Ragismic family
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[[toc]] =Ragisma= Comma: 4375/4374 7-limit [|1 0 0 0>, |-1/7 0 4/7 1/7>, |0 0 1 0>, |0 0 0 1>] Eigenmonzos: 2, 8/7, 5/4 9-limit [|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, 4/3, 7/5 Lattice basis: 10/9 length=0.789 6/5 length=0.921 Angle(10/9, 6/5) = 105.299 Map to lattice: [<0 -1 -1 -3|, <0 -1 -2 1|] Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|] Generators: 2, 3, 5 Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 [[Projection pair]]: 7 4374/625 Scales: [[ragismic19]] ==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 Badness: 0.0000888 Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11 ==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 Badness: 0.000322 Scales: [[donar46]] ==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 Badness: 0.000341 ==Rym== Commas: 4375/4374, 3025/3024, 4096/4095 Map: [<2 0 0 2 5 22|, <0 1 0 7 5 -9|, <0 0 1 -4 -3 3|] EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 Badness: 0.000549 =Vidar= Commas: 4375/4374, 100663296/100656875 =Bragi= Commas: 4375/4374, 2097152/2096325 =Beyla= Commas: 4374/4375, 385/384 Map: [<1 0 0 1 6|, <0 1 0 7 -6|, <0 0 1 -4 3|] EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde Badness: 0.000721 ==13-limit== Commas: 169/168, 325/324, 385/384 Map: [<1 0 0 1 6 2|, <0 1 0 7 -6 4|, <0 0 1 -4 3 -2|] EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef Badness: 0.000840
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<html><head><title>Ragisma family</title></head><body><!-- ws:start:WikiTextTocRule:20:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 1em;"><a href="#Ragisma">Ragisma</a></div> <!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 2em;"><a href="#Ragisma-11 limit children">11 limit children</a></div> <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#Thor">Thor</a></div> <!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#Thor-Donar">Donar</a></div> <!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 2em;"><a href="#Thor-Thunor">Thunor</a></div> <!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Thor-Rym">Rym</a></div> <!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Vidar">Vidar</a></div> <!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 1em;"><a href="#Bragi">Bragi</a></div> <!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#Beyla">Beyla</a></div> <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#Beyla-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --></div> <!-- ws:end:WikiTextTocRule:31 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Ragisma"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ragisma</h1> Comma: 4375/4374<br /> <br /> 7-limit<br /> [|1 0 0 0>, |-1/7 0 4/7 1/7>, |0 0 1 0>, |0 0 0 1>]<br /> Eigenmonzos: 2, 8/7, 5/4<br /> <br /> 9-limit<br /> [|1 0 0 0>, |0 1 0 0>, |1/5 7/5 1/5 -1/5>, <br /> |1/5 7/5 -4/5 4/5>]<br /> Eigenmonzos: 2, 4/3, 7/5<br /> <br /> Lattice basis: 10/9 length=0.789 6/5 length=0.921<br /> Angle(10/9, 6/5) = 105.299<br /> Map to lattice: [<0 -1 -1 -3|, <0 -1 -2 1|]<br /> <br /> Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|]<br /> Generators: 2, 3, 5<br /> Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 <br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 7 4374/625<br /> <br /> Scales: <a class="wiki_link" href="/ragismic19">ragismic19</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Ragisma-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit children</h2> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Thor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Thor</h1> 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 /> Badness: 0.0000888<br /> <br /> Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Thor-Donar"></a><!-- ws:end:WikiTextHeadingRule:6 -->Donar</h2> 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 /> Badness: 0.000322<br /> <br /> Scales: <a class="wiki_link" href="/donar46">donar46</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Thor-Thunor"></a><!-- ws:end:WikiTextHeadingRule:8 -->Thunor</h2> 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<br /> Badness: 0.000341<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Thor-Rym"></a><!-- ws:end:WikiTextHeadingRule:10 -->Rym</h2> Commas: 4375/4374, 3025/3024, 4096/4095<br /> <br /> Map: [<2 0 0 2 5 22|, <0 1 0 7 5 -9|, <0 0 1 -4 -3 3|]<br /> EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870<br /> Badness: 0.000549 <br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Vidar"></a><!-- ws:end:WikiTextHeadingRule:12 -->Vidar</h1> Commas: 4375/4374, 100663296/100656875<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Bragi"></a><!-- ws:end:WikiTextHeadingRule:14 -->Bragi</h1> Commas: 4375/4374, 2097152/2096325<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Beyla"></a><!-- ws:end:WikiTextHeadingRule:16 -->Beyla</h1> Commas: 4374/4375, 385/384<br /> <br /> Map: [<1 0 0 1 6|, <0 1 0 7 -6|, <0 0 1 -4 3|]<br /> EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde<br /> Badness: 0.000721<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Beyla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> Commas: 169/168, 325/324, 385/384<br /> <br /> Map: [<1 0 0 1 6 2|, <0 1 0 7 -6 4|, <0 0 1 -4 3 -2|]<br /> EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef<br /> Badness: 0.000840</body></html>