Kalismic temperaments: Difference between revisions

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 * ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]]
-Considered below are odin, loki, and van gogh, but we can begin by looking at the rank-4 temperament.
+Considered below are odin, loki, van gogh, rishi, and gersemi, but we can begin by looking at the rank-4 temperament.
 == Kalismic ==
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 [[Badness]]: 0.297 × 10<sup>-3</sup>
+== Rishi ==
+The 7-limit comma [65 -84 10 16⟩ ~ 0.13c 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)<sup>-2</sup>, 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]]: [{{val| 2 0 3 -10 -4 }}, {{val| 0 1 2 4 4 }}, {{val| 0 0 8 -5 3 }}]
+Mapping generators: ~99/70, ~3, ~17364375/14172488
+{{Val list|legend=1| 24, 34d, 58, 150cdee, 208ccddee, 252ccddeee, 262ccdee, 286ccdee, 310cddee, 320ccee, 344cdee, 378ce, 402de, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}
+[[Badness]]: 2.10 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+[[Comma list]]: 9801/9800, 10648/10647, 371293/371250
+[[Mapping]]: [{{val| 2 0 3 -10 -4 2 }}, {{val| 0 1 2 4 4 3 }}, {{val| 0 0 8 -5 3 7 }}]
+Mapping generators: ~99/70, ~3, ~364/297
+{{Val list|legend=1| 24, 34d, 58, 150cdeef, 208ccddeeff, 252ccddeeefff, 262ccdeefff, 286ccdeeff, 310cddeeff, 320cceeff, 344cdeef, 378cef, 402def, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}
+[[Badness]]: 0.505 × 10<sup>-3</sup>
+== Gersemi ==
+To the wizma [-6 -8 2 5⟩ = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]].
+/7 is a possible equave. Fokker blocks of 128 notes are available for it, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)<sup>3</sup> ~ 17/1 via the [[5832/5831|chlorisma]]. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings.
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 9801/9800, 41503/41472
+[[Mapping]]: [{{val| 2 0 1 2 6 }}, {{val| 0 1 4 0 2 }}, {{val| 0 0 -5 2 -3 }}]
+Mapping generators: ~99/70, ~3, ~144/77
+{{Val list|legend=1| 10c, 18bcd, 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}
+[[Badness]]: 0.368 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+[[Comma list]]: 4225/4224, 9801/9800, 41503/41472
+[[Mapping]]: [{{val| 2 0 1 2 6 9 }}, {{val| 0 1 9 -2 5 -6 }}, {{val| 0 0 -10 4 -6 7 }}]
+Mapping generators: ~99/70, ~3, ~154/65
+{{Val list|legend=1| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }}
+[[Badness]]: 1.06 × 10<sup>-3</sup>
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+[[Comma list]]: 1089/1088, 1225/1224, 2025/2023, 4225/4224
+[[Mapping]]: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}]
+Mapping generators: ~99/70, ~3, ~154/65
+{{Val list|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}
+[[Badness]]: 1.46 × 10<sup>-3</sup>
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.19
+[[Comma list]]: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757
+[[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 }}, {{val| 0 1 9 -2 5 -6 12 11 }}, {{val| 0 0 -10 4 -6 7 -12 -11 }}]
+Mapping generators: ~99/70, ~3, ~45/19
+{{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}
+[[Badness]]: 1.11 × 10<sup>-3</sup>
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.19.23
+[[Comma list]]: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925
+[[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 7 }}, {{val| 0 1 9 -2 5 -6 12 11 3 }}, {{val| 0 0 -10 4 -6 7 -12 -11 -3 }}]
+Mapping generators: ~99/70, ~3, ~45/19
+{{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}
+[[Badness]]: 1.23 × 10<sup>-3</sup>
 [[Category:Temperament collections]]
 [[Category:Kalismic temperaments| ]] <!-- main article -->
 [[Category:Rank 3]]