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>, and flipping that yields <<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 <24 38 55| and [[31edo|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 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>, 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|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.

~~==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 <<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

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

Badness: 0.0130

==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: [<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

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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

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

EDOs: 4, 7, 18bc, 25bcd

=Flat=

Commas: 21/20, 25/24

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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 tuning~~|POTE generator]]: 357.938

[[POTE_tuning|POTE generator]]: 357.938

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

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

==11-limit==

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

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

[[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

[[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

[[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

==Decibel==

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

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

EDOs: 4, 6, 10

Badness: 0.0324

=Dichotic=

Commas: 25/24, 64/63

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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

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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

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

EDOs: 3, 10

Badness: 0.0414

=Jamesbond=

Commas: 25/24, 81/80

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

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

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

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

==11-limit==

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

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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

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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

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

[[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

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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

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

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

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"><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>

[[Category:dicot]]

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 />

[[Category:family]]

~~<br />~~

[[Category:list]]

~~<br />~~

[[Category:overview]]

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

[[Category:theory]]

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 />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 2|, &lt;0 2 1|]<br />~~

EDOs: <a class="wiki_link" href="/3edo">3</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/13edo">13</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/20edo">20</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/31edo">31c</a><br />

~~Badness: 0.0130<br />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<br />~~

~~Map: [&lt;1 1 2 2 2|, &lt;0 2 1 3 5|]<br />~~

~~EDOs: 4e, 7<br />~~

~~Badness: 0.0199<br />~~

~~<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 />~~

~~<br />~~

~~Map: [&lt;1 1 2 2 4|, &lt;0 2 1 3 -2|~~]~~<br />~~

~~EDOs: 4, 7, 18bc, 25bcd<br />~~

~~<br />~~

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

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

~~<br />~~

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

~~<br />~~

~~Map: [&lt;1 1 2 3|, &lt;0 2 1 -1|~~]~~<br />~~

~~Wedgie: &lt;&lt;2 1 -1 -3 -7 -5||<br />~~

~~EDOs: 3, 4, 11cd<br />~~

~~Badness: 0.0254<br />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 2 1 2|, &lt;0 2 1 6 5|]<br />~~

~~EDOs~~: ~~10, 17d, 27cde<br />~~

~~Badness: 0.0224<br />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<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 />~~

~~<br />~~

~~Map:~~ [~~&lt;2 0 3 4 7|, &lt;0 2 1 1 0|]<br />~~

~~EDOs~~: ~~4, 6, 10<br />~~

~~Badness: 0.0324<br />~~

~~<br />~~

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

~~<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 />~~

~~<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 />~~

~~<h2 id="toc14"><a name="Dichotic-Dichosis"></a>Dichosis</h2>~~

~~Commas: 25/24, 35/33, 64/63<br />~~

~~<br />~~

~~POTE generator: ~5/4 = 360.659<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 2 4 5|, &lt;0 2 1 -4 -5|]<br />~~

~~EDOs: 3, 10<br />~~

~~Badness: 0.0414<br />~~

~~<br />~~

~~<h1 id="toc15"><a name="Jamesbond"></a>Jamesbond</h1>~~

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

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 258.139<br />~~

~~<br />~~

~~Map:~~ [~~&lt;7 11 16 0|, &lt;0 0 0 1|]<br />~~

~~EDOs~~: ~~7, <a class="wiki_link" href="/14edo">14c</a><br />~~

~~<br />~~

~~<h2 id="toc16"><a name="Jamesbond-11-limit"></a>11-limit</h2>~~

~~11-limit jamesbond is called &quot;septimal&quot; on the Regular Temperament Finder.<br />~~

~~<br />~~

~~Commas: 25/24, 33/32, 45/44<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 258.910<br />~~

~~<br />~~

~~Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|~~]~~<br />~~

~~EDOs: 7, 14c<br />~~

~~Badness: 0.0235<br />~~

~~<br />~~

~~<h2 id="toc17"><a name="Jamesbond-13-limit"></a>13-limit</h2>~~

~~Commas: 25/24 27/26 33/32 45/44<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 250.764<br />~~

~~<br />~~

~~Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|~~]~~<br />~~

~~EDOs: 7, 14c<br />~~

~~Badness: 0.0230<br />~~

~~<br />~~

~~<h2 id="toc18"><a name="Jamesbond-Septimal"></a>Septimal</h2>~~

~~Commas: 25/24, 33/32, 45/44, 65/63<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 247.447<br />~~

~~<br />~~

~~Map:~~ [~~&lt;7 11 16 0 24 6|, &lt;0 0 0 1 0 1|]<br />~~

~~EDOs: 7, 14cf<br />~~

~~Badness: 0.0226<br />~~

~~<br />~~

~~<h1 id="toc19"><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 />~~

~~<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 />~~

~~<h2 id="toc20"><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 />~~

~~<br />~~

~~Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|~~]~~<br />~~

~~EDOs: 14c, 17, 45ce, 59bccde<br />~~

~~Badness: 0.0330<br />~~

~~<br />~~

~~<h1 id="toc21"><a name="Quad"></a>Quad</h1>~~

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

~~<br />~~

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

~~<br />~~

~~Map: [&lt;4 6 9 0|, &lt;0 0 0 1|~~]~~<br />~~

~~Wedgie: &lt;&lt;0 0 4 0 6 9||<br />~~

~~EDOs: 4, 12bcd<br />~~

~~Badness: 0.0460</body></html></pre></div>~~

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+__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
@@ Line 19: / Line 12: @@
 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]]
 Badness: 0.0130
 ==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|]
 Wedgie: &lt;&lt;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
@@ Line 38: / Line 36: @@
 Map: [&lt;1 1 2 2 2|, &lt;0 2 1 3 5|]
 EDOs: 4e, 7
 Badness: 0.0199
 ==Eudicot==
 Commas: 15/14, 25/24, 33/32
@@ Line 47: / Line 47: @@
 Map: [&lt;1 1 2 2 4|, &lt;0 2 1 3 -2|]
 EDOs: 4, 7, 18bc, 25bcd
 =Flat=
 Commas: 21/20, 25/24
@@ Line 55: / Line 56: @@
 Map: [&lt;1 1 2 3|, &lt;0 2 1 -1|]
 Wedgie: &lt;&lt;2 1 -1 -3 -7 -5||
 EDOs: 3, 4, 11cd
 Badness: 0.0254
 =Sharp=
 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|]
 EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]
 ==11-limit==
 Commas: 25/24, 28/27, 35/33
@@ Line 73: / Line 78: @@
 Map: [&lt;1 1 2 1 2|, &lt;0 2 1 6 5|]
 EDOs: 10, 17d, 27cde
 Badness: 0.0224
 =Decimal=
 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|]
 Wedgie: &lt;&lt;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
+[[POTE_tuning|POTE generator]]: ~7/6 = 253.493
 Map: [&lt;2 0 3 4 -1|, &lt;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
+[[POTE_tuning|POTE generator]]: ~7/6 = 255.066
 Map: [&lt;2 0 3 4 10|, &lt;0 2 1 1 -2|]
 EDOs: 4, 10e, 14c
 Badness: 0.0315
 ==Decibel==
 Commas: 25/24, 35/33, 49/48
@@ Line 110: / Line 124: @@
 Map: [&lt;2 0 3 4 7|, &lt;0 2 1 1 0|]
 EDOs: 4, 6, 10
 Badness: 0.0324
 =Dichotic=
 Commas: 25/24, 64/63
@@ Line 119: / Line 135: @@
 Map: [&lt;1 1 2 4|, &lt;0 2 1 -4|]
 Wedgie: &lt;&lt;2 1 -4 -3 -12 -12||
 EDOs: 7, 10, 17, 27c, 37c
 Badness: 0.0376
 ==11-limit==
 Commas: 25/24, 45/44, 64/63
@@ Line 129: / Line 148: @@
 Map: [&lt;1 1 2 4 2|, &lt;0 2 1 -4 5|]
 EDOs: 7, 10, 17, 27ce, 44ce
 Badness: 0.0307
 ==Dichosis==
 Commas: 25/24, 35/33, 64/63
@@ Line 138: / Line 159: @@
 Map: [&lt;1 1 2 4 5|, &lt;0 2 1 -4 -5|]
 EDOs: 3, 10
 Badness: 0.0414
 =Jamesbond=
 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|]
 EDOs: 7, [[14edo|14c]]
 ==11-limit==
 -limit jamesbond is called "septimal" on the Regular Temperament Finder.
@@ Line 157: / Line 181: @@
 Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]
 EDOs: 7, 14c
 Badness: 0.0235
 ==13-limit==
 Commas: 25/24 27/26 33/32 45/44
@@ Line 166: / Line 192: @@
 Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|]
 EDOs: 7, 14c
 Badness: 0.0230
 ==Septimal==
 Commas: 25/24, 33/32, 45/44, 65/63
@@ Line 175: / Line 203: @@
 Map: [&lt;7 11 16 0 24 6|, &lt;0 0 0 1 0 1|]
 EDOs: 7, 14cf
 Badness: 0.0226
 =Sidi=
 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|]
 EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
 Badness: 0.0566
 ==11-limit==
 Commas: 25/24, 45/44, 99/98
@@ Line 193: / Line 225: @@
 Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]
 EDOs: 14c, 17, 45ce, 59bccde
 Badness: 0.0330
 =Quad=
 Commas: 9/8, 25/24
@@ Line 202: / Line 236: @@
 Map: [&lt;4 6 9 0|, &lt;0 0 0 1|]
 Wedgie: &lt;&lt;0 0 4 0 6 9||
 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;
--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>