Subgroup temperaments
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- This revision was by author genewardsmith and made on 2011-02-13 16:38:31 UTC.
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Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. =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 ==Mechy== 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 = 115.507 [[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.<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-Mechy"></a><!-- ws:end:WikiTextHeadingRule:4 -->Mechy</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 = 115.507<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>