Ragismic family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The ragismic family of temperaments are rank-3 microtemperaments which temper out 4375/4374.
Temperaments discussed elsewhere include:
Considered below are beyla, ulmo, thor, heimdall, bragi, and vidar.
Ragismic
Subgroup: 2.3.5.7
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°
- 7-odd-limit unchanged-interval (eigenmonzo) basis: 2.5.7
- 9-odd-limit unchanged-interval (eigenmonzo) basis: 2.3.7/5
Optimal ET sequence: 19, 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, Ragismic chromatic
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]]
Optimal ET sequence: 7, 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]]
Optimal ET sequence: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff
Badness: 0.840 × 10-3
Ulmo
Subgroup: 2.3.5.7.11
Comma list: 176/175, 2200/2187
Mapping: [⟨1 0 0 1 -3], ⟨0 1 0 7 7], ⟨0 0 1 -4 -2]]
Optimal ET sequence: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
Badness: 1.23 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324
Mapping: [⟨1 0 0 1 -3 2], ⟨0 1 0 7 7 4], ⟨0 0 1 -4 -2 -2]]
Optimal ET sequence: 7, 39, 46, 53, 80, 133d, 179, 312cdf
Badness: 0.932 × 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
Optimal ET sequence: 26, 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 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 unchanged-interval (eigenmonzo) basis: 2.9/7.13
Optimal ET sequence: 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]]
Optimal ET sequence: 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 unchanged-interval (eigenmonzo) basis: 2.7.11/5
- 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11
Optimal ET sequence: 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 ET sequence: 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d
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 ET sequence: 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee
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]]
Optimal ET sequence: 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f
Vidar
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 100663296/100656875
Mapping: [⟨1 0 0 1 5], ⟨0 1 4 -9 -3], ⟨0 0 -5 20 4]]
- mapping generators: ~2, ~3, ~96/55
Optimal ET sequence: 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894
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 4 -9 -3 -5], ⟨0 0 -5 20 4 7]]
Optimal ET sequence: 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f