Trisedodge family: Difference between revisions
No edit summary |
Temperament maps reviewed and +mapping generators |
||
| Line 8: | Line 8: | ||
[[Comma list]]: 30958682112/30517578125 | [[Comma list]]: 30958682112/30517578125 | ||
[[Mapping]]: [{{val| 5 7 | [[Mapping]]: [{{val| 5 1 7 }}, {{val| 0 3 2 }}] | ||
Mapping generators: ~144/125, ~864/625 | |||
[[POTE generator]]: ~25/24 = 74.0077 | [[POTE generator]]: ~25/24 = 74.0077 | ||
| Line 16: | Line 18: | ||
[[Badness]]: 0.252724 | [[Badness]]: 0.252724 | ||
== | == Septimal trisedodge == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: 4000/3969, 110592/109375 | [[Comma list]]: 4000/3969, 110592/109375 | ||
[[Mapping]]: [{{val| 5 7 | [[Mapping]]: [{{val| 5 1 7 21 }}, {{val| 0 3 2 -3 }}] | ||
[[POTE generator]]: ~25/24 = 74.9480 | [[POTE generator]]: ~25/24 = 74.9480 | ||
| Line 34: | Line 36: | ||
Comma list: 176/175, 1331/1323, 2560/2541 | Comma list: 176/175, 1331/1323, 2560/2541 | ||
Mapping: [{{val| 5 7 | Mapping: [{{val| 5 1 7 21 19 }}, {{val| 0 3 2 -3 1 }}] | ||
POTE generator: ~25/24 = 74.9401 | POTE generator: ~25/24 = 74.9401 | ||
| Line 74: | Line 76: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Trisedodge]] | [[Category:Trisedodge family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 12:21, 28 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
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