Catalog of rank-4 temperaments
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==441/440== ===Commas 441/440, 364/363=== 13-limit minimax [|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>] Eigenmonzos: 2, 11/10, 8/7, 16/13 15-limit minimax [|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, |5/4 -3/4 5/4 -1/4 -1/4 1/4>, |17/8 -11/8 5/8 -1/8 3/8 1/8>, |5/2 -3/2 1/2 -1/2 1/2 1/2>, |17/8 -11/8 5/8 -9/8 3/8 9/8>] Eigenmonzos: 2, 14/13, 6/5, 11/9 Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657 Map to lattice: [<0 1 1 -1 -1 0|, <0 0 1 0 -1 -2|, <0 0 1 1 1 1|] Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <0 0 1 0 -1 -2|, <0 0 0 1 2 3|] Generators: 2, 3, 5 Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393 ===Commas 441/440, 351/350=== ==385/384== ===Commas 385/384, 325/324=== 13 and 15 limit minimax [<1 0 0 0 0 0|, <0 1 0 0 0 0|, <2/3 4/3 1/3 0 0 -1/3|, <19/6 -1/6 -1/6 1/2 -1/2 1/6|, <19/6 -1/6 -1/6 -1/2 1/2 1/6|, <2/3 4/3 -2/3 0 0 2/3|] Eigenmonzos: 2, 14/11, 13/10, 4/3 Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247 Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|] Generators: 2, 3, 5, 7 Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253 ==9801/9800== ===Commas 2080/2079, 1716/1715=== 13 and 15 limit minimax [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>] Eigenmonzos: 2, 6/5, 16/13, 9/7 Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299 Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, <0 0 1 0 1 0|, <0 0 0 1 1 2|] Generators: 99/70, 3, 5, 7 Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892
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<html><head><title>Rank four temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-441/440"></a><!-- ws:end:WikiTextHeadingRule:0 -->441/440</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-441/440-Commas 441/440, 364/363"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas 441/440, 364/363</h3> <br /> 13-limit minimax<br /> [|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, <br /> |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, <br /> |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]<br /> Eigenmonzos: 2, 11/10, 8/7, 16/13<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, <br /> |5/4 -3/4 5/4 -1/4 -1/4 1/4>, <br /> |17/8 -11/8 5/8 -1/8 3/8 1/8>, <br /> |5/2 -3/2 1/2 -1/2 1/2 1/2>, <br /> |17/8 -11/8 5/8 -9/8 3/8 9/8>]<br /> Eigenmonzos: 2, 14/13, 6/5, 11/9<br /> <br /> Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657<br /> Map to lattice: [<0 1 1 -1 -1 0|, <br /> <0 0 1 0 -1 -2|, <0 0 1 1 1 1|]<br /> <br /> Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <br /> <0 0 1 0 -1 -2|, <0 0 0 1 2 3|]<br /> Generators: 2, 3, 5<br /> Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-441/440-Commas 441/440, 351/350"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas 441/440, 351/350</h3> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-385/384"></a><!-- ws:end:WikiTextHeadingRule:6 -->385/384</h2> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-385/384-Commas 385/384, 325/324"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas 385/384, 325/324</h3> <br /> 13 and 15 limit minimax<br /> [<1 0 0 0 0 0|, <0 1 0 0 0 0|, <br /> <2/3 4/3 1/3 0 0 -1/3|, <br /> <19/6 -1/6 -1/6 1/2 -1/2 1/6|, <br /> <19/6 -1/6 -1/6 -1/2 1/2 1/6|, <br /> <2/3 4/3 -2/3 0 0 2/3|]<br /> Eigenmonzos: 2, 14/11, 13/10, 4/3<br /> <br /> Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247<br /> <br /> Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <br /> <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]<br /> Generators: 2, 3, 5, 7<br /> Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253<br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-9801/9800"></a><!-- ws:end:WikiTextHeadingRule:10 -->9801/9800</h2> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x-9801/9800-Commas 2080/2079, 1716/1715"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas 2080/2079, 1716/1715</h3> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, <br /> |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, <br /> |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]<br /> Eigenmonzos: 2, 6/5, 16/13, 9/7<br /> <br /> Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299<br /> <br /> Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, <br /> <0 0 1 0 1 0|, <0 0 0 1 1 2|]<br /> Generators: 99/70, 3, 5, 7<br /> Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892</body></html>