Dicot family: Difference between revisions

Revision as of 21:09, 3 January 2012

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2012-01-03 21:09:19 UTC.

The original revision id was 289404847.

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:

[[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.


==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

POTE generator: ~5/4 = 348.594

Map: [<1 1 2|, <0 2 1|]
EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]]
Badness: 0.0130

==7-limit==
[[Comma]]s: 15/14, 25/24

[[POTE tuning|POTE generator]]: ~5/4 = 336.381

Map: [<1 1 2 3|, <0 2 1 3|]
Wedgie: <<2 1 3 -3 -1 4||
EDOs: 4, 7, [[11edo|11c]], [[14edo|14cd]], [[18edo|18bc]], [[25edo|25bcd]]
Badness: 0.0199

==11-limit==
Commas: 15/14, 22/21, 25/24

POTE generator: ~5/4 = 342.125

Map: [<1 1 2 2 2|, <0 2 1 3 5|]
EDOs: 4e, 7
Badness: 0.0199

=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]]: ~7/6 = 251.557

Map: [<2 0 3 4|, <0 2 1 1|]
Wedgie: <<4 2 2 -6 -8 -1||
EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]
Badness: 0.0283

==11-limit==
Commas: 25/24, 45/44, 49/48

[[POTE tuning|POTE generator]]: ~7/6 = 253.493

Map: [<2 0 3 4 -1|, <0 2 1 1 5|]
EDOs: 10, 14c, 24c, 38cd
Badness: 0.0267

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

[[POTE tuning|POTE generator]]: ~7/6 = 255.066

Map: [<2 0 3 4 10|, <0 2 1 1 -2|]
EDOs: 4, 10e, 14c
Badness: 0.0315

=Dichotic=
Commas: 25/24, 64/63

POTE generator: ~5/4 = 356.264

Map: [<1 1 2 4|, <0 2 1 -4|]
Wedgie: <<2 1 -4 -3 -12 -12||
EDOs: 7, 10, 17, 27c, 37c
Badness: 0.0376

==11-limit==
Commas: 25/24, 45/44, 64/63

POTE generator: ~5/4 = 354.262

Map: [<1 1 2 4 2|, <0 2 1 -4 5|]
EDOs: 7, 10, 17, 27ce, 44ce
Badness: 0.0307

=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]]: ~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

==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

Original HTML content:

<html><head><title>Dicot family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Dicot">Dicot</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Decimal">Decimal</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Sidi">Sidi</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: -->
<!-- ws:end:WikiTextTocRule:40 --><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 />
<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, 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 />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Dicot</h1>
Comma: 25/24<br />
<br />
POTE generator: ~5/4 = 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 />
Badness: 0.0130<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Dicot-7-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->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 />
<br />
Map: [&lt;1 1 2 3|, &lt;0 2 1 3|]<br />
Wedgie: &lt;&lt;2 1 3 -3 -1 4||<br />
EDOs: 4, 7, <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 />
Badness: 0.0199<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Dicot-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2>
Commas: 15/14, 22/21, 25/24<br />
<br />
POTE generator: ~5/4 = 342.125<br />
<br />
Map: [&lt;1 1 2 2 2|, &lt;0 2 1 3 5|]<br />
EDOs: 4e, 7<br />
Badness: 0.0199<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Sharp"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sharp</h1>
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:10:&lt;h1&gt; --><h1 id="toc5"><a name="Decimal"></a><!-- ws:end:WikiTextHeadingRule:10 -->Decimal</h1>
Commas: 25/24, 49/48<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 251.557<br />
<br />
Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]<br />
Wedgie: &lt;&lt;4 2 2 -6 -8 -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 />
Badness: 0.0283<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Decimal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->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 />
<br />
Map: [&lt;2 0 3 4 -1|, &lt;0 2 1 1 5|]<br />
EDOs: 10, 14c, 24c, 38cd<br />
Badness: 0.0267<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Decimal-Decimated"></a><!-- ws:end:WikiTextHeadingRule:14 -->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 />
<br />
Map: [&lt;2 0 3 4 10|, &lt;0 2 1 1 -2|]<br />
EDOs: 4, 10e, 14c<br />
Badness: 0.0315<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Dichotic"></a><!-- ws:end:WikiTextHeadingRule:16 -->Dichotic</h1>
Commas: 25/24, 64/63<br />
<br />
POTE generator: ~5/4 = 356.264<br />
<br />
Map: [&lt;1 1 2 4|, &lt;0 2 1 -4|]<br />
Wedgie: &lt;&lt;2 1 -4 -3 -12 -12||<br />
EDOs: 7, 10, 17, 27c, 37c<br />
Badness: 0.0376<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Dichotic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2>
Commas: 25/24, 45/44, 64/63<br />
<br />
POTE generator: ~5/4 = 354.262<br />
<br />
Map: [&lt;1 1 2 4 2|, &lt;0 2 1 -4 5|]<br />
EDOs: 7, 10, 17, 27ce, 44ce<br />
Badness: 0.0307<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Jamesbond"></a><!-- ws:end:WikiTextHeadingRule:20 -->Jamesbond</h1>
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:22:&lt;h1&gt; --><h1 id="toc11"><a name="Sidi"></a><!-- ws:end:WikiTextHeadingRule:22 -->Sidi</h1>
Commas: 25/24, 245/243<br />
<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|<br />
Badness: 0.0566<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Sidi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->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>

@@ 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>2012-01-03 21:06:09 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-03 21:09:19 UTC</tt>.<br>
-: The original revision id was <tt>289404311</tt>.<br>
+: The original revision id was <tt>289404847</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 14: / Line 14: @@
 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.
-[[POTE tuning|POTE generator]]: 348.594
+=Dicot=
+Comma: 25/24
+POTE generator: ~5/4 = 348.594
 Map: [&lt;1 1 2|, &lt;0 2 1|]
 EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]]
+Badness: 0.0130
-=7-limit dicot=
+==7-limit==
 [[Comma]]s: 15/14, 25/24
@@ Line 119: / Line 123: @@
 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:24:&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:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#x7-limit dicot"&gt;7-limit dicot&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;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Decimal"&gt;Decimal&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;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&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;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Sidi"&gt;Sidi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&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:26:&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:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Dicot"&gt;Dicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&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="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Decimal"&gt;Decimal&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:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Sidi"&gt;Sidi&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:37 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:40 --&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 127: / Line 131: @@
 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;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 348.594&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;
+&lt;br /&gt;
+POTE generator: ~5/4 = 348.594&lt;br /&gt;
 &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="/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;
+Badness: 0.0130&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="x7-limit dicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit dicot&lt;/h1&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;br /&gt;
@@ Line 142: / Line 150: @@
 Badness: 0.0199&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x7-limit dicot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&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;
 &lt;br /&gt;
@@ Line 151: / Line 159: @@
 Badness: 0.0199&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Sharp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Sharp&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Sharp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Sharp&lt;/h1&gt;
 Commas: 25/24, 28/27&lt;br /&gt;
 &lt;br /&gt;
@@ Line 159: / Line 167: @@
 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:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Decimal&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Decimal&lt;/h1&gt;
 Commas: 25/24, 49/48&lt;br /&gt;
 &lt;br /&gt;
@@ Line 169: / Line 177: @@
 Badness: 0.0283&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Decimal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Decimal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
 Commas: 25/24, 45/44, 49/48&lt;br /&gt;
 &lt;br /&gt;
@@ Line 178: / Line 186: @@
 Badness: 0.0267&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Decimal-Decimated"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Decimated&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Decimal-Decimated"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Decimated&lt;/h2&gt;
 Commas: 25/24, 33/32, 49/48&lt;br /&gt;
 &lt;br /&gt;
@@ Line 187: / Line 195: @@
 Badness: 0.0315&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Dichotic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Dichotic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Dichotic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Dichotic&lt;/h1&gt;
 Commas: 25/24, 64/63&lt;br /&gt;
 &lt;br /&gt;
@@ Line 197: / Line 205: @@
 Badness: 0.0376&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Dichotic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Dichotic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
 Commas: 25/24, 45/44, 64/63&lt;br /&gt;
 &lt;br /&gt;
@@ Line 206: / Line 214: @@
 Badness: 0.0307&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Jamesbond&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Jamesbond&lt;/h1&gt;
 Commas: 25/24, 81/80&lt;br /&gt;
 &lt;br /&gt;
@@ Line 214: / Line 222: @@
 EDOs: 7, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Sidi&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Sidi&lt;/h1&gt;
 Commas: 25/24, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 223: / Line 231: @@
 Badness: 0.0566&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Sidi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Sidi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
 Commas: 25/24, 45/44, 99/98&lt;br /&gt;
 &lt;br /&gt;

Dicot family: Difference between revisions

Revision as of 21:09, 3 January 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search