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 }}. | ||
Temperaments discussed elsewhere include [[Trienstonic clan #Quindecic|quindecic]]. | |||
== Trisedodge == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
Comma list: 30958682112/30517578125 | [[Comma list]]: 30958682112/30517578125 | ||
Mapping: [{{val| 5 7 11 }}, {{val| 0 3 2 }}] | [[Mapping]]: [{{val| 5 7 11 }}, {{val| 0 3 2 }}] | ||
POTE generator: ~25/24 = 74.0077 | [[POTE generator]]: ~25/24 = 74.0077 | ||
{{Val list|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | {{Val list|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | ||
[[Badness]]: 0.252724 | |||
=== 7-limit === | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 25: | Line 27: | ||
{{Val list|legend=1| 15, 50d, 65d, 80 }} | {{Val list|legend=1| 15, 50d, 65d, 80 }} | ||
[[Badness]]: 0.137695 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 35: | Line 38: | ||
POTE generator: ~25/24 = 74.9401 | POTE generator: ~25/24 = 74.9401 | ||
{{Val list | Vals: {{Val list| 15, 50d, 65d, 80 }} | ||
Badness: 0.043508 | |||
== Coblack | == Coblack == | ||
{{see also| Cloudy clan #Coblack }} | {{see also| Cloudy clan #Coblack }} | ||
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{{Val list|legend=1| 15, 35, 50, 65, 115d }} | {{Val list|legend=1| 15, 35, 50, 65, 115d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.107282 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 64: | Line 68: | ||
POTE generator: ~21/20 = 73.264 | POTE generator: ~21/20 = 73.264 | ||
{{Val list | Vals: {{Val list| 15, 35, 50, 65, 115d }} | ||
Badness: 0.045070 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 11:12, 5 June 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 7 11], ⟨0 3 2]]
POTE generator: ~25/24 = 74.0077
Badness: 0.252724
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
Badness: 0.137695
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
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