Kalismic temperaments
These are rank-3 temperaments tempering out 9801/9800. Temperaments discussed elsewhere are:
- Jubilee (+50/49 or 99/98) → Jubilismic family
- Fantastic (+225/224) → Marvel family
- Bisector (+121/120 or 245/243) → Sensamagic family
- Julius or varda (+176/175) → Diaschismic rank three family
- Hagrid (+243/242) → Cataharry family
- Uniwiz (+385/384) → Keenanismic temperaments
- Varuna (+441/440) → Werckismic temperaments
- Hades (+540/539) → Swetismic temperaments
- Dimcomp (+1375/1372) → Dimcomp family
- Baldur (+2401/2400) → Breed family
- Thor (+3025/3024 or 4375/4374) → Ragismic family
- Semiporwell (+6144/6125) → Porwell family
- Semicanou (+14641/14580) → Canou family
Considered below are odin, lycoris, van gogh, hnoss, sif, loki, pessoal and rishi. For the rank-4 temperament, see Rank-4 temperament #Kalismic (9801/9800).
Odin
- See also: Landscape family
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 151263/151250
Mapping: [⟨6 0 0 8 17], ⟨0 1 0 -2 -4], ⟨0 0 1 2 3]]
- mapping generators: ~55/49, ~3, ~5
Optimal ET sequence: 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e
Badness: 0.116 × 10-3
Lycoris
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 1771561/1771470
Mapping: [⟨2 0 4 -6 1], ⟨0 1 1 3 2], ⟨0 0 -6 5 -1]]
- mapping generators: ~99/70, ~3, ~81/70
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.9439, ~81/70 = 252.6028
Optimal ET sequence: 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e
Badness: 0.249 × 10-3
Higanbana
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 10648/10647, 1399680/1399489
Mapping: [⟨2 1 5 -3 3 8], ⟨0 2 2 6 4 1], ⟨0 0 -6 5 -1 4]]
- mapping generators: ~99/70, ~1458/1001, ~81/70
Optimal tuning (CTE): ~99/70 = 1\2, ~1458/1001 = 650.9715, ~81/70 = 252.6037
Optimal ET sequence: 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938
Badness: 0.416 × 10-3
Van gogh
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 199297406/199290375
Mapping: [⟨2 0 8 0 11], ⟨0 1 1 2 1], ⟨0 0 -9 -1 -10]]
- mapping generators: ~99/70, ~3, ~9/7
Optimal ET sequence: 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992
Badness: 0.297 × 10-3
Hnoss
To the wizma [-6 -8 2 5⟩ = 420175/419904, the kalisma is a natural complement, as their product is the tinge.
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472
Mapping: [⟨2 0 1 2 6], ⟨0 1 4 0 2], ⟨0 0 -5 2 -3]]
- mapping generators: ~99/70, ~3, ~144/77
Optimal ET sequence: 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee
Badness: 0.368 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 17303/17280
Mapping: [⟨2 0 1 2 6 -3], ⟨0 1 4 0 2 1], ⟨0 0 -5 2 -3 4]]
Optimal ET sequence: 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef
Badness: 0.867 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1089/1088, 1225/1224, 2025/2023
Mapping: [⟨2 0 1 2 6 -3 0], ⟨0 1 4 0 2 1 6], ⟨0 0 -5 2 -3 4 -6]]
Optimal ET sequence: 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f
Badness: 0.862 × 10-3
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199
Mapping: [⟨2 0 1 2 6 -3 0 13], ⟨0 1 4 0 2 1 6 2], ⟨0 0 -5 2 -3 4 -6 -6]]
Optimal ET sequence: 72, 94, 166g, 198g, 270, 436, 634g, 706f
Badness: 0.901 × 10-3
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736
Mapping: [⟨2 0 1 2 6 -3 0 13 19], ⟨0 1 4 0 2 1 6 2 -2], ⟨0 0 -5 2 -3 4 -6 -6 -2]]
Optimal ET sequence: 72, 94, 166g, 270, 342f, 436, 706fi
Badness: 1.14 × 10-3
Gersemi
The extension to 13-limit with 4225/4224 is weak but facilitates the use of 18/7 as the equave. Fokker blocks of 128 notes are available for the latter, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)3 ~ 17/1 via the chlorisma. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings.
Subgroup: 2.3.5.7.11.13
Comma list: 4225/4224, 9801/9800, 41503/41472
Mapping: [⟨2 0 1 2 6 9], ⟨0 1 9 -2 5 -6], ⟨0 0 -10 4 -6 7]]
- mapping generators: ~99/70, ~3, ~154/65
Optimal ET sequence: 44, 50, 94, 144, 176, 220, 270, 590, 684, 954
Badness: 1.06 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1089/1088, 1225/1224, 2025/2023, 4225/4224
Mapping: [⟨2 0 1 2 6 9 0], ⟨0 1 9 -2 5 -6 12], ⟨0 0 -10 4 -6 7 -12]]
Optimal ET sequence: 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684
Badness: 1.46 × 10-3
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757
Mapping: [⟨2 0 1 2 6 9 0 1], ⟨0 1 9 -2 5 -6 12 11], ⟨0 0 -10 4 -6 7 -12 -11]]
Optimal ET sequence: 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h
Badness: 1.11 × 10-3
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925
Mapping: [⟨2 0 1 2 6 9 0 1 7], ⟨0 1 9 -2 5 -6 12 11 3], ⟨0 0 -10 4 -6 7 -12 -11 -3]]
Optimal ET sequence: 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi
Badness: 1.23 × 10-3
Sif
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 2097152/2096325
Mapping: [⟨2 0 1 7 11], ⟨0 1 0 1 -1], ⟨0 0 4 -5 -1]]
- mapping generators: ~99/70, ~3
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.9492, ~48/35 = 546.6041
Optimal ET sequence: 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee
Badness: 0.423 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 6656/6655, 9801/9800
Mapping: [⟨2 0 1 7 11 16], ⟨0 1 0 1 -1 -3], ⟨0 0 4 -5 -1 1]]
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.9902, ~48/35 = 546.6064
Optimal ET sequence: 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff
Badness: 0.339 × 10-3
Loki
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800
Mapping: [⟨2 0 0 -21 -18], ⟨0 1 0 4 2], ⟨0 0 1 3 4]]
- mapping generators: ~99/70, ~3, ~5
Optimal ET sequence: 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c
Badness: 0.493 × 10-3
Pessoal
- See also: Pessoalisma
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 131072/130977
Mapping: [⟨2 0 1 10 14], ⟨0 1 0 -1 -3], ⟨0 0 3 -1 2]]
- mapping generators: ~99/70, ~3, ~32/21
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0759, ~32/21 = 728.7910
Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde
Badness: 0.499 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 4096/4095
Mapping: [⟨2 0 1 10 14 13], ⟨0 1 0 -1 -3 -1], ⟨0 0 3 -1 2 -2]]
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786
Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d
Badness: 0.391 × 10-3
Linus
- Main article: Linus
Linus tempers out the linus comma, [11 -10 -10 10⟩ in the 7-limit and can be described as the 80 & 130 & 270 temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.
7-limit
Subgroup: 2.3.5.7
Comma list: 578509309952/576650390625
Mapping: [⟨10 0 0 -11], ⟨0 1 0 1], ⟨0 0 1 1]]
- mapping generators: ~15/14, ~3, ~5
Optimal tuning (CTE): ~15/14 = 1\10, ~3/2 = 702.0437, ~5/4 = 386.5040
Optimal ET sequence: 50, 60, 80, 130, 270, 1270, 1540, 1810, 1940, 2080, 2210c, 2480c
Badness: 1.12 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 391314/390625
Mapping: [⟨10 0 0 -11 4], ⟨0 1 0 1 -1], ⟨0 0 1 1 2]]
Optimal tuning (CTE): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5927
Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c
Badness: 1.12 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455
Mapping: [⟨10 0 0 -11 4 37], ⟨0 1 0 1 -1 0], ⟨0 0 1 1 2 0]]
Optimal tuning (CTE): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5928
Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def
Badness: 0.771 × 10-3
Rishi
The 7-limit comma [65 -84 10 16⟩ ~ 0.13¢ has the ratio of the exponents of 3 and 2 that is close to the one in 81/8. The square root of the latter is close to 35/11. This suggests tempering out (81/8)(35/11)-2, which is the kalisma.
Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another equave that comes to mind is 3/2, especially after tempering out the chalmersia. When 3/2 is chosen as the equave, Fokker blocks of 34 notes can be used that are close to 34edf and 58edo.
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 572145834917888/571919811374025
Mapping: [⟨2 0 3 -10 -4], ⟨0 1 2 4 4], ⟨0 0 8 -5 3]]
- mapping generators: ~99/70, ~3, ~17364375/14172488
Optimal ET sequence: 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e
Badness: 2.10 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 10648/10647, 371293/371250
Mapping: [⟨2 0 3 -10 -4 2], ⟨0 1 2 4 4 3], ⟨0 0 8 -5 3 7]]
Optimal ET sequence: 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e
Badness: 0.505 × 10-3