Kalismic temperaments: Difference between revisions

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@@ Line 72: / Line 72: @@
 Badness: 0.416 × 10<sup>-3</sup>
-== Loki ==
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 5632/5625, 9801/9800
-[[Mapping]]: [{{val| 2 0 0 -21 -18 }}, {{val| 0 1 0 4 2 }}, {{val| 0 0 1 3 4 }}]
-Mapping generators: ~99/70, ~3, ~5
-{{Val list|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>
 == Van Gogh ==
@@ Line 98: / Line 85: @@
 [[Badness]]: 0.297 × 10<sup>-3</sup>
-== Pessoal ==
-{{See also| Pessoalisma }}
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 9801/9800, 131072/130977
-[[Mapping]]: [{{val| 2 0 1 10 14 }}, {{val| 0 1 0 -1 -3 }}, {{val| 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
-{{Val list|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
-[[Badness]]: 0.499 × 10<sup>-3</sup>
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 1716/1715, 2080/2079, 4096/4095
-Mapping: [{{val| 2 0 1 10 14 13 }}, {{val| 0 1 0 -1 -3 -1 }}, {{val| 0 0 3 -1 2 -2 }}]
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786
-Optimal GPV sequence: {{Val list| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
-Badness: 0.391 × 10<sup>-3</sup>
-== Rishi ==
-The 7-limit comma {{monzo| 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)<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, …, 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
-Optimal GPV sequence: {{Val list| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}
-[[Badness]]: 0.505 × 10<sup>-3</sup>
 == Hnoss ==
@@ Line 267: / Line 194: @@
 Badness: 1.23 × 10<sup>-3</sup>
+== Loki ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 5632/5625, 9801/9800
+[[Mapping]]: [{{val| 2 0 0 -21 -18 }}, {{val| 0 1 0 4 2 }}, {{val| 0 0 1 3 4 }}]
+Mapping generators: ~99/70, ~3, ~5
+{{Val list|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>
+== Pessoal ==
+{{See also| Pessoalisma }}
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 9801/9800, 131072/130977
+[[Mapping]]: [{{val| 2 0 1 10 14 }}, {{val| 0 1 0 -1 -3 }}, {{val| 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
+{{Val list|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
+[[Badness]]: 0.499 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1716/1715, 2080/2079, 4096/4095
+Mapping: [{{val| 2 0 1 10 14 13 }}, {{val| 0 1 0 -1 -3 -1 }}, {{val| 0 0 3 -1 2 -2 }}]
+Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786
+Optimal GPV sequence: {{Val list| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
+Badness: 0.391 × 10<sup>-3</sup>
+== Rishi ==
+The 7-limit comma {{monzo| 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)<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, …, 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
+Optimal GPV sequence: {{Val list| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}
+[[Badness]]: 0.505 × 10<sup>-3</sup>
 [[Category:Temperament collections]]
 [[Category:Kalismic temperaments| ]] <!-- main article -->
 [[Category:Rank 3]]