Mirkwai family
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[[toc|flat]] The mirkwai family of [[planar temperament]]s tempers out the mirkwai comma, 16875/16807. =Vital statistics= [[Comma]]: mirkwai 16875/16807 7-limit minimax [|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5 9-limit minimax [|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7 Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|] [[Generator|Generators]]: 2, 3, 7/5 [[edo|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]] Badness: 0.000342 [[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5 =Indra= [[Comma|Commas]]: 540/539, 1375/1372 [[Minimax tuning]] [|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>, |6 6 -1 0 -3>, |20 18 -6 0 -9>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4 Lattice basis: 15/14 length 0.6184 55/36 length 0.7585 Angle(15/14, 55/36) = 68.1048 cents Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|] Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|] [[Generator|Generators]]: 2, 3, 7/5 [[edo|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]] Badness: 0.000266 [[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5 Scales: [[indra31]] ==Shibi== Commas: 540/539, 729/728, 1375/1372 Map: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|] EDOs: 41, 72, 111, 183, 224, 703 Badness: 0.000721 ==Yajna== [[Comma|Commas]]: 540/539, 625/624, 1375/1372 13-limit minimax [|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>, |8/5 2/5 -3/5 0 0 2/5>, |44/25 26/25 -24/25 0 0 11/25>, |62/25 48/25 -27/25 0 0 3/25>, |8/5 2/5 -8/5 0 0 7/5>] [[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10 15-limit minimax [|1 0 0 0 0 0>, |0 1 0 0 0 0>, |5/4 1/2 0 -5/16 0 5/16>, |1 1 0 -1/4 0 1/4>, |5/4 3/2 0 3/16 0 -3/16>, |1 1 0 -5/4 0 5/4>] [[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3 Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|] [[Generator|Generators]]: 2, 3, 7/5 [[edo|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703 Badness: 0.000700 ==Vibhu== [[Comma|Commas]]: 540/539, 1375/1372, 351/350 Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|] EDOs: 31, 72, 103, 111, 152, 183 Badness: 0.000826 ==Vish== [[Comma|Commas]]: 325/324, 364/363, 540/539 Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|] EDOs: 41, 72, 121, 193 Badness: 0.000930
Original HTML content:
<html><head><title>Mirkwai family</title></head><body><!-- ws:start:WikiTextTocRule:12:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Vital statistics">Vital statistics</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Indra">Indra</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> <!-- ws:end:WikiTextTocRule:19 --><br /> <br /> The mirkwai family of <a class="wiki_link" href="/planar%20temperament">planar temperament</a>s tempers out the mirkwai comma, 16875/16807.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h1> <a class="wiki_link" href="/Comma">Comma</a>: mirkwai 16875/16807<br /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |0 4/7 -4/7 5/7>, <br /> |0 -3/7 3/7 5/7>, |0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7, 6/5<br /> <br /> 9-limit minimax<br /> [|1 0 0 0>, |0 8/11 -4/11 5/11>, <br /> |0 -6/11 3/11 10/11>, |0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 8/7<br /> <br /> Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/224edo">224</a>, <a class="wiki_link" href="/296edo">296</a>, <a class="wiki_link" href="/327edo">327</a>, <a class="wiki_link" href="/775edo">775</a><br /> Badness: 0.000342<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 to 2.3.7/5<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Indra"></a><!-- ws:end:WikiTextHeadingRule:2 -->Indra</h1> <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>, <br /> |6 6 -1 0 -3>, |20 18 -6 0 -9>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 5/4<br /> <br /> Lattice basis: 15/14 length 0.6184 55/36 length 0.7585<br /> Angle(15/14, 55/36) = 68.1048 cents<br /> Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]<br /> <br /> Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br /> <a class="wiki_link" href="/edo">Edos</a>: 31, 41, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/224edo">224</a>, <a class="wiki_link" href="/296edo">296</a>, <a class="wiki_link" href="/703edo">703</a><br /> Badness: 0.000266<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5<br /> <br /> Scales: <a class="wiki_link" href="/indra31">indra31</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Indra-Shibi"></a><!-- ws:end:WikiTextHeadingRule:4 -->Shibi</h2> Commas: 540/539, 729/728, 1375/1372<br /> <br /> Map: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]<br /> EDOs: 41, 72, 111, 183, 224, 703<br /> Badness: 0.000721<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Indra-Yajna"></a><!-- ws:end:WikiTextHeadingRule:6 -->Yajna</h2> <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 625/624, 1375/1372<br /> <br /> 13-limit minimax<br /> [|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>, <br /> |8/5 2/5 -3/5 0 0 2/5>, <br /> |44/25 26/25 -24/25 0 0 11/25>, <br /> |62/25 48/25 -27/25 0 0 3/25>, <br /> |8/5 2/5 -8/5 0 0 7/5>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 13/10<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |0 1 0 0 0 0>, <br /> |5/4 1/2 0 -5/16 0 5/16>,<br /> |1 1 0 -1/4 0 1/4>, <br /> |5/4 3/2 0 3/16 0 -3/16>, <br /> |1 1 0 -5/4 0 5/4>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/13, 4/3<br /> <br /> Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/103edo">103</a>, <a class="wiki_link" href="/193edo">193</a>, 224, 296, 520, 703<br /> Badness: 0.000700<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Indra-Vibhu"></a><!-- ws:end:WikiTextHeadingRule:8 -->Vibhu</h2> <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372, 351/350<br /> <br /> Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]<br /> EDOs: 31, 72, 103, 111, 152, 183<br /> Badness: 0.000826<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Indra-Vish"></a><!-- ws:end:WikiTextHeadingRule:10 -->Vish</h2> <a class="wiki_link" href="/Comma">Commas</a>: 325/324, 364/363, 540/539<br /> <br /> Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]<br /> EDOs: 41, 72, 121, 193<br /> Badness: 0.000930</body></html>