Ragismic family

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The ragismic family of temperaments are rank-3 microtemperaments which temper out 4375/4374.

Temperaments not discussed here include ennealimmic.

Ragismic

Subgroup: 2.3.5.7

Comma list: 4375/4374

Mapping: [1 0 0 1], 0 1 0 7], 0 0 1 -4]]

Mapping generators: ~2, ~3, ~5

Mapping to lattice: [0 -1 -1 -3], 0 -1 -2 1]]

Lattice basis:

10/9 length = 0.789, 6/5 length = 0.921
Angle (10/9, 6/5) = 105.299°

Minimax tuning:

Optimal GPV sequence19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c

Projection pair: ~7 = ~4374/625

Scales: Ragismic19

Beyla

Subgroup: 2.3.5.7.11

Comma list: 385/384, 4375/4374

Mapping: [1 0 0 1 6], 0 1 0 7 -6], 0 0 1 -4 3]]

Mapping generators: ~2, ~3, ~5

Optimal GPV sequence7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee

Badness: 0.721 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 385/384

Mapping: [1 0 0 1 6 2], 0 1 0 7 -6 4], 0 0 1 -4 3 -2]]

Mapping generators: ~2, ~3, ~5

Vals: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff

Badness: 0.840 × 10-3

Thor

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374

Mapping: [2 0 0 2 5], 0 1 0 7 5], 0 0 1 -4 -3]]

Mapping generators: ~99/70, ~3, ~5

Minimax tuning:

Optimal GPV sequence26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee

Badness: 0.0888 × 10-3

Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11

Thunor

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 3025/3024

Mapping: [2 0 0 2 5 -3], 0 1 0 7 5 15], 0 0 1 -4 -3 -8]]

Mapping generators: ~99/70, ~3, ~5

Mapping to lattice: [0 -1 -2 -3 -2 -7], 0 -1 -2 1 1 1]]

Lattice basis:

10/9 length = 0.4234, 6/5 length = 0.8426
Angle (10/9, 6/5) = 84.126°

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzos: 2, 16/13, 9/7

Vals: 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258

Badness: 0.341 × 10-3

Rym

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4096/4095, 4375/4374

Mapping: [2 0 0 2 5 22], 0 1 0 7 5 -9], 0 0 1 -4 -3 3]]

Mapping generators: ~99/70, ~3, ~5

Vals: 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870

Badness: 0.549 × 10-3

Donar

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4225/4224, 4375/4374

Mapping: [2 0 1 -2 2 7], 0 1 0 7 5 3], 0 0 2 -8 -6 -5]]

Mapping generators: ~99/70, ~3, ~220/117

Mapping to lattice: [0 2 2 6 4 1], 0 -1 -2 1 1 2]]

Lattice basis:

44/39 length = 0.3480, 6/5 length = 0.7828
Angle (44/39, 6/5) = 85.3977°

Minimax tuning:

  • 13-odd-limit eigenmonzos: 2, 11/10, 8/7
  • 15-odd-limit eigenmonzos: 2, 8/7, 15/11

Vals: 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff

Badness: 0.322 × 10-3

Scales: Donar46

Heimdall

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 117649/117612

Mapping: [1 0 0 1 2], 0 2 0 14 37], 0 0 1 -4 -12]]

Mapping generators: ~2, ~343/198, ~5

Optimal GPV sequence270, 342, 612, 954, 1547, 1817

Bragi

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 2097152/2096325

Mapping: [1 0 2 -7 8], 0 1 0 7 -3], 0 0 3 -12 2]]

Mapping generators: 2, ~3, ~320/297

Optimal GPV sequence46, 224, 270, 494, 764, 1053, 1547

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4375/4374, 10985/10976

Mapping: [1 0 2 -7 8 -6], 0 1 0 7 -3 7], 0 0 3 -12 2 -13]]

Mapping generators: 2, ~3, ~14/13

Vals: 19, 46, 224, 270, 494, 764

Vidar

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 100663296/100656875

Mapping: [1 0 0 1 5], 0 1 -1 11 1], 0 0 5 -20 -4]]

Mapping generators: ~2, ~3, ~55/32

Optimal GPV sequence46, 224, 270, 494, 764, 1395, 1889

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 4225/4224, 4375/4374, 6656/6655

Mapping: [1 0 0 1 5 6], 0 1 -1 11 1 2], 0 0 5 -20 -4 -7]]

Mapping generators: ~2, ~3, ~55/32

Vals: 46, 224, 270, 494, 764, 1395, 1889