Dicot family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 148455089 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 190198000 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2010- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-29 10:58:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>190198000</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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==Seven limit children== | ==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, | 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. | ||
===Septimal dicot=== | |||
Commas: 15/14, 25/24 | |||
[[POTE tuning|POTE generator]]: 336.381 | |||
Map: [<1 1 2 3|, <0 2 1 3|] | |||
EDOs: 4, 7, 25 | |||
===Sharp=== | |||
Commas: 25/24, 28/27 | |||
[[POTE tuning|POTE generator]]: 357.938 | |||
Map: [<1 1 2 1|, <0 2 1 6|] | |||
EDOs: 7, 10, 57 | |||
===Decimal=== | |||
Commas: 25/24, 49/48 | |||
[[POTE tuning|POTE generator]]: 251.557 | |||
Map: [<2 0 3 4|, <0 2 1 1|] | |||
EDOs: 4, 10, 14, 24, 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, 595, 609 | |||
===Sidi=== | |||
Commas: 25/24, 245/243 | |||
[[POTE tuning|POTE generator]]: 427.208 | |||
Map: [<1 3 3 6|, <0 -4 -2 -9|] | |||
EDOs: 14, 59 | |||
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<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> | <!-- 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 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, both retaining the same period and generator. Decimal with wedgie &lt;&lt;4 2 2 -6 -8 -1|| adds 49/48, | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> 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, both 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;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Septimal dicot"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal dicot</h3> | |||
Commas: 15/14, 25/24<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 336.381<br /> | |||
<br /> | |||
Map: [&lt;1 1 2 3|, &lt;0 2 1 3|]<br /> | |||
EDOs: 4, 7, 25<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><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: [&lt;1 1 2 1|, &lt;0 2 1 6|]<br /> | |||
EDOs: 7, 10, 57<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><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: [&lt;2 0 3 4|, &lt;0 2 1 1|]<br /> | |||
EDOs: 4, 10, 14, 24, 62<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><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: [&lt;7 11 16 20|, &lt;0 0 0 -1|]<br /> | |||
EDOs: 7, 14, 595, 609<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><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: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]<br /> | |||
EDOs: 14, 59</body></html></pre></div> | |||
Revision as of 10:58, 29 December 2010
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 2010-12-29 10:58:40 UTC.
- The original revision id was 190198000.
- 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:
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. ===Septimal dicot=== Commas: 15/14, 25/24 [[POTE tuning|POTE generator]]: 336.381 Map: [<1 1 2 3|, <0 2 1 3|] EDOs: 4, 7, 25 ===Sharp=== Commas: 25/24, 28/27 [[POTE tuning|POTE generator]]: 357.938 Map: [<1 1 2 1|, <0 2 1 6|] EDOs: 7, 10, 57 ===Decimal=== Commas: 25/24, 49/48 [[POTE tuning|POTE generator]]: 251.557 Map: [<2 0 3 4|, <0 2 1 1|] EDOs: 4, 10, 14, 24, 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, 595, 609 ===Sidi=== Commas: 25/24, 245/243 [[POTE tuning|POTE generator]]: 427.208 Map: [<1 3 3 6|, <0 -4 -2 -9|] EDOs: 14, 59
Original HTML content:
<html><head><title>Dicot family</title></head><body>The 5-limit parent comma 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 /> <!-- 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 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.<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> Commas: 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, 25<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, 10, 57<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: 4, 10, 14, 24, 62<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, 595, 609<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, 59</body></html>