Subgroup temperaments: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 209796456 - Original comment: ** |
Wikispaces>guest **Imported revision 242268791 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-07-21 10:57:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>242268791</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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<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">Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. | <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">Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. | ||
=2.3.7.11= | =2.3.7.11= | ||
==Ennea== | ==Ennea== | ||
Commas: 41503/41472, 43923/43904 | Commas: 41503/41472, 43923/43904 | ||
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Badness: 0.00426 | Badness: 0.00426 | ||
==Supra== | ==Supra== | ||
Commas: 64/63, 99/98 | Commas: 64/63, 99/98 | ||
| Line 28: | Line 28: | ||
Badness: 0.00933 | Badness: 0.00933 | ||
==Skwares== | ==Skwares== | ||
Commas: 99/98, 243/242 | Commas: 99/98, 243/242 | ||
| Line 37: | Line 37: | ||
Badness: 0.0107 | Badness: 0.0107 | ||
==Hemif== | ==Hemif== | ||
Commas: 243/242, 896/891 | Commas: 243/242, 896/891 | ||
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Badness: 0.0109 | Badness: 0.0109 | ||
=2.9.7.11= | =2.9.7.11= | ||
==Machine== | ==Machine== | ||
Commas: 64/63, 99/98 | Commas: 64/63, 99/98 | ||
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Badness: 0.00233 | Badness: 0.00233 | ||
==Apparatus== | ==Apparatus== | ||
Commas: 41503/41472, 322102/321489 | Commas: 41503/41472, 322102/321489 | ||
[[POTE tuning|POTE generator]]: ~77/72 = 115. | [[POTE tuning|POTE generator]]: ~77/72 = 115.570 | ||
[[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] | [[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] | ||
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Badness: 0.00263 | Badness: 0.00263 | ||
==Mechanism== | ==Mechanism== | ||
Commas: 896/891, 26411/26244 | Commas: 896/891, 26411/26244 | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7.11</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7.11</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ennea</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ennea</h2> | ||
Commas: 41503/41472, 43923/43904<br /> | Commas: 41503/41472, 43923/43904<br /> | ||
<br /> | <br /> | ||
POTE generator: ~99/98 = 17.6258<br /> | POTE generator: ~99/98 = 17.6258<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:4 -->Supra</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:4 -->Supra</h2> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:6 -->Skwares</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:6 -->Skwares</h2> | ||
Commas: 99/98, 243/242<br /> | Commas: 99/98, 243/242<br /> | ||
<br /> | <br /> | ||
POTE generator: ~9/7 = 425.244<br /> | POTE generator: ~9/7 = 425.244<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemif</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemif</h2> | ||
Commas: 243/242, 896/891<br /> | Commas: 243/242, 896/891<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 351.535<br /> | POTE generator: ~11/9 = 351.535<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:10 -->2.9.7.11</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:10 -->2.9.7.11</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:12 -->Machine</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:12 -->Machine</h2> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:14 -->Apparatus</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:14 -->Apparatus</h2> | ||
Commas: 41503/41472, 322102/321489<br /> | Commas: 41503/41472, 322102/321489<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115. | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115.570<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]<br /> | <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mechanism</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mechanism</h2> | ||
Commas: 896/891, 26411/26244<br /> | Commas: 896/891, 26411/26244<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br /> | ||
Revision as of 10:57, 21 July 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2011-07-21 10:57:09 UTC.
- The original revision id was 242268791.
- 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:
Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. =2.3.7.11= ==Ennea== Commas: 41503/41472, 43923/43904 POTE generator: ~99/98 = 17.6258 Sval map: [<9 0 11 24|, <0 2 2 1|] EDOs: 54, 63, 72, 135, 342, 477, 1089, 1566 Badness: 0.00426 ==Supra== Commas: 64/63, 99/98 [[POTE tuning|POTE generator]]: ~3/2 = 707.192 Sval map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 12, 17, 39, 56 Badness: 0.00933 ==Skwares== Commas: 99/98, 243/242 POTE generator: ~9/7 = 425.244 Sval map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 14, 17, 31, 48, 79, 127, 206 Badness: 0.0107 ==Hemif== Commas: 243/242, 896/891 POTE generator: ~11/9 = 351.535 Sval map: [<1 1 -1 2|, <0 2 13 5|] EDOs: 7, 17, 41, 58, 99 Badness: 0.0109 =2.9.7.11= ==Machine== Commas: 64/63, 99/98 [[POTE tuning|POTE generator]]: ~8/7 = 214.384 [[Smonzos and Svals|Sval map]]: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 Badness: 0.00233 ==Apparatus== Commas: 41503/41472, 322102/321489 [[POTE tuning|POTE generator]]: ~77/72 = 115.570 [[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623 Badness: 0.00263 ==Mechanism== Commas: 896/891, 26411/26244 [[POTE tuning|POTE generator]]: ~9/7 = 438.465 [[Smonzos and Svals|Sval map]]: [<1 5 5 2|, <0 -5 -6 4|] EDOs: 8, 11, 30, 41, 52 Badness: 0.00439
Original HTML content:
<html><head><title>Subgroup temperaments</title></head><body>Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ennea</h2> Commas: 41503/41472, 43923/43904<br /> <br /> POTE generator: ~99/98 = 17.6258<br /> <br /> Sval map: [<9 0 11 24|, <0 2 2 1|]<br /> EDOs: 54, 63, 72, 135, 342, 477, 1089, 1566<br /> Badness: 0.00426<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:4 -->Supra</h2> Commas: 64/63, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br /> <br /> Sval map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 12, 17, 39, 56<br /> Badness: 0.00933<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:6 -->Skwares</h2> Commas: 99/98, 243/242<br /> <br /> POTE generator: ~9/7 = 425.244<br /> <br /> Sval map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 14, 17, 31, 48, 79, 127, 206<br /> Badness: 0.0107<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemif</h2> Commas: 243/242, 896/891<br /> <br /> POTE generator: ~11/9 = 351.535<br /> <br /> Sval map: [<1 1 -1 2|, <0 2 13 5|]<br /> EDOs: 7, 17, 41, 58, 99<br /> Badness: 0.0109<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:10 -->2.9.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:12 -->Machine</h2> Commas: 64/63, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> Badness: 0.00233<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:14 -->Apparatus</h2> Commas: 41503/41472, 322102/321489<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115.570<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 5 3 5|, <0 -19 -2 -16|]<br /> EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623<br /> Badness: 0.00263<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mechanism</h2> Commas: 896/891, 26411/26244<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 5 5 2|, <0 -5 -6 4|]<br /> EDOs: 8, 11, 30, 41, 52<br /> Badness: 0.00439</body></html>