Dicot family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
__FORCETOC__
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-10-16 12:12:05 UTC</tt>.<br>
The [[5-limit|5-limit]] parent [[Comma|comma]] for the dicot family is 25/24, the [[chromatic_semitone|chromatic semitone]]. Its [[monzo|monzo]] is |-3 -1 2&gt;, and flipping that yields &lt;&lt;2 1 -3|| for the [[wedgie|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|7edo]], [[24edo|24edo]] using the val &lt;24 38 55| and [[31edo|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 original revision id was <tt>595544904</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.


==Seven limit children==
The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit|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.


==Seven limit children==
=Dicot=
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
Comma: 25/24


Line 19: Line 12:


Map: [&lt;1 1 2|, &lt;0 2 1|]
Map: [&lt;1 1 2|, &lt;0 2 1|]
EDOs: [[3edo|3]], [[4edo|4]], [[6edo|6]], [[7edo|7]], [[10edo|10]], [[13edo|13]], [[14edo|14c]], [[17edo|17]], [[20edo|20]], [[24edo|24c]], [[31edo|31c]]
EDOs: [[3edo|3]], [[4edo|4]], [[6edo|6]], [[7edo|7]], [[10edo|10]], [[13edo|13]], [[14edo|14c]], [[17edo|17]], [[20edo|20]], [[24edo|24c]], [[31edo|31c]]
Badness: 0.0130
Badness: 0.0130


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


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


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


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


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


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


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Map: [&lt;1 1 2 2 4|, &lt;0 2 1 3 -2|]
Map: [&lt;1 1 2 2 4|, &lt;0 2 1 3 -2|]
EDOs: 4, 7, 18bc, 25bcd
EDOs: 4, 7, 18bc, 25bcd


=Flat=  
=Flat=
Commas: 21/20, 25/24
Commas: 21/20, 25/24


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Map: [&lt;1 1 2 3|, &lt;0 2 1 -1|]
Map: [&lt;1 1 2 3|, &lt;0 2 1 -1|]
Wedgie: &lt;&lt;2 1 -1 -3 -7 -5||
Wedgie: &lt;&lt;2 1 -1 -3 -7 -5||
EDOs: 3, 4, 11cd
EDOs: 3, 4, 11cd
Badness: 0.0254
Badness: 0.0254


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


[[POTE tuning|POTE generator]]: 357.938
[[POTE_tuning|POTE generator]]: 357.938


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


==11-limit==  
==11-limit==
Commas: 25/24, 28/27, 35/33
Commas: 25/24, 28/27, 35/33


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Map: [&lt;1 1 2 1 2|, &lt;0 2 1 6 5|]
Map: [&lt;1 1 2 1 2|, &lt;0 2 1 6 5|]
EDOs: 10, 17d, 27cde
EDOs: 10, 17d, 27cde
Badness: 0.0224
Badness: 0.0224


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


[[POTE tuning|POTE generator]]: ~7/6 = 251.557
[[POTE_tuning|POTE generator]]: ~7/6 = 251.557


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


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


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


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


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


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


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


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


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Map: [&lt;2 0 3 4 7|, &lt;0 2 1 1 0|]
Map: [&lt;2 0 3 4 7|, &lt;0 2 1 1 0|]
EDOs: 4, 6, 10
EDOs: 4, 6, 10
Badness: 0.0324
Badness: 0.0324


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


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


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


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


==Dichosis==  
==Dichosis==
Commas: 25/24, 35/33, 64/63
Commas: 25/24, 35/33, 64/63


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Map: [&lt;1 1 2 4 5|, &lt;0 2 1 -4 -5|]
Map: [&lt;1 1 2 4 5|, &lt;0 2 1 -4 -5|]
EDOs: 3, 10
EDOs: 3, 10
Badness: 0.0414
Badness: 0.0414


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


[[POTE tuning|POTE generator]]: ~8/7 = 258.139
[[POTE_tuning|POTE generator]]: ~8/7 = 258.139


Map: [&lt;7 11 16 0|, &lt;0 0 0 1|]
Map: [&lt;7 11 16 0|, &lt;0 0 0 1|]
EDOs: 7, [[14edo|14c]]
EDOs: 7, [[14edo|14c]]


==11-limit==  
==11-limit==
11-limit jamesbond is called "septimal" on the Regular Temperament Finder.
11-limit jamesbond is called "septimal" on the Regular Temperament Finder.


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Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]
Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]
EDOs: 7, 14c
EDOs: 7, 14c
Badness: 0.0235
Badness: 0.0235


==13-limit==  
==13-limit==
Commas: 25/24 27/26 33/32 45/44
Commas: 25/24 27/26 33/32 45/44


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Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|]
Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|]
EDOs: 7, 14c
EDOs: 7, 14c
Badness: 0.0230
Badness: 0.0230


==Septimal==  
==Septimal==
Commas: 25/24, 33/32, 45/44, 65/63
Commas: 25/24, 33/32, 45/44, 65/63


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Map: [&lt;7 11 16 0 24 6|, &lt;0 0 0 1 0 1|]
Map: [&lt;7 11 16 0 24 6|, &lt;0 0 0 1 0 1|]
EDOs: 7, 14cf
EDOs: 7, 14cf
Badness: 0.0226
Badness: 0.0226


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


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


Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
Badness: 0.0566
Badness: 0.0566


==11-limit==  
==11-limit==
Commas: 25/24, 45/44, 99/98
Commas: 25/24, 45/44, 99/98


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Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]
Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]
EDOs: 14c, 17, 45ce, 59bccde
EDOs: 14c, 17, 45ce, 59bccde
Badness: 0.0330
Badness: 0.0330


=Quad=  
=Quad=
Commas: 9/8, 25/24
Commas: 9/8, 25/24


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Map: [&lt;4 6 9 0|, &lt;0 0 0 1|]
Map: [&lt;4 6 9 0|, &lt;0 0 0 1|]
Wedgie: &lt;&lt;0 0 4 0 6 9||
Wedgie: &lt;&lt;0 0 4 0 6 9||
EDOs: 4, 12bcd
EDOs: 4, 12bcd
Badness: 0.0460</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0460
<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:44:&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:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt; | &lt;a href="#Dicot"&gt;Dicot&lt;/a&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;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Flat"&gt;Flat&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Decimal"&gt;Decimal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Sidi"&gt;Sidi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Quad"&gt;Quad&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;
[[Category:dicot]]
&lt;!-- ws:end:WikiTextTocRule:67 --&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;
[[Category:family]]
&lt;br /&gt;
[[Category:list]]
&lt;br /&gt;
[[Category:overview]]
&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;
[[Category:theory]]
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;
&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="/3edo"&gt;3&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &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="/13edo"&gt;13&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="/20edo"&gt;20&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: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;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 336.381&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 2 1 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 1 3 -3 -1 4||&lt;br /&gt;
EDOs: 4, 7, &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;
Badness: 0.0199&lt;br /&gt;
&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;
&lt;br /&gt;
POTE generator: ~5/4 = 342.125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 2 2|, &amp;lt;0 2 1 3 5|]&lt;br /&gt;
EDOs: 4e, 7&lt;br /&gt;
Badness: 0.0199&lt;br /&gt;
&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;
&lt;br /&gt;
POTE generator: ~5/4 = 336.051&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 2 4|, &amp;lt;0 2 1 3 -2|]&lt;br /&gt;
EDOs: 4, 7, 18bc, 25bcd&lt;br /&gt;
&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;
&lt;br /&gt;
POTE generator: ~5/4 = 331.916&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 2 1 -1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 1 -1 -3 -7 -5||&lt;br /&gt;
EDOs: 3, 4, 11cd&lt;br /&gt;
Badness: 0.0254&lt;br /&gt;
&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;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 357.938&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 1|, &amp;lt;0 2 1 6|]&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: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;
&lt;br /&gt;
POTE generator: ~5/4 = 356.106&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 1 2|, &amp;lt;0 2 1 6 5|]&lt;br /&gt;
EDOs: 10, 17d, 27cde&lt;br /&gt;
Badness: 0.0224&lt;br /&gt;
&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;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 251.557&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 3 4|, &amp;lt;0 2 1 1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;4 2 2 -6 -8 -1||&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;
Badness: 0.0283&lt;br /&gt;
&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;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 253.493&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 3 4 -1|, &amp;lt;0 2 1 1 5|]&lt;br /&gt;
EDOs: 10, 14c, 24c, 38cd&lt;br /&gt;
Badness: 0.0267&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="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;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 255.066&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 3 4 10|, &amp;lt;0 2 1 1 -2|]&lt;br /&gt;
EDOs: 4, 10e, 14c&lt;br /&gt;
Badness: 0.0315&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="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;
&lt;br /&gt;
POTE generator: ~8/7 = 243.493&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 3 4 7|, &amp;lt;0 2 1 1 0|]&lt;br /&gt;
EDOs: 4, 6, 10&lt;br /&gt;
Badness: 0.0324&lt;br /&gt;
&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;
&lt;br /&gt;
POTE generator: ~5/4 = 356.264&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 4|, &amp;lt;0 2 1 -4|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 1 -4 -3 -12 -12||&lt;br /&gt;
EDOs: 7, 10, 17, 27c, 37c&lt;br /&gt;
Badness: 0.0376&lt;br /&gt;
&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;
&lt;br /&gt;
POTE generator: ~5/4 = 354.262&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 4 2|, &amp;lt;0 2 1 -4 5|]&lt;br /&gt;
EDOs: 7, 10, 17, 27ce, 44ce&lt;br /&gt;
Badness: 0.0307&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Dichotic-Dichosis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Dichosis&lt;/h2&gt;
Commas: 25/24, 35/33, 64/63&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 360.659&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 4 5|, &amp;lt;0 2 1 -4 -5|]&lt;br /&gt;
EDOs: 3, 10&lt;br /&gt;
Badness: 0.0414&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Jamesbond&lt;/h1&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;: ~8/7 = 258.139&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 11 16 0|, &amp;lt;0 0 0 1|]&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:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Jamesbond-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
11-limit jamesbond is called &amp;quot;septimal&amp;quot; on the Regular Temperament Finder.&lt;br /&gt;
&lt;br /&gt;
Commas: 25/24, 33/32, 45/44&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 258.910&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 11 16 0 24|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
EDOs: 7, 14c&lt;br /&gt;
Badness: 0.0235&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Jamesbond-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
Commas: 25/24 27/26 33/32 45/44&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 250.764&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 11 16 0 24 26|, &amp;lt;0 0 0 1 0 0|]&lt;br /&gt;
EDOs: 7, 14c&lt;br /&gt;
Badness: 0.0230&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Jamesbond-Septimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Septimal&lt;/h2&gt;
Commas: 25/24, 33/32, 45/44, 65/63&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 247.447&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 11 16 0 24 6|, &amp;lt;0 0 0 1 0 1|]&lt;br /&gt;
EDOs: 7, 14cf&lt;br /&gt;
Badness: 0.0226&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&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;: ~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;br /&gt;
Badness: 0.0566&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Sidi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&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;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Quad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Quad&lt;/h1&gt;
Commas: 9/8, 25/24&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 324.482&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;4 6 9 0|, &amp;lt;0 0 0 1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;0 0 4 0 6 9||&lt;br /&gt;
EDOs: 4, 12bcd&lt;br /&gt;
Badness: 0.0460&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

|

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 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: 3, 4, 6, 7, 10, 13, 14c, 17, 20, 24c, 31c

Badness: 0.0130

7-limit

Commas: 15/14, 25/24

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, 11c, 14cd, 18bc, 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

Eudicot

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

POTE generator: ~5/4 = 336.051

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

EDOs: 4, 7, 18bc, 25bcd

Flat

Commas: 21/20, 25/24

POTE generator: ~5/4 = 331.916

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

Wedgie: <<2 1 -1 -3 -7 -5||

EDOs: 3, 4, 11cd

Badness: 0.0254

Sharp

Commas: 25/24, 28/27

POTE generator: 357.938

Map: [<1 1 2 1|, <0 2 1 6|]

EDOs: 10, 37cd, 57bcd

11-limit

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

POTE generator: ~5/4 = 356.106

Map: [<1 1 2 1 2|, <0 2 1 6 5|]

EDOs: 10, 17d, 27cde

Badness: 0.0224

Decimal

Commas: 25/24, 49/48

POTE generator: ~7/6 = 251.557

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

Wedgie: <<4 2 2 -6 -8 -1||

EDOs: 10, 14c, 24c, 38cd

Badness: 0.0283

11-limit

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

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 generator: ~7/6 = 255.066

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

EDOs: 4, 10e, 14c

Badness: 0.0315

Decibel

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

POTE generator: ~8/7 = 243.493

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

EDOs: 4, 6, 10

Badness: 0.0324

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

Dichosis

Commas: 25/24, 35/33, 64/63

POTE generator: ~5/4 = 360.659

Map: [<1 1 2 4 5|, <0 2 1 -4 -5|]

EDOs: 3, 10

Badness: 0.0414

Jamesbond

Commas: 25/24, 81/80

POTE generator: ~8/7 = 258.139

Map: [<7 11 16 0|, <0 0 0 1|]

EDOs: 7, 14c

11-limit

11-limit jamesbond is called "septimal" on the Regular Temperament Finder.

Commas: 25/24, 33/32, 45/44

POTE generator: ~8/7 = 258.910

Map: [<7 11 16 0 24|, <0 0 0 1 0|]

EDOs: 7, 14c

Badness: 0.0235

13-limit

Commas: 25/24 27/26 33/32 45/44

POTE generator: ~8/7 = 250.764

Map: [<7 11 16 0 24 26|, <0 0 0 1 0 0|]

EDOs: 7, 14c

Badness: 0.0230

Septimal

Commas: 25/24, 33/32, 45/44, 65/63

POTE generator: ~8/7 = 247.447

Map: [<7 11 16 0 24 6|, <0 0 0 1 0 1|]

EDOs: 7, 14cf

Badness: 0.0226

Sidi

Commas: 25/24, 245/243

POTE generator: ~9/7 = 427.208

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

EDOs: 14c, 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

Quad

Commas: 9/8, 25/24

POTE generator: ~5/4 = 324.482

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

Wedgie: <<0 0 4 0 6 9||

EDOs: 4, 12bcd

Badness: 0.0460

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