Trisedodge family: Difference between revisions
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The '''trisedodge family''' tempers out the trisedodge comma, 30958682112/30517578125 = {{monzo| 19 10 -15 }}. | The '''trisedodge family''' tempers out the trisedodge comma, 30958682112/30517578125 = {{monzo| 19 10 -15 }}. | ||
= Trisedodge = | == Trisedodge == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 13: | Line 13: | ||
{{Val list|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | {{Val list|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | ||
= 7-limit = | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 25: | Line 25: | ||
{{Val list|legend=1| 15, 50d, 65d, 80 }} | {{Val list|legend=1| 15, 50d, 65d, 80 }} | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 37: | Line 37: | ||
{{Val list|legend=1| 15, 50d, 65d, 80 }} | {{Val list|legend=1| 15, 50d, 65d, 80 }} | ||
= Coblack = | == Coblack == | ||
{{see also| Cloudy clan #Coblack }} | {{see also| Cloudy clan #Coblack }} | ||
| Line 54: | Line 54: | ||
[[Badness]]: 0.1073 | [[Badness]]: 0.1073 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 66: | Line 66: | ||
{{Val list|legend=1| 15, 35, 50, 65, 115d }} | {{Val list|legend=1| 15, 35, 50, 65, 115d }} | ||
= Quindecic = | == Quindecic == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 21:41, 1 June 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