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Kalismic temperaments: Difference between revisions

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m →Lycoris: actually there's an even simpler basis
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 26: Line 26:
Mapping generators: ~99/70, ~3, ~5, ~7
Mapping generators: ~99/70, ~3, ~5, ~7


{{Val list|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}


== Odin ==
== Odin ==
Line 39: Line 39:
Mapping generators: ~55/49, ~3, ~5
Mapping generators: ~55/49, ~3, ~5


{{Val list|legend=1| 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e }}
{{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]]: 0.116 × 10<sup>-3</sup>
Line 54: Line 54:
[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 701.9439, ~81/70 = 252.6028
[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 701.9439, ~81/70 = 252.6028


{{Val list|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}
{{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]]: 0.249 × 10<sup>-3</sup>
Line 69: Line 69:
Optimal tuning (CTE): ~99/70 = 1\2, ~1458/1001 = 650.9715, ~81/70 = 252.6037
Optimal tuning (CTE): ~99/70 = 1\2, ~1458/1001 = 650.9715, ~81/70 = 252.6037


Optimal GPV sequence: {{Val list| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
{{Optimal ET sequence|legend=1| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}


Badness: 0.416 × 10<sup>-3</sup>
Badness: 0.416 × 10<sup>-3</sup>
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Mapping generators: ~99/70, ~3, ~9/7
Mapping generators: ~99/70, ~3, ~9/7


{{Val list|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }}
{{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]]: 0.297 × 10<sup>-3</sup>
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Mapping generators: ~99/70, ~3, ~144/77
Mapping generators: ~99/70, ~3, ~144/77


{{Val list|legend=1| 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}


[[Badness]]: 0.368 × 10<sup>-3</sup>
[[Badness]]: 0.368 × 10<sup>-3</sup>
Line 108: Line 108:
Mapping: [{{val| 2 0 1 2 6 -3 }}, {{val| 0 1 4 0 2 1 }}, {{val| 0 0 -5 2 -3 4 }}]
Mapping: [{{val| 2 0 1 2 6 -3 }}, {{val| 0 1 4 0 2 1 }}, {{val| 0 0 -5 2 -3 4 }}]


Optimal GPV sequence: {{Val list| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}
{{Optimal ET sequence|legend=1| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}


Badness: 0.867 × 10<sup>-3</sup>
Badness: 0.867 × 10<sup>-3</sup>
Line 119: Line 119:
Mapping: [{{val| 2 0 1 2 6 -3 0 }}, {{val| 0 1 4 0 2 1 6 }}, {{val| 0 0 -5 2 -3 4 -6 }}]
Mapping: [{{val| 2 0 1 2 6 -3 0 }}, {{val| 0 1 4 0 2 1 6 }}, {{val| 0 0 -5 2 -3 4 -6 }}]


Optimal GPV sequence: {{Val list| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}
{{Optimal ET sequence|legend=1| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}


Badness: 0.862 × 10<sup>-3</sup>
Badness: 0.862 × 10<sup>-3</sup>
Line 130: Line 130:
Mapping: [{{val| 2 0 1 2 6 -3 0 13 }}, {{val| 0 1 4 0 2 1 6 2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 }}]
Mapping: [{{val| 2 0 1 2 6 -3 0 13 }}, {{val| 0 1 4 0 2 1 6 2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 }}]


Optimal GPV sequence: {{Val list| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}
{{Optimal ET sequence|legend=1| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}


Badness: 0.901 × 10<sup>-3</sup>
Badness: 0.901 × 10<sup>-3</sup>
Line 141: Line 141:
Mapping: [{{val| 2 0 1 2 6 -3 0 13 19 }}, {{val| 0 1 4 0 2 1 6 2 -2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 -2 }}]
Mapping: [{{val| 2 0 1 2 6 -3 0 13 19 }}, {{val| 0 1 4 0 2 1 6 2 -2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 -2 }}]


Optimal GPV sequence: {{Val list| 72, 94, 166g, 270, 342f, 436, 706fi }}
{{Optimal ET sequence|legend=1| 72, 94, 166g, 270, 342f, 436, 706fi }}


Badness: 1.14 × 10<sup>-3</sup>
Badness: 1.14 × 10<sup>-3</sup>
Line 156: Line 156:
Mapping generators: ~99/70, ~3, ~154/65
Mapping generators: ~99/70, ~3, ~154/65


Optimal GPV sequence: {{Val list| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }}
{{Optimal ET sequence|legend=1| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }}


Badness: 1.06 × 10<sup>-3</sup>
Badness: 1.06 × 10<sup>-3</sup>
Line 167: Line 167:
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: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}]


Optimal GPV sequence: {{Val list| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}
{{Optimal ET sequence|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}


Badness: 1.46 × 10<sup>-3</sup>
Badness: 1.46 × 10<sup>-3</sup>
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Mapping generators: ~99/70, ~3, ~45/19
Mapping generators: ~99/70, ~3, ~45/19


Optimal GPV sequence: {{Val list| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}
{{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}


Badness: 1.11 × 10<sup>-3</sup>
Badness: 1.11 × 10<sup>-3</sup>
Line 191: Line 191:
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: [{{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 }}]


Optimal GPV sequence: {{Val list| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}
{{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}


Badness: 1.23 × 10<sup>-3</sup>
Badness: 1.23 × 10<sup>-3</sup>
Line 204: Line 204:
Mapping generators: ~99/70, ~3, ~5
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 }}
{{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]]: 0.493 × 10<sup>-3</sup>
Line 221: Line 221:
[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 702.0759, ~32/21 = 728.7910
[[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 }}
{{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]]: 0.499 × 10<sup>-3</sup>
Line 234: Line 234:
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786
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 }}
{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}


Badness: 0.391 × 10<sup>-3</sup>
Badness: 0.391 × 10<sup>-3</sup>
Line 251: Line 251:
Mapping generators: ~99/70, ~3, ~17364375/14172488
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 }}
{{Optimal ET sequence|legend=1| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}


[[Badness]]: 2.10 × 10<sup>-3</sup>
[[Badness]]: 2.10 × 10<sup>-3</sup>
Line 264: Line 264:
Mapping generators: ~99/70, ~3, ~364/297
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 }}
{{Optimal ET sequence|legend=1| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}


[[Badness]]: 0.505 × 10<sup>-3</sup>
[[Badness]]: 0.505 × 10<sup>-3</sup>
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