Trisedodge family: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~25/24 = 74.0077 | [[POTE generator]]: ~25/24 = 74.0077 | ||
{{ | {{Optimal ET sequence|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | ||
[[Badness]]: 0.252724 | [[Badness]]: 0.252724 | ||
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POTE generator: ~25/24 = 74.1247 | POTE generator: ~25/24 = 74.1247 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 210e, 275e, 340ce }} | ||
RMS error: 0.3198 cents | RMS error: 0.3198 cents | ||
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[[POTE generator]]: ~25/24 = 74.9480 | [[POTE generator]]: ~25/24 = 74.9480 | ||
{{ | {{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | ||
[[Badness]]: 0.137695 | [[Badness]]: 0.137695 | ||
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POTE generator: ~25/24 = 74.9401 | POTE generator: ~25/24 = 74.9401 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | ||
Badness: 0.043508 | Badness: 0.043508 | ||
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[[POTE generator]]: ~21/20 = 73.044 | [[POTE generator]]: ~21/20 = 73.044 | ||
{{ | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | ||
[[Badness]]: 0.107282 | [[Badness]]: 0.107282 | ||
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POTE generator: ~21/20 = 73.264 | POTE generator: ~21/20 = 73.264 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | ||
Badness: 0.045070 | Badness: 0.045070 | ||
Revision as of 16:20, 7 May 2023
The trisedodge family tempers out the trisedodge comma, 30958682112/30517578125 = [19 10 -15⟩.
Temperaments discussed elsewhere include quindecic and decistearn.
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
Optimal ET sequence: 15, 50, 65, 340c, 405c, 470c, 535c, 600c
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
Optimal ET sequence: 15, 35, 50, 65, 210e, 275e, 340ce
RMS error: 0.3198 cents
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
Optimal ET sequence: 15, 50d, 65d, 80
Badness: 0.137695
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 2560/2541
Mapping: [⟨5 1 7 21 15], ⟨0 3 2 -3 1]]
POTE generator: ~25/24 = 74.9401
Optimal ET sequence: 15, 50d, 65d, 80
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
Optimal ET sequence: 15, 35, 50, 65, 115d
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
Optimal ET sequence: 15, 35, 50, 65, 115d
Badness: 0.045070