt;br /&gt;