Horwell family
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[[toc|flat]] The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536. =Horwell= Comma: 65625/65536 7-limit minimax [|1 0 0 0>, |16/7 6/7 -5/7 -1/7>, |16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>] Eigenmonzos: 2, 7/6, 6/5 9-limit minimax [|1 0 0 0>, |16/13 12/13 -5/13 -1/13>, |32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>] Eigenmonzos: 2, 9/7, 7/5 Lattice basis: 5/4 length=0.6213 16/15 length=1.3863 Angle(5/4, 16/15) = 64.6379 Map to lattice: [<0 -1 1 -4|, <0 -1 0 -1|] Map: [<1 0 0 16|, <0 1 0 -1|, <0 0 1 -5|] Generators: 2, 3, 5 Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995 Badness: 0.000173 [[Projection pair]]: 7 65536/9375 =Horwellic= Commas: 3025/3024, 65625/65536 Map: [<1 0 0 16 10|, <0 1 0 -1 1|, <0 0 2 -10 -7|] EDOs: 31, 87, 118, 193, 224, 311, 342 Badness: 0.000505
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<html><head><title>Horwell family</title></head><body><!-- ws:start:WikiTextTocRule:4:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Horwell">Horwell</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Horwellic">Horwellic</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> <!-- ws:end:WikiTextTocRule:7 --><br /> <br /> The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Horwell"></a><!-- ws:end:WikiTextHeadingRule:0 -->Horwell</h1> Comma: 65625/65536<br /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |16/7 6/7 -5/7 -1/7>, <br /> |16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>]<br /> Eigenmonzos: 2, 7/6, 6/5<br /> <br /> 9-limit minimax<br /> [|1 0 0 0>, |16/13 12/13 -5/13 -1/13>, <br /> |32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>]<br /> Eigenmonzos: 2, 9/7, 7/5<br /> <br /> Lattice basis: 5/4 length=0.6213 16/15 length=1.3863<br /> Angle(5/4, 16/15) = 64.6379<br /> Map to lattice: [<0 -1 1 -4|, <0 -1 0 -1|]<br /> <br /> Map: [<1 0 0 16|, <0 1 0 -1|, <0 0 1 -5|]<br /> Generators: 2, 3, 5<br /> Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995<br /> Badness: 0.000173<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 7 65536/9375<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Horwellic"></a><!-- ws:end:WikiTextHeadingRule:2 -->Horwellic</h1> Commas: 3025/3024, 65625/65536<br /> <br /> Map: [<1 0 0 16 10|, <0 1 0 -1 1|, <0 0 2 -10 -7|]<br /> EDOs: 31, 87, 118, 193, 224, 311, 342<br /> Badness: 0.000505</body></html>