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
- Odin (+151263/151250) → Landscape 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
Lycoris tempers out the parimo in addition to the kalisma, and splits the syntonic comma into three equal parts, one for 121/120, and two for 243/242. It is therefore supported by third-comma equal temperaments. 342edo shows an excellent example of this, but it can be tuned much more accurate.
It was named by Flora Canou in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime.
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
- 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
- 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
Sif tempers out 2097152/2096325, and extends to a strong 13-limit temperament by virtue of the identity 2097152/2096325 = (4096/4095)⋅(6656/6655). It was named by Flora Canou in 2023 as a sharp-tending counterpart of thor.
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
- 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
- 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
Pessoal tempers out the olympia. It was named by Aura in 2023, meaning "personal", for the fact that it is associated with abigail, which is in turn a person's name.
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
- 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
- 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]]
- 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