Subgroup temperaments
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[[toc|flat]] 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= ==[[Semiphore and Godzilla|Semiphore]]== Comma: 49/48 POTE generator: ~8/7~7/6 = 250.385 Map: [<1 2 3|, <0 -2 -1|] EDOs: 5, 19, 24 ==I'd like a name for this please== Could be thought of as "no-5's dominant" or "no-5's superpyth" Comma: 64/63 POTE generator: ~4/3 = 490.678 Map: [<1 2 2|, <0 -1 2|] EDOs: 5, 12, 17, 22, 27 ==[[Slendric]]== Comma: 1029/1024 POTE generator: ~8/7 = 233.688 Map: [<1 1 3|, <0 3 -1|] EDOs: 5, 21, 26, 31, 36, 77, 113, 190 Badness: 0.00461 =2.5.7.11= ==Larry== Commas: 243/242, 4000/3993 Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]] POTE generator: ~40/27 = 683.166 Map: [<1 5 12 12|, <0 -6 -17 -15|] EDOs: 7, 58, 65, 137, 202 Badness: 0.0125 =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
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<html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:30:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#x2.5.7.11">2.5.7.11</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> <!-- ws:end:WikiTextTocRule:46 -->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"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7</h1> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x2.3.7-Semiphore"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Semiphore%20and%20Godzilla">Semiphore</a></h2> Comma: 49/48<br /> <br /> POTE generator: ~8/7~7/6 = 250.385<br /> <br /> Map: [<1 2 3|, <0 -2 -1|]<br /> EDOs: 5, 19, 24<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x2.3.7-I'd like a name for this please"></a><!-- ws:end:WikiTextHeadingRule:4 -->I'd like a name for this please</h2> Could be thought of as "no-5's dominant" or "no-5's superpyth"<br /> Comma: 64/63<br /> <br /> POTE generator: ~4/3 = 490.678<br /> <br /> Map: [<1 2 2|, <0 -1 2|]<br /> EDOs: 5, 12, 17, 22, 27<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x2.3.7-Slendric"></a><!-- ws:end:WikiTextHeadingRule:6 --><a class="wiki_link" href="/Slendric">Slendric</a></h2> Comma: 1029/1024<br /> <br /> POTE generator: ~8/7 = 233.688<br /> <br /> Map: [<1 1 3|, <0 3 -1|]<br /> EDOs: 5, 21, 26, 31, 36, 77, 113, 190<br /> Badness: 0.00461<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x2.5.7.11"></a><!-- ws:end:WikiTextHeadingRule:8 -->2.5.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x2.5.7.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:10 -->Larry</h2> Commas: 243/242, 4000/3993<br /> Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br /> <br /> POTE generator: ~40/27 = 683.166<br /> <br /> Map: [<1 5 12 12|, <0 -6 -17 -15|]<br /> EDOs: 7, 58, 65, 137, 202<br /> Badness: 0.0125<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:12 -->2.3.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:14 -->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:16:<h2> --><h2 id="toc8"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:<h2> --><h2 id="toc9"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:18 -->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:20:<h2> --><h2 id="toc10"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:<h1> --><h1 id="toc11"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:22 -->2.9.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:24 -->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:26:<h2> --><h2 id="toc13"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:26 -->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:28:<h2> --><h2 id="toc14"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:28 -->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>