Kalismic temperaments: Difference between revisions

Revision as of 14:21, 19 April 2026

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 odin, lycoris, van gogh, sif, loki, pessoal, and linus. 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 (Smith): 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 = 600.0000 ¢, ~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 (Smith): 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 = 600.0000 ¢, ~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 (Smith): 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 (Smith): 0.297 × 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 = 600.0000 ¢, ~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 (Smith): 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 = 600.0000 ¢, ~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 (Smith): 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 (Smith): 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 = 600.0000 ¢, ~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 (Smith): 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 = 600.0000 ¢, ~3/2 = 702.0637 ¢, ~32/21 = 728.7786 ¢

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

Badness (Smith): 0.391 × 10^-3

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 tuning (CTE): ~15/14 = 120.0000 ¢, ~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 (Smith): 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 = 1200.0000 ¢, ~3/2 = 702.0010 ¢, ~5/4 = 386.5928 ¢

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

Badness (Smith): 0.771 × 10^-3

@@ Line 1: / Line 1: @@
 __FORCETOC__
 {{Technical data page}}
-These are [[rank-3 temperament]]s tempering out [[9801/9800]]. Temperaments discussed elsewhere are:
+This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the kalisma, [[9801/9800]]. These temperaments always split the octave into halves.
+Temperaments discussed elsewhere are:
 * ''[[Jubilismic]]'' (+50/49) → [[Jubilismic family #Undecimal jubilismic|Jubilismic family]]
 * ''[[Fantastic]]'' (+225/224) → [[Marvel family #Fantastic|Marvel family]]
@@ Line 26: / Line 28: @@
 {{Mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}
 : mapping generators: ~55/49, ~3, ~5
 {{Optimal ET sequence|legend=1| 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<sup>-3</sup>
+[[Badness]] (Smith): 0.116 × 10<sup>-3</sup>
 == Lycoris ==
@@ Line 39: / Line 40: @@
 {{Mapping|legend=1| 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 tuning]] ([[CTE]]): ~99/70 = 600.0000{{c}}, ~3/2 = 701.9439{{c}}, ~81/70 = 252.6028{{c}}
 {{Optimal ET sequence|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}
-[[Badness]]: 0.249 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.249 × 10<sup>-3</sup>
 === Higanbana ===
@@ Line 54: / Line 54: @@
 Mapping: {{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 tuning (CTE): ~99/70 = 600.0000{{c}}, ~1458/1001 = 650.9715{{c}}, ~81/70 = 252.6037{{c}}
-{{Optimal ET sequence|legend=1| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
+{{Optimal ET sequence|legend=0| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
-Badness: 0.416 × 10<sup>-3</sup>
+Badness (Smith): 0.416 × 10<sup>-3</sup>
 == Van gogh ==
@@ Line 69: / Line 68: @@
 {{Mapping|legend=1| 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|legend=1| 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<sup>-3</sup>
+[[Badness]] (Smith): 0.297 × 10<sup>-3</sup>
 == Sif ==
@@ Line 82: / Line 80: @@
 {{Mapping|legend=1| 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 tuning]] ([[CTE]]): ~99/70 = 600.0000{{c}}, ~3/2 = 701.9492{{c}}, ~48/35 = 546.6041{{c}}
 {{Optimal ET sequence|legend=1| 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<sup>-3</sup>
+[[Badness]] (Smith): 0.423 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 98: / Line 95: @@
 Mapping: {{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 tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.9902{{c}}, ~48/35 = 546.6064{{c}}
-{{Optimal ET sequence|legend=1| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}
+{{Optimal ET sequence|legend=0| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}
-Badness: 0.339 × 10<sup>-3</sup>
+Badness (Smith): 0.339 × 10<sup>-3</sup>
 == Loki ==
@@ Line 110: / Line 107: @@
 {{Mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}
 : mapping generators: ~99/70, ~3, ~5
 {{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
-[[Badness]]: 0.493 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.493 × 10<sup>-3</sup>
 == Pessoal ==
@@ Line 125: / Line 121: @@
 {{Mapping|legend=1| 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 tuning]] ([[CTE]]): ~99/70 = 600.0000{{c}}, ~3/2 = 702.0759{{c}}, ~32/21 = 728.7910{{c}}
 {{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
-[[Badness]]: 0.499 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.499 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 141: / Line 136: @@
 Mapping: {{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 tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 702.0637{{c}}, ~32/21 = 728.7786{{c}}
-{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
+{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
-Badness: 0.391 × 10<sup>-3</sup>
+Badness (Smith): 0.391 × 10<sup>-3</sup>
 == Linus ==
@@ Line 159: / Line 154: @@
 {{Mapping|legend=1| 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 tuning]] ([[CTE]]): ~15/14 = 120.0000{{c}}, ~3/2 = 702.0010{{c}}, ~5/4 = 386.5927{{c}}
 {{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }}
-[[Badness]]: 1.12 × 10<sup>-3</sup>
+[[Badness]] (Smith): 1.12 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 172: / Line 167: @@
 Mapping: {{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 tuning (CTE): ~15/14 = 1200.0000{{c}}, ~3/2 = 702.0010{{c}}, ~5/4 = 386.5928{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}
+{{Optimal ET sequence|legend=0| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}
-Badness: 0.771 × 10<sup>-3</sup>
+Badness (Smith): 0.771 × 10<sup>-3</sup>
 [[Category:Temperament collections]]
 [[Category:Kalismic temperaments| ]] <!-- main article -->
-[[Category:Kalismic| ]] <!-- key article -->
 [[Category:Rank 3]]

Kalismic temperaments: Difference between revisions

Revision as of 14:21, 19 April 2026

Contents

Odin

Lycoris

Higanbana

Van gogh

Sif

13-limit

Loki

Pessoal

13-limit

Linus

13-limit

Navigation menu

Kalismic temperaments: Difference between revisions

Revision as of 14:21, 19 April 2026

Odin

Lycoris

Higanbana

Van gogh

Sif

13-limit

Loki

Pessoal

13-limit

Linus

13-limit

Navigation menu

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