Misty family: Difference between revisions
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[[Badness]]: 0.106540 | [[Badness]]: 0.106540 | ||
= 7-limit = | == 7-limit == | ||
{{see also|Hemimean clan #Misty}} | {{see also|Hemimean clan #Misty}} | ||
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Badness: 0.022923 | Badness: 0.022923 | ||
= Fog = | |||
The ''fog'' temperament (12&63, named by [[User:Xenllium|Xenllium]]) tempers out the [[225/224|marvel comma]] 225/224. | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 156250/151263 | |||
[[Mapping]]: [{{val|3 5 6 7}}, {{val|0 -1 4 6}}] | |||
{{Multival|legend=1| 3 -12 -18 -26 -37 -8 }} | |||
[[POTE generator]]: ~3/2 = 704.118 | |||
{{Val list|legend=1| 12, 51, 63, 75 }} | |||
[[Badness]]: 0.086866 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 100/99, 225/224, 2420/2401 | |||
Mapping: [{{val|3 5 6 7 8}}, {{val|0 -1 4 6 10}}] | |||
POTE generator: ~3/2 = 704.411 | |||
Vals: {{Val list| 12, 51, 63, 138de }} | |||
Badness: 0.051348 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 15:56, 11 May 2021
The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩.
Misty
Subgroup: 2.3.5
Comma list: 67108864/66430125
Mapping: [⟨3 0 26], ⟨0 1 -4]]
POTE generator: ~3/2 = 703.111
Badness: 0.106540
7-limit
Subgroup: 2.3.5.7
Comma list: 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]
Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]
POTE generator: ~3/2 = 703.021
Badness: 0.036802
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 4375/4356
Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]
POTE generator: ~3/2 = 703.210
Vals: Template:Val list
Badness: 0.035932
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 625/624
Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]
POTE generator: ~3/2 = 703.303
Vals: Template:Val list
Badness: 0.027820
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]
POTE generator: ~3/2 = 703.233
Vals: Template:Val list
Badness: 0.023908
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]
POTE generator: ~3/2 = 703.253
Vals: Template:Val list
Badness: 0.019878
Mystic
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 441/440, 896/891, 1001/1000
Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]
POTE generator: ~3/2 = 703.311
Vals: Template:Val list
Badness: 0.036872
Hemimist
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]
POTE generator: ~11/8 = 551.527
Vals: Template:Val list
Badness: 0.047439
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 3025/3024
Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]
POTE generator: ~11/8 = 551.525
Vals: Template:Val list
Badness: 0.022923
Fog
The fog temperament (12&63, named by Xenllium) tempers out the marvel comma 225/224.
Subgroup: 2.3.5.7
Comma list: 225/224, 156250/151263
Mapping: [⟨3 5 6 7], ⟨0 -1 4 6]]
Wedgie: ⟨⟨ 3 -12 -18 -26 -37 -8 ]]
POTE generator: ~3/2 = 704.118
Badness: 0.086866
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 2420/2401
Mapping: [⟨3 5 6 7 8], ⟨0 -1 4 6 10]]
POTE generator: ~3/2 = 704.411
Vals: Template:Val list
Badness: 0.051348