Dicot family
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- This revision was by author xenwolf and made on 2011-06-19 16:17:58 UTC.
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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, both 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]], [[17edo|17]], [[24edo|24]], [[31edo|31]] ===Septimal dicot=== [[Comma]]s: 15/14, 25/24 [[POTE tuning|POTE generator]]: 336.381 Map: [<1 1 2 3|, <0 2 1 3|] EDOs: 4, 7, [[25edo|25]] ===Sharp=== Commas: 25/24, 28/27 [[POTE tuning|POTE generator]]: 357.938 Map: [<1 1 2 1|, <0 2 1 6|] EDOs: 7, [[10edo|10]], [[57edo|57]] ===Decimal=== Commas: 25/24, 49/48 [[POTE tuning|POTE generator]]: 251.557 Map: [<2 0 3 4|, <0 2 1 1|] EDOs: [[4edo|4]], 10, [[14edo|14]], 24, [[62edo|62]] ===Jamesbond=== Commas: 25/24, 81/80 [[POTE tuning|POTE generator]]: 86.710 Map: [<7 11 16 20|, <0 0 0 -1|] EDOs: 7, 14, [[595edo|595]], [[609edo|609]] ===Sidi=== Commas: 25/24, 245/243 [[POTE tuning|POTE generator]]: 427.208 Map: [<1 3 3 6|, <0 -4 -2 -9|] EDOs: 14, [[59edo|59]]
Original HTML content:
<html><head><title>Dicot family</title></head><body>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, both 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="/17edo">17</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/31edo">31</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Seven limit children-Septimal dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal dicot</h3> <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: 4, 7, <a class="wiki_link" href="/25edo">25</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Seven limit children-Sharp"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sharp</h3> 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: 7, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/57edo">57</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Seven limit children-Decimal"></a><!-- ws:end:WikiTextHeadingRule:6 -->Decimal</h3> Commas: 25/24, 49/48<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 251.557<br /> <br /> Map: [<2 0 3 4|, <0 2 1 1|]<br /> EDOs: <a class="wiki_link" href="/4edo">4</a>, 10, <a class="wiki_link" href="/14edo">14</a>, 24, <a class="wiki_link" href="/62edo">62</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Seven limit children-Jamesbond"></a><!-- ws:end:WikiTextHeadingRule:8 -->Jamesbond</h3> 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, 14, <a class="wiki_link" href="/595edo">595</a>, <a class="wiki_link" href="/609edo">609</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Seven limit children-Sidi"></a><!-- ws:end:WikiTextHeadingRule:10 -->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: 14, <a class="wiki_link" href="/59edo">59</a></body></html>