Trisedodge family: Difference between revisions
m Cleanup; +categories |
m Cleanup +1 |
||
| Line 38: | Line 38: | ||
= Coblack = | = Coblack = | ||
{{see also| | {{see also| Cloudy clan #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. | 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. | ||
| Line 45: | Line 45: | ||
[[Comma list]]: 126/125, 16807/16384 | [[Comma list]]: 126/125, 16807/16384 | ||
[[Mapping]]: [{{val| 5 1 7 14 }}, {{val| 0 3 2 0 }}] | |||
[[POTE generator]]: ~21/20 = 73.044 | [[POTE generator]]: ~21/20 = 73.044 | ||
{{Val list|legend=1| 15, 35, 50, 65, 115d }} | {{Val list|legend=1| 15, 35, 50, 65, 115d }} | ||
| Line 59: | Line 59: | ||
Comma list: 126/125, 245/242, 385/384 | Comma list: 126/125, 245/242, 385/384 | ||
Mapping: [{{val| 5 1 7 14 15 }}, {{val| 0 3 2 0 1 }}] | |||
POTE generator: ~21/20 = 73.264 | POTE generator: ~21/20 = 73.264 | ||
{{Val list|legend=1| 15, 35, 50, 65, 115d }} | {{Val list|legend=1| 15, 35, 50, 65, 115d }} | ||
| Line 72: | Line 72: | ||
Comma list: 28/27, 49/48, 55/54, 77/75 | Comma list: 28/27, 49/48, 55/54, 77/75 | ||
Mapping: [{{val| 15 24 35 42 52 0 }}, {{val| 0 0 0 0 0 1 }}] | |||
POTE generator: ~66/65 = 27.0764 | POTE generator: ~66/65 = 27.0764 | ||
Revision as of 08:13, 18 April 2021
The trisedodge family tempers out the trisedodge comma, 30958682112/30517578125 = [19 10 -15⟩.
Trisedodge
Subgroup: 2.3.5
Comma list: 30958682112/30517578125
Mapping: [⟨5 7 11], ⟨0 3 2]]
POTE generator: ~25/24 = 74.0077
7-limit
Subgroup: 2.3.5.7
Comma list: 4000/3969, 110592/109375
Mapping: [⟨5 7 11 15], ⟨0 3 2 -3]]
POTE generator: ~25/24 = 74.9480
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 2560/2541
Mapping: [⟨5 7 11 15 17], ⟨0 3 2 -3 1]]
POTE generator: ~25/24 = 74.9401
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: 0.1073
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
Quindecic
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 49/48, 55/54, 77/75
Mapping: [⟨15 24 35 42 52 0], ⟨0 0 0 0 0 1]]
POTE generator: ~66/65 = 27.0764