Didymus rank-3 family
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- This revision was by author genewardsmith and made on 2010-12-11 23:31:50 UTC.
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Original Wikitext content:
These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. ==Euterpe== Commas: 81/80, 99/98 Minimax tuning [|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, |0 0 0 1 0>, |-1 0 -1/2 2 0>] Eigenmonzos: 2, 5, 7 Map: [<1 0 -4 0 1|, <0 1 4 0 -2|, <0 0 0 1 2|] EDOs: 31, 74, 88, 105 ==Calliope== Commas: 81/80, 45/44 Minimax tuning [|1 0 0 0 0>, |1 0 0 0 1/6>, |0 0 0 0 2/3>, |1 -1 0 1 1/6>, |0 0 0 0 1>] Eigenmonzos: 2, 7/3, 11 Map: [<1 0 -4 0 -6|, <0 1 4 0 6|, <0 0 0 1 0|] EDOs: 19, 26, 45 ==Clio== Commas: 81/80, 176/175 Minimax tuning ||1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, |0 0 0 1 0>, |-4 0 2 1 0>] Eigenmonzos: 2, 5, 7 Map: [<1 0 -4 0 -12|, <0 1 4 0 8|, <0 0 0 1 1|] EDOs: 31, 74, 98, 105, 129 ==Polyhymnia== Commas: 81/80, 385/384 ==Thalia== Commas: 81/80, 55/54 ==Melpomene== Commas: 81/80, 56/55 ==Urania== Commas: 81/80, 121/120 ==Terpsichore== Commas: 81/80, 540/539
Original HTML content:
<html><head><title>Didymus rank three family</title></head><body>These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Euterpe"></a><!-- ws:end:WikiTextHeadingRule:0 -->Euterpe</h2> Commas: 81/80, 99/98<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, <br /> |0 0 0 1 0>, |-1 0 -1/2 2 0>]<br /> Eigenmonzos: 2, 5, 7<br /> <br /> Map: [<1 0 -4 0 1|, <0 1 4 0 -2|, <0 0 0 1 2|]<br /> EDOs: 31, 74, 88, 105<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Calliope"></a><!-- ws:end:WikiTextHeadingRule:2 -->Calliope</h2> Commas: 81/80, 45/44<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |1 0 0 0 1/6>, |0 0 0 0 2/3>, <br /> |1 -1 0 1 1/6>, |0 0 0 0 1>]<br /> Eigenmonzos: 2, 7/3, 11<br /> <br /> Map: [<1 0 -4 0 -6|, <0 1 4 0 6|, <0 0 0 1 0|]<br /> EDOs: 19, 26, 45<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Clio"></a><!-- ws:end:WikiTextHeadingRule:4 -->Clio</h2> Commas: 81/80, 176/175<br /> <br /> Minimax tuning<br /> ||1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, <br /> |0 0 0 1 0>, |-4 0 2 1 0>]<br /> Eigenmonzos: 2, 5, 7<br /> <br /> Map: [<1 0 -4 0 -12|, <0 1 4 0 8|, <0 0 0 1 1|]<br /> EDOs: 31, 74, 98, 105, 129<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Polyhymnia"></a><!-- ws:end:WikiTextHeadingRule:6 -->Polyhymnia</h2> Commas: 81/80, 385/384<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-Thalia"></a><!-- ws:end:WikiTextHeadingRule:8 -->Thalia</h2> Commas: 81/80, 55/54<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-Melpomene"></a><!-- ws:end:WikiTextHeadingRule:10 -->Melpomene</h2> Commas: 81/80, 56/55<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Urania"></a><!-- ws:end:WikiTextHeadingRule:12 -->Urania</h2> Commas: 81/80, 121/120<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-Terpsichore"></a><!-- ws:end:WikiTextHeadingRule:14 -->Terpsichore</h2> Commas: 81/80, 540/539</body></html>