Dicot family
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[[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. [[POTE tuning|POTE generator]]: 348.594 Map: [<1 1 2|, <0 2 1|] EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]] =Septimal dicot= [[Comma]]s: 15/14, 25/24 [[POTE tuning|POTE generator]]: 336.381 Map: [<1 1 2 3|, <0 2 1 3|] EDOs: [[11edo|11c]], [[14edo|14cd]], [[18edo|18bc]], [[25edo|25bcd]] =Sharp= Commas: 25/24, 28/27 [[POTE tuning|POTE generator]]: 357.938 Map: [<1 1 2 1|, <0 2 1 6|] EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]] =Decimal= Commas: 25/24, 49/48 [[POTE tuning|POTE generator]]: ~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 =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]]: 427.208 Map: [<1 3 3 6|, <0 -4 -2 -9|] EDOs: [[14edo|14c]], [[45edo|45c]], <59 93 135 165|
Original HTML content:
<html><head><title>Dicot family</title></head><body><!-- ws:start:WikiTextTocRule:18:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Septimal dicot">Septimal dicot</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Sharp">Sharp</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Decimal">Decimal</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Dichotic">Dichotic</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Jamesbond">Jamesbond</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> <!-- ws:end:WikiTextTocRule:28 --><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>, and flipping that yields <<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 <24 38 55| and <a class="wiki_link" href="/31edo">31edo</a> 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.<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><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 <<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.<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 348.594<br /> <br /> Map: [<1 1 2|, <0 2 1|]<br /> EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/24edo">24c</a>, <a class="wiki_link" href="/31edo">31c</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Septimal dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal dicot</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 15/14, 25/24<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 336.381<br /> <br /> Map: [<1 1 2 3|, <0 2 1 3|]<br /> EDOs: <a class="wiki_link" href="/11edo">11c</a>, <a class="wiki_link" href="/14edo">14cd</a>, <a class="wiki_link" href="/18edo">18bc</a>, <a class="wiki_link" href="/25edo">25bcd</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Sharp"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sharp</h1> Commas: 25/24, 28/27<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 357.938<br /> <br /> Map: [<1 1 2 1|, <0 2 1 6|]<br /> EDOs: <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/37edo">37cd</a>, <a class="wiki_link" href="/57edo">57bcd</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Decimal"></a><!-- ws:end:WikiTextHeadingRule:6 -->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: [<2 0 3 4|, <0 2 1 1|]<br /> Wedgie: <<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:8:<h2> --><h2 id="toc4"><a name="Decimal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->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: [<2 0 3 4 -1|, <0 2 1 1 5|]<br /> EDOs: 10, 14c, 24c, 38cd<br /> Badness: 0.0267<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Dichotic"></a><!-- ws:end:WikiTextHeadingRule:10 -->Dichotic</h1> Commas: 25/24, 64/63<br /> <br /> POTE generator: ~5/4 = 356.264<br /> <br /> Map: [<1 1 2 4|, <0 2 1 -4|]<br /> Wedgie: <<2 1 -4 -3 -12 -12||<br /> EDOs: 7, 10, 17, 27c, 37c<br /> Badness: 0.0376<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Dichotic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> Commas: 25/24, 45/44, 64/63<br /> <br /> POTE generator: ~5/4 = 354.262<br /> <br /> Map: [<1 1 2 4 2|, <0 2 1 -4 5|]<br /> EDOs: 7, 10, 17, 27ce, 44ce<br /> Badness: 0.0307<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Jamesbond"></a><!-- ws:end:WikiTextHeadingRule:14 -->Jamesbond</h1> Commas: 25/24, 81/80<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 86.710<br /> <br /> Map: [<7 11 16 20|, <0 0 0 -1|]<br /> EDOs: 7, <a class="wiki_link" href="/14edo">14c</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="Jamesbond--Sidi"></a><!-- ws:end:WikiTextHeadingRule:16 -->Sidi</h3> Commas: 25/24, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 427.208<br /> <br /> Map: [<1 3 3 6|, <0 -4 -2 -9|]<br /> EDOs: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/45edo">45c</a>, <59 93 135 165|</body></html>