Trisedodge family: Difference between revisions
Temperament maps reviewed and +mapping generators |
→Trisedodge: +countdown, a 2.3.5.11 extension found in the temp finder |
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[[Badness]]: 0.252724 | [[Badness]]: 0.252724 | ||
=== Countdown === | |||
Subgroup: 2.3.5.11 | |||
Comma list: 4000/3993, 6912/6875 | |||
Sval mapping: [{{val| 5 1 7 15 }}, {{val| 0 3 2 1 }}] | |||
POTE generator: ~25/24 = 74.1247 | |||
Vals: {{Val list| 15, 35, 50, 65, 210e, 275e, 340ce }} | |||
Badness: 0.0255 | |||
== Septimal trisedodge == | == Septimal trisedodge == | ||
Revision as of 11:13, 29 July 2021
The trisedodge family tempers out the trisedodge comma, 30958682112/30517578125 = [19 10 -15⟩.
Temperaments discussed elsewhere include quindecic.
Trisedodge
Subgroup: 2.3.5
Comma list: 30958682112/30517578125
Mapping: [⟨5 1 7], ⟨0 3 2]]
Mapping generators: ~144/125, ~864/625
POTE generator: ~25/24 = 74.0077
Badness: 0.252724
Countdown
Subgroup: 2.3.5.11
Comma list: 4000/3993, 6912/6875
Sval mapping: [⟨5 1 7 15], ⟨0 3 2 1]]
POTE generator: ~25/24 = 74.1247
Vals: Template:Val list
Badness: 0.0255
Septimal trisedodge
Subgroup: 2.3.5.7
Comma list: 4000/3969, 110592/109375
Mapping: [⟨5 1 7 21], ⟨0 3 2 -3]]
POTE generator: ~25/24 = 74.9480
Badness: 0.137695
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 2560/2541
Mapping: [⟨5 1 7 21 19], ⟨0 3 2 -3 1]]
POTE generator: ~25/24 = 74.9401
Vals: Template:Val list
Badness: 0.043508
Coblack
In addition to 126/125, the coblack temperament tempers out the cloudy comma, 16807/16384, which is the amount by which five septimal supermajor seconds (8/7) fall short of an octave.
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]
POTE generator: ~21/20 = 73.044
Badness: 0.107282
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]
POTE generator: ~21/20 = 73.264
Vals: Template:Val list
Badness: 0.045070