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Misty family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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{{Main| Misty }}
{{Main| Misty }}


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 67108864/66430125
[[Comma list]]: 67108864/66430125


[[Mapping]]: [{{val| 3 0 26 }}, {{val| 0 1 -4 }}]
{{Mapping|legend=1| 3 0 26 | 0 1 -4 }}


[[POTE generator]]: ~3/2 = 703.111
[[Optimal tuning]] ([[POTE]]): ~512/405 = 1\3, ~3/2 = 703.111


{{Optimal ET sequence|legend=1| 12, 51, 63, 75, 87, 99, 285, 384 }}
{{Optimal ET sequence|legend=1| 12, 51, 63, 75, 87, 99, 285, 384 }}
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{{Main| Misty }}
{{Main| Misty }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 5120/5103
[[Comma list]]: 3136/3125, 5120/5103


[[Mapping]]: [{{val| 3 0 26 56 }}, {{val| 0 1 -4 -10 }}]
{{Mapping|legend=1| 3 0 26 56 | 0 1 -4 -10 }}


{{Multival|legend=1| 3 -12 -30 -26 -56 -36 }}
{{Multival|legend=1| 3 -12 -30 -26 -56 -36 }}


[[POTE generator]]: ~3/2 = 703.021
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~3/2 = 703.021


{{Optimal ET sequence|legend=1| 12, 87, 99 }}
{{Optimal ET sequence|legend=1| 12, 87, 99 }}
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Comma list: 441/440, 3136/3125, 4375/4356
Comma list: 441/440, 3136/3125, 4375/4356


Mapping: [{{val| 3 0 26 56 77 }}, {{val| 0 1 -4 -10 -14 }}]
Mapping: {{mapping| 3 0 26 56 77 | 0 1 -4 -10 -14 }}


POTE generator: ~3/2 = 703.210
Optimal tuning (POTE): ~44/35 = 1\3, ~3/2 = 703.210


{{Optimal ET sequence|legend=1| 12, 87, 99e, 186e }}
{{Optimal ET sequence|legend=1| 12, 87, 99e, 186e }}
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Comma list: 196/195, 352/351, 364/363, 625/624
Comma list: 196/195, 352/351, 364/363, 625/624


Mapping: [{{val| 3 0 26 56 77 92 }}, {{val| 0 1 -4 -10 -14 -17 }}]
Mapping: {{mapping| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}


POTE generator: ~3/2 = 703.303
Optimal tuning (POTE): ~44/35 = 1\3, ~3/2 = 703.303


{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186ef, 273ef }}
{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186ef, 273ef }}
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Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594


Mapping: [{{val| 3 0 26 56 77 92 -2 }}, {{val| 0 1 -4 -10 -14 -17 3 }}]
Mapping: {{mapping| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}


POTE generator: ~3/2 = 703.233
Optimal tuning (POTE): ~34/27 = 1\3, ~3/2 = 703.233


{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186efg }}
{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186efg }}
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Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594


Mapping: [{{val| 3 0 26 56 77 92 -2 8 }}, {{val| 0 1 -4 -10 -14 -17 3 1 }}]
Mapping: {{mapping| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}


POTE generator: ~3/2 = 703.253
Optimal tuning (POTE): ~34/27 = 1\3, ~3/2 = 703.253


{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186efgh }}
{{Optimal ET sequence|legend=1| 12f, 87, 99ef, 186efgh }}
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Comma list: 325/324, 441/440, 896/891, 1001/1000
Comma list: 325/324, 441/440, 896/891, 1001/1000


Mapping: [{{val| 3 0 26 56 77 -46 }}, {{val| 0 1 -4 -10 -14 12 }}]
Mapping: {{mapping| 3 0 26 56 77 -46 | 0 1 -4 -10 -14 12 }}


POTE generator: ~3/2 = 703.311
Optimal tuning (POTE): ~44/35 = 1\3, ~3/2 = 703.311


{{Optimal ET sequence|legend=1| 12, 87, 186e, 273e }}
{{Optimal ET sequence|legend=1| 12, 87, 186e, 273e }}
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Comma list: 3136/3125, 5120/5103, 9801/9800
Comma list: 3136/3125, 5120/5103, 9801/9800


Mapping: [{{val| 6 0 52 112 173 }}, {{val| 0 1 -4 -10 -16 }}]
Mapping: {{mapping| 6 0 52 112 173 | 0 1 -4 -10 -16 }}


Mapping generators: ~55/49, ~3
: mapping generators: ~55/49, ~3


POTE generator: ~3/2 = 702.9764
Optimal tuning (POTE): ~55/49 = 1\6, ~3/2 = 702.9764


{{Optimal ET sequence|legend=1| 12, 174e, 186, 198, 408cde, 606bcde }}
{{Optimal ET sequence|legend=1| 12, 174e, 186, 198, 408cde, 606bcde }}
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Comma list: 352/351, 847/845, 1716/1715, 3136/3125
Comma list: 352/351, 847/845, 1716/1715, 3136/3125


Mapping: [{{val| 6 0 52 112 173 203 }}, {{val| 0 1 -4 -10 -16 -19 }}]
Mapping: {{mapping| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}


POTE generator: ~3/2 = 703.0087
Optimal tuning (POTE): ~55/49 = 1\6, ~3/2 = 703.0087


{{Optimal ET sequence|legend=1| 12f, 174ef, 186, 198 }}
{{Optimal ET sequence|legend=1| 12f, 174ef, 186, 198 }}
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Comma list: 3025/3024, 3136/3125, 5120/5103
Comma list: 3025/3024, 3136/3125, 5120/5103


Mapping: [{{val| 3 0 26 56 8 }}, {{val| 0 2 -8 -20 1 }}]
Mapping: {{mapping| 3 0 26 56 8 | 0 2 -8 -20 1 }}


Mapping generators: ~63/50, ~693/400
: mapping generators: ~63/50, ~400/231


POTE generator: ~693/400 = 951.527
Optimal tuning (POTE): ~63/50 = 1\3, ~400/231 = 951.527


{{Optimal ET sequence|legend=1| 24d, 87, 111, 198 }}
{{Optimal ET sequence|legend=1| 24d, 87, 111, 198 }}
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Comma list: 352/351, 676/675, 847/845, 3025/3024
Comma list: 352/351, 676/675, 847/845, 3025/3024


Mapping: [{{val| 3 0 26 56 8 23 }}, {{val| 0 2 -8 -20 1 -5 }}]
Mapping: {{mapping| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}


POTE generator: ~26/15 = 951.525
Optimal tuning (POTE): ~63/50 = 1\3, ~26/15 = 951.525


{{Optimal ET sequence|legend=1| 24d, 87, 111, 198 }}
{{Optimal ET sequence|legend=1| 24d, 87, 111, 198 }}
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== Fog ==
== Fog ==
The ''fog'' temperament (12&63) tempers out the marvel comma, [[225/224]].
The fog temperament (12 & 63) tempers out the marvel comma, [[225/224]].


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 156250/151263
[[Comma list]]: 225/224, 156250/151263


[[Mapping]]: [{{val|3 5 6 7}}, {{val|0 -1 4 6}}]
{{Mapping|legend=1| 3 5 6 7 | 0 -1 4 6 }}


{{Multival|legend=1| 3 -12 -18 -26 -37 -8 }}
{{Multival|legend=1| 3 -12 -18 -26 -37 -8 }}


[[POTE generator]]: ~3/2 = 704.118
[[Optimal tuning]] ([[POTE]]): ~80/63 = 1\3, ~3/2 = 704.118


{{Optimal ET sequence|legend=1| 12, 51, 63, 75 }}
{{Optimal ET sequence|legend=1| 12, 51, 63, 75 }}
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Comma list: 100/99, 225/224, 2420/2401
Comma list: 100/99, 225/224, 2420/2401


Mapping: [{{val|3 5 6 7 8}}, {{val|0 -1 4 6 10}}]
Mapping: {{mapping| 3 5 6 7 8 | 0 -1 4 6 10 }}


POTE generator: ~3/2 = 704.411
Optimal tuning (POTE): ~44/35 = 1\3, ~3/2 = 704.411


{{Optimal ET sequence|legend=1| 12, 51, 63, 138de }}
{{Optimal ET sequence|legend=1| 12, 51, 63, 138de }}
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