Kalismic temperaments

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.

This is a collection of rank-3 temperaments that temper out the kalisma, 9801/9800. These temperaments always split the octave into halves.

Temperaments discussed elsewhere are:

• Jubilismic (+50/49) → Jubilismic family
• Fantastic (+225/224) → Marvel family
• Bisector (+121/120 or 245/243) → Sensamagic family
• Varda (+176/175) → Diaschismic rank-3 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 lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing badness. For the rank-4 temperament, see Rank-4 temperament #Kalismic (9801/9800).

Lycoris

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1771561/1771470

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

mapping generators: ~99/70, ~3, ~11/9

Optimal tunings:

• WE: ~99/70 = 600.0018 ¢, ~3/2 = 701.9411 ¢, ~11/9 = 347.3976 ¢

error map: ⟨+0.004 -0.010 +0.013 -0.018 -0.031]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9414 ¢, ~11/9 = 347.3969 ¢

error map: ⟨0.000 -0.014 +0.009 +0.014 -0.038]

Optimal ET sequence: 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e

Badness (Sintel): 0.299

Higanbana

Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 10648/10647, 1399680/1399489

Mapping: [⟨2 1 -1 2 2 4], ⟨0 2 2 6 4 1], ⟨0 0 6 -5 1 4]]

mapping generators: ~99/70, ~1458/1001, ~81/70

Optimal tunings:

• WE: ~99/70 = 599.9996 ¢, ~1458/1001 = 650.9717 ¢, ~11/9 = 347.3963 ¢
• CWE: ~99/70 = 600.0000 ¢, ~1458/1001 = 650.9718 ¢, ~11/9 = 347.3964 ¢

Optimal ET sequence: 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938

Badness (Sintel): 0.389

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, ~11/10

Optimal tunings:

• WE: ~99/70 = 600.0022 ¢, ~3/2 = 701.9464 ¢, ~11/9 = 164.9319 ¢

error map: ⟨+0.004 -0.004 +0.022 +0.005 -0.046]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9469 ¢, ~11/9 = 164.9316 ¢

error map: ⟨0.000 -0.008 +0.018 -0.000 -0.055]

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 (Sintel): 0.358

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 tunings:

• WE: ~99/70 = 599.9863 ¢, ~3/2 = 701.9658 ¢, ~48/35 = 546.5930 ¢

error map: ⟨-0.027 -0.017 +0.045 +0.052 +0.000]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9755 ¢, ~48/35 = 546.6052 ¢

error map: ⟨0.000 +0.021 +0.107 +0.124 +0.101]

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 (Sintel): 0.508

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 tunings:

• WE: ~99/70 = 599.9857 ¢, ~3/2 = 701.9705 ¢, ~48/35 = 546.5927 ¢
• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9877 ¢, ~48/35 = 546.6058 ¢

Optimal ET sequence: 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff

Badness (Sintel): 0.317

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 tunings:

• WE: ~99/70 = 599.9481 ¢, ~3/2 = 702.1195 ¢, ~5/4 = 386.7636 ¢

error map: ⟨-0.104 +0.061 +0.242 -0.005 -0.128]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.1647 ¢, ~5/4 = 386.7768 ¢

error map: ⟨0.000 +0.210 +0.463 +0.163 +0.119]

Optimal ET sequence: 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c

Badness (Sintel): 0.592

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 tunings:

• WE: ~99/70 = 599.9711 ¢, ~3/2 = 702.0265 ¢, ~32/21 = 728.7942 ¢

error map: ⟨-0.058 +0.014 +0.040 +0.122 -0.040]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0635 ¢, ~32/21 = 728.8214 ¢

error map: ⟨0.000 +0.109 +0.150 +0.289 +0.134]

Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde

Badness (Sintel): 0.599

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 tunings:

• WE: ~99/70 = 599.9835 ¢, ~3/2 = 702.0253 ¢, ~32/21 = 728.7700 ¢
• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0477 ¢, ~32/21 = 728.7882 ¢

Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d

Badness (Sintel): 0.366

Linus

Main article: Linus

For the 7-limit version, see Miscellaneous 7-limit temperaments #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.

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 tunings:

• WE: ~15/14 = 119.9975 ¢, ~3/2 = 702.0188 ¢, ~5/4 = 386.6399 ¢

error map: ⟨-0.025 +0.039 +0.276 -0.215 -0.143]

• CWE: ~15/14 = 120.0000 ¢, ~3/2 = 702.0181 ¢, ~5/4 = 386.6218 ¢

error map: ⟨0.000 +0.063 +0.308 -0.186 -0.092]

Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c

Badness (Sintel): 1.34

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 tunings:

• WE: ~15/14 = 120.0054 ¢, ~3/2 = 701.9625 ¢, ~5/4 = 386.4910 ¢
• CWE: ~15/14 = 120.0000 ¢, ~3/2 = 701.9533 ¢, ~5/4 = 386.5119 ¢

Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def

Badness (Sintel): 0.721