Ragismic family: Difference between revisions
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=Ragisma= | = Ragisma = | ||
Comma: 4375/4374 | Comma: 4375/4374 | ||
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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 | 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]] | Scales: [[Ragismic19]] | ||
=Thor= | = Thor = | ||
Commas: 4375/4374 | Commas: 3025/3024, 4375/4374 | ||
Minimax tuning | Minimax tuning | ||
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Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11 | Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11 | ||
==Donar== | == Donar == | ||
Commas: | Commas: 3025/3024, 4225/4224, 4375/4374 | ||
13-limit minimax | 13-limit minimax | ||
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Scales: [[Donar46]] | Scales: [[Donar46]] | ||
==Thunor== | == Thunor == | ||
Commas: | Commas: 1716/1715, 3025/3024, 4375/4374 | ||
13 and 15 limit minimax | 13 and 15 limit minimax | ||
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Badness: 0.000341 | Badness: 0.000341 | ||
==Rym== | == Rym == | ||
Commas: | Commas: 3025/3024, 4096/4095, 4375/4374 | ||
Map: [<2 0 0 2 5 22|, <0 1 0 7 5 -9|, <0 0 1 -4 -3 3|] | Map: [<2 0 0 2 5 22|, <0 1 0 7 5 -9|, <0 0 1 -4 -3 3|] | ||
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Badness: 0.000549 | Badness: 0.000549 | ||
=Vidar= | = Vidar = | ||
Commas: 4375/4374, 100663296/100656875 | Commas: 4375/4374, 100663296/100656875 | ||
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EDOs: 46, 224, 270, 494, 764, 1395, 1889 | EDOs: 46, 224, 270, 494, 764, 1395, 1889 | ||
==13-limit== | == 13-limit == | ||
Commas: 4225/4224, 4375/4374, 6656/6655 | Commas: 4225/4224, 4375/4374, 6656/6655 | ||
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EDOs: 46, 224, 270, 494, 764, 1395, 1889 | EDOs: 46, 224, 270, 494, 764, 1395, 1889 | ||
=Bragi= | = Bragi = | ||
Commas: 4375/4374, 2097152/2096325 | Commas: 4375/4374, 2097152/2096325 | ||
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EDOs: 46, 224, 270, 494, 764, 1053, 1547 | EDOs: 46, 224, 270, 494, 764, 1053, 1547 | ||
=Beyla= | = Beyla = | ||
Commas: | Commas: 385/384, 4375/4374 | ||
Map: [<1 0 0 1 6|, <0 1 0 7 -6|, <0 0 1 -4 3|] | Map: [<1 0 0 1 6|, <0 1 0 7 -6|, <0 0 1 -4 3|] | ||
| Line 150: | Line 150: | ||
Badness: 0.000721 | Badness: 0.000721 | ||
==13-limit== | == 13-limit == | ||
Commas: 169/168, 325/324, 385/384 | Commas: 169/168, 325/324, 385/384 | ||
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[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Ragisma]] | [[Category:Ragisma]] | ||
[[Category:Rank 3]] | |||
Revision as of 06:07, 6 January 2021
Ragisma
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, 8/7, 5/4
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, 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
Thor
Commas: 3025/3024, 4375/4374
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: 3025/3024, 4225/4224, 4375/4374
13-limit minimax
[|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: 1716/1715, 3025/3024, 4375/4374
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: 3025/3024, 4096/4095, 4375/4374
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
Map: [<1 0 0 1 5|, <0 1 -1 11 1|, <0 0 5 -20 -4|]
EDOs: 46, 224, 270, 494, 764, 1395, 1889
13-limit
Commas: 4225/4224, 4375/4374, 6656/6655
Map: [<1 0 0 1 5 6|, <0 1 -1 11 1 2|, <0 0 5 -20 -4 -7|]
EDOs: 46, 224, 270, 494, 764, 1395, 1889
Bragi
Commas: 4375/4374, 2097152/2096325
Map: [<1 0 2 -7 8|, <0 1 0 7 -3|, <0 0 3 -12 2|]
EDOs: 46, 224, 270, 494, 764, 1053, 1547
Beyla
Commas: 385/384, 4375/4374
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