Hemifamity family
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[[toc|flat]] =Vital statistics= [[Comma]] c = 5120/5103 7-limit minimax: 3 and 7 1/7c sharp, 5 just [|1 0 0 0>, |10/7 1/7 1/7 -1/7>, |0 0 1 0>, |10/7 -6/7 1/7 6/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 7/6 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp [|1 0 0 0>, |5/4 1/4 1/8 -1/8>, |0 0 1 0>, |5/2 -3/2 1/4 3/4>] [[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7 Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063 Angle(3/2, 10/9) = 82.112 degrees Map to lattice: [<0 1 2 -4|, <0 0 1 1|] Map: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|] Generators: 2, 3, 5 [[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]] Badness: 0.000153 [[Projection pair]]s: 7 5120/729 ==Music== By Gene Ward Smith [[http://www.archive.org/details/Choraled|Choraled]] [[http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3|play]] By Chris Vaisvil [[http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3|Hemifamity27]] =Pele= [[Comma|Commas]]: 441/440, 896/891 [[Minimax tuning]] [|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>, |17/5 -2 6/5 0 -1/5>, |16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>] [[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9 Lattice basis: 3/2 length 0.3812 56/55 length 1.5893 Angle(3/2, 56/55) = 90.4578 degrees Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|] Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|] [[Generator|Generators]]: 2, 3, 5 [[edo|Edos]]: [[87edo|87]], [[128edo|128]], [[145edo|145]], [[232edo|232]] Badness: 0.000648 Projection pairs: 7 5120/729 11 655360/59049 ==13-limit== Commas: 196/195, 352/351, 364/363 13-limit minimax Eigenmonzos: 2, 10/9, 13/10 15-limit minimax Eigenmonzos: 2, 15/13, 6/5 Map: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|] EDOs: 29, 41, 46, 58, 87, 145, 232 Badness: 0.000703 =Laka= [[Comma|Commas]]: 5120/5103, 540/539 [[Minimax tuning]] [|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, |0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, |2 0 3/7 -5/7 5/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 14/11 Projection pairs: 5120/729 11 14348907/1310720 ==13 limit== [[Comma|Commas]]: 352/351, 540/539, 847/845 13 and 15 limit minimax tuning [|1 0 0 0 0 0>, |13/8 -1/2 1/8 0 0 1/8>, |13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>, |25/8 -9/2 5/8 0 0 13/8>, |13/4 -3 1/4 0 0 5/4>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13 ==17 limit== [[Comma|Commas]]: 352/351, 540/539, 847/845, 442/441 17-limit minimax [|1 0 0 0 0 0 0>, |13/12 0 0 1/12 1/6 -1/12 0>, |-7/4 0 0 5/4 3/2 -5/4 0>, |7/4 0 0 3/4 1/2 -3/4 0>, |0 0 0 0 1 0 0>, |7/4 0 0 -1/4 1/2 1/4 0>, |35/12 0 0 23/12 5/6 -23/12 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13 Map: [<1 0 0 10 -18 -13 32|, <0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|] [[Generator|Generators]]: 2, 3, 5 [[edo|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]] =Akea= [[Comma|Commas]]: 385/384, 2200/2187 [[Minimax tuning]] [|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>, |26/9 0 13/18 -7/18 -1/3>, |26/9 0 -5/18 11/18 -1/3>, |26/9 0 -5/18 -7/18 2/3>] [[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 7/5 Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|] [[Generator|Generators]]: 2, 3, 5 EDOs: 34, 41, 53, 87, 140, 181, 321 Badness: 0.000998 ==13-limit== Commas: 325/324, 352/351, 385/384 13 and 15 limit minimax [|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, |26/9 0 13/18 -7/18 -1/3 0>, |26/9 0 -5/18 11/18 -1/3 0>, |26/9 0 -5/18 -7/18 2/3 0>, |26/9 0 -7/9 1/9 2/3 0>] Eigenmonzos: 2, 14/11, 7/5 Lattice basis: 3/2 length 0.5354 27/20 length 1.0463 Angle(3/2, 27/20) = 80.5628 degrees Map to lattice: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|] Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|] Generators: 2, 3, 5 [[edo|EDOs]]: [[94edo|94]], [[140edo|140]], [[181edo|181]], [[408edo|408]] Badness: 0.000822 Scales: [[akea46_13]] =Kapo= [[Comma|Commas]]: 5120/5103, 3025/3024 [[Minimax tuning]] [|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>, |14/5 6/5 0 7/15 -16/15>, |16/5 -6/5 0 13/15 -4/15>, |16/5 -6/5 0 -2/15 11/15>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7 Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|] [[Generator|Generators]]: 2, 3, 128/99 [[edo|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]] EDOs: 41, 87, 111, 152, 239, 391 Badness: 0.000994 =Lono= Commas: 176/175, 5120/5103 Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|] EDOs: 7, 12, 39, 46, 53, 58, 99, 111 Badness: 0.00118 =Namaka= Commas: 3388/3375, 5120/5103 Map: [<1 0 0 10 -6|, <0 2 0 -12 9|, <0 0 1 1 1|] EDOs: 29, 53, 58, 87, 111, 140, 198 Badness: 0.00174 ==13-limit== Commas: 352/351, 676/675, 847/845 Map: [<1 0 0 10 -6 -1|, <0 2 0 -12 9 3|, <0 0 1 1 1 1|] EDOs: 29, 53, 58, 87, 111, 140, 198 Badness: 0.000781
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<html><head><title>Hemifamity family</title></head><body><!-- ws:start:WikiTextTocRule:26:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Vital statistics">Vital statistics</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Pele">Pele</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Laka">Laka</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: --> | <a href="#Akea">Akea</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Kapo">Kapo</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Lono">Lono</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Namaka">Namaka</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> <!-- ws:end:WikiTextTocRule:40 --><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> c = 5120/5103<br /> <br /> 7-limit minimax: 3 and 7 1/7c sharp, 5 just<br /> [|1 0 0 0>, |10/7 1/7 1/7 -1/7>, <br /> |0 0 1 0>, |10/7 -6/7 1/7 6/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 7/6<br /> <br /> 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br /> [|1 0 0 0>, |5/4 1/4 1/8 -1/8>, <br /> |0 0 1 0>, |5/2 -3/2 1/4 3/4>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 9/7<br /> <br /> Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063<br /> Angle(3/2, 10/9) = 82.112 degrees<br /> Map to lattice: [<0 1 2 -4|, <0 0 1 1|]<br /> <br /> Map: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]<br /> Generators: 2, 3, 5<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/292edo">292</a>, <a class="wiki_link" href="/490edo">490</a>, <a class="wiki_link" href="/531edo">531</a><br /> Badness: 0.000153<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 7 5120/729<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Vital statistics-Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h2> By Gene Ward Smith<br /> <a class="wiki_link_ext" href="http://www.archive.org/details/Choraled" rel="nofollow">Choraled</a> <a class="wiki_link_ext" href="http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3" rel="nofollow">play</a><br /> By Chris Vaisvil<br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3" rel="nofollow">Hemifamity27</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Pele"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pele</h1> <a class="wiki_link" href="/Comma">Commas</a>: 441/440, 896/891<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>, <br /> |17/5 -2 6/5 0 -1/5>,<br /> |16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 11/9<br /> <br /> Lattice basis: 3/2 length 0.3812 56/55 length 1.5893<br /> Angle(3/2, 56/55) = 90.4578 degrees<br /> Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]<br /> <br /> Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/128edo">128</a>, <a class="wiki_link" href="/145edo">145</a>, <a class="wiki_link" href="/232edo">232</a><br /> Badness: 0.000648<br /> <br /> Projection pairs: 7 5120/729 11 655360/59049<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Pele-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 196/195, 352/351, 364/363<br /> <br /> 13-limit minimax<br /> Eigenmonzos: 2, 10/9, 13/10<br /> <br /> 15-limit minimax<br /> Eigenmonzos: 2, 15/13, 6/5<br /> <br /> Map: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|]<br /> EDOs: 29, 41, 46, 58, 87, 145, 232<br /> Badness: 0.000703<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Laka"></a><!-- ws:end:WikiTextHeadingRule:8 -->Laka</h1> <a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 540/539<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, <br /> |0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, <br /> |2 0 3/7 -5/7 5/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 14/11<br /> <br /> Projection pairs: 5120/729 11 14348907/1310720<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Laka-13 limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13 limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 352/351, 540/539, 847/845<br /> <br /> 13 and 15 limit minimax tuning<br /> [|1 0 0 0 0 0>, |13/8 -1/2 1/8 0 0 1/8>, <br /> |13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>, <br /> |25/8 -9/2 5/8 0 0 13/8>, <br /> |13/4 -3 1/4 0 0 5/4>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 14/13<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Laka-17 limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->17 limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 352/351, 540/539, 847/845, 442/441<br /> <br /> 17-limit minimax<br /> [|1 0 0 0 0 0 0>, <br /> |13/12 0 0 1/12 1/6 -1/12 0>, <br /> |-7/4 0 0 5/4 3/2 -5/4 0>, <br /> |7/4 0 0 3/4 1/2 -3/4 0>, <br /> |0 0 0 0 1 0 0>, <br /> |7/4 0 0 -1/4 1/2 1/4 0>, <br /> |35/12 0 0 23/12 5/6 -23/12 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 14/13<br /> <br /> Map: [<1 0 0 10 -18 -13 32|, <br /> <0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/111edo">111</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/205edo">205</a>, <a class="wiki_link" href="/345edo">345</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Akea"></a><!-- ws:end:WikiTextHeadingRule:14 -->Akea</h1> <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 2200/2187<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>, <br /> |26/9 0 13/18 -7/18 -1/3>,<br /> |26/9 0 -5/18 11/18 -1/3>, <br /> |26/9 0 -5/18 -7/18 2/3>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/11, 7/5<br /> <br /> Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> EDOs: 34, 41, 53, 87, 140, 181, 321<br /> Badness: 0.000998<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Akea-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> Commas: 325/324, 352/351, 385/384<br /> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, <br /> |26/9 0 13/18 -7/18 -1/3 0>, <br /> |26/9 0 -5/18 11/18 -1/3 0>, <br /> |26/9 0 -5/18 -7/18 2/3 0>, <br /> |26/9 0 -7/9 1/9 2/3 0>]<br /> Eigenmonzos: 2, 14/11, 7/5<br /> <br /> Lattice basis: 3/2 length 0.5354 27/20 length 1.0463<br /> Angle(3/2, 27/20) = 80.5628 degrees<br /> Map to lattice: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|]<br /> <br /> Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]<br /> Generators: 2, 3, 5<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/181edo">181</a>, <a class="wiki_link" href="/408edo">408</a><br /> Badness: 0.000822<br /> Scales: <a class="wiki_link" href="/akea46_13">akea46_13</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Kapo"></a><!-- ws:end:WikiTextHeadingRule:18 -->Kapo</h1> <a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 3025/3024<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>, <br /> |14/5 6/5 0 7/15 -16/15>, <br /> |16/5 -6/5 0 13/15 -4/15>, <br /> |16/5 -6/5 0 -2/15 11/15>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br /> <br /> Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 128/99<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/198edo">198</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/350edo">350</a>, <a class="wiki_link" href="/391edo">391</a>, <a class="wiki_link" href="/478edo">478</a>, <a class="wiki_link" href="/589edo">589</a><br /> EDOs: 41, 87, 111, 152, 239, 391<br /> Badness: 0.000994<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Lono"></a><!-- ws:end:WikiTextHeadingRule:20 -->Lono</h1> Commas: 176/175, 5120/5103<br /> <br /> Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|]<br /> EDOs: 7, 12, 39, 46, 53, 58, 99, 111<br /> Badness: 0.00118<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="Namaka"></a><!-- ws:end:WikiTextHeadingRule:22 -->Namaka</h1> Commas: 3388/3375, 5120/5103<br /> <br /> Map: [<1 0 0 10 -6|, <0 2 0 -12 9|, <0 0 1 1 1|]<br /> EDOs: 29, 53, 58, 87, 111, 140, 198<br /> Badness: 0.00174<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Namaka-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> Commas: 352/351, 676/675, 847/845<br /> <br /> Map: [<1 0 0 10 -6 -1|, <0 2 0 -12 9 3|, <0 0 1 1 1 1|]<br /> EDOs: 29, 53, 58, 87, 111, 140, 198<br /> Badness: 0.000781</body></html>