Ragismic family
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Comma: 4375/4374 7-limit minimax [|1 0 0 0>, |-1/7 0 4/7 1/7>, |0 0 1 0>, |0 0 0 1>] Eigenmonzos: 2, 5, 7 9-limit minimax ||1 0 0 0>, |0 1 0 0>, |1/5 7/5 1/5 -1/5>, |1/5 7/5 -4/5 4/5>] Eigenmonzos: 2, 3, 7/5 Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|] Generators: 2, 3, 5 Edos: 7, 19, 26, 27, 45, 46, 53, 65, 72, 80, 91, 99, 171, 270, 441, 612, 935, 1106, 1277, 1376, 1547, 1718, 1889, 2923, 3166, 3436, 3877, 3535, 4390, 5496, 5937, 6450, 9058 ==11 limit children== ===Thor=== Commas: 4375/4374, 3025/3024 Minimax tuning [|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |25/16 0 7/8 5/8 -7/8>, |0 0 0 1 0>, |25/16 0 -1/8 5/8 1/8>] Eigenmonzos: 2, 11/10, 8/7 Map: [<2 0 0 2 5|, <0 1 0 7 5|, <0 0 1 -4 -3|] Generators: 99/70, 3, 5 13-limit ====Donar==== Commas: 4375/4374, 3025/3024, 4225/4224 13-limit ||1 0 0 0 0 0>, |3/4 0 1/2 1/2 -1/2 0>, |25/16 0 7/8 5/8 -7/8 0>, |0 0 0 1 0 0>, |25/16 0 -1/8 5/8 1/8 0>, |99/32 0 -11/16 -1/16 11/16 0>] Eigenmonzos: 2, 11/10, 8/7 15-limit minimax [|1 0 0 0 0 0>, |1/2 1/3 1/3 1/3 -1/3 0>, |9/8 7/12 7/12 1/3 -7/12 0>, |0 0 0 1 0 0>, |13/8 -1/12 -1/12 2/3 1/12 0>, |55/16 -11/24 -11/24 1/6 11/24 0>] Eigenmonzos: 2, 8/7, 15/11 Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828 Angle(44/39, 6/5) = 85.3977 Map to lattice: [<0 2 2 6 4 1|, <0 -1 -2 1 1 2|] Map: [<2 0 1 -2 2 7|, <0 1 0 7 5 3|, <0 0 2 -8 -6 -5|] Generators: 99/70, 3, 220/117 Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390 ====Thunor==== Commas: 4375/4374, 3025/3024, 1716/1715 13 and 15 limit minimax [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |9/8 3/2 0 -3/4 0 1/4>, |7/5 -2/5 0 1/5 0 2/5>, |21/8 -1/2 0 1/4 0 1/4>, |0 0 0 0 0 1>] Eigenmonzos: 2, 16/13, 9/7 Lattice basis: 10/9 length 0.4234 6/5 length 0.8426 Angle(10/9, 6/5) = 84.126 degrees Map to lattice: [<0 -1 -2 -3 -2 -7|, <0 -1 -2 1 1 1|] Map: [<2 0 0 2 5 -3|, <0 1 0 7 5 15|, <0 0 1 -4 -3 -8|] Generators: 99/70, 3, 5 Edos: 26, 46, 72, 178, 224, 270, 494
Original HTML content:
<html><head><title>Ragisma family</title></head><body>Comma: 4375/4374<br /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |-1/7 0 4/7 1/7>, <br /> |0 0 1 0>, |0 0 0 1>]<br /> Eigenmonzos: 2, 5, 7<br /> <br /> 9-limit minimax<br /> ||1 0 0 0>, |0 1 0 0>, <br /> |1/5 7/5 1/5 -1/5>, |1/5 7/5 -4/5 4/5>]<br /> Eigenmonzos: 2, 3, 7/5<br /> <br /> Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|]<br /> Generators: 2, 3, 5<br /> Edos: 7, 19, 26, 27, 45, 46, 53, 65, 72, 80, 91, 99, 171, 270, 441, 612, 935, 1106, 1277, 1376, 1547, 1718, 1889, 2923, 3166, 3436, 3877, 3535, 4390, 5496, 5937, 6450, 9058<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->11 limit children</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-11 limit children-Thor"></a><!-- ws:end:WikiTextHeadingRule:2 -->Thor</h3> Commas: 4375/4374, 3025/3024<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, <br /> |25/16 0 7/8 5/8 -7/8>, |0 0 0 1 0>, <br /> |25/16 0 -1/8 5/8 1/8>]<br /> Eigenmonzos: 2, 11/10, 8/7<br /> <br /> Map: [<2 0 0 2 5|, <0 1 0 7 5|, <0 0 1 -4 -3|]<br /> Generators: 99/70, 3, 5<br /> <br /> 13-limit<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h4> --><h4 id="toc2"><a name="x-11 limit children-Thor-Donar"></a><!-- ws:end:WikiTextHeadingRule:4 -->Donar</h4> Commas: 4375/4374, 3025/3024, 4225/4224<br /> <br /> 13-limit<br /> ||1 0 0 0 0 0>, |3/4 0 1/2 1/2 -1/2 0>, <br /> |25/16 0 7/8 5/8 -7/8 0>, |0 0 0 1 0 0>, <br /> |25/16 0 -1/8 5/8 1/8 0>, <br /> |99/32 0 -11/16 -1/16 11/16 0>]<br /> Eigenmonzos: 2, 11/10, 8/7<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |1/2 1/3 1/3 1/3 -1/3 0>, <br /> |9/8 7/12 7/12 1/3 -7/12 0>, |0 0 0 1 0 0>, <br /> |13/8 -1/12 -1/12 2/3 1/12 0>, <br /> |55/16 -11/24 -11/24 1/6 11/24 0>]<br /> Eigenmonzos: 2, 8/7, 15/11<br /> <br /> Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828<br /> Angle(44/39, 6/5) = 85.3977<br /> Map to lattice: [<0 2 2 6 4 1|, <0 -1 -2 1 1 2|]<br /> <br /> Map: [<2 0 1 -2 2 7|, <0 1 0 7 5 3|, <0 0 2 -8 -6 -5|]<br /> Generators: 99/70, 3, 220/117<br /> Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h4> --><h4 id="toc3"><a name="x-11 limit children-Thor-Thunor"></a><!-- ws:end:WikiTextHeadingRule:6 -->Thunor</h4> Commas: 4375/4374, 3025/3024, 1716/1715<br /> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, <br /> |9/8 3/2 0 -3/4 0 1/4>, |7/5 -2/5 0 1/5 0 2/5>, |21/8 -1/2 0 1/4 0 1/4>, |0 0 0 0 0 1>]<br /> Eigenmonzos: 2, 16/13, 9/7<br /> <br /> Lattice basis: 10/9 length 0.4234 6/5 length 0.8426<br /> Angle(10/9, 6/5) = 84.126 degrees<br /> Map to lattice: [<0 -1 -2 -3 -2 -7|, <0 -1 -2 1 1 1|] <br /> <br /> Map: [<2 0 0 2 5 -3|, <0 1 0 7 5 15|, <0 0 1 -4 -3 -8|]<br /> Generators: 99/70, 3, 5<br /> Edos: 26, 46, 72, 178, 224, 270, 494</body></html>