Greenwoodmic temperaments: Difference between revisions
m Removing from Category:Theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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| Line 16: | Line 16: | ||
[[POTE generator]]: ~8/7 = 241.490 | [[POTE generator]]: ~8/7 = 241.490 | ||
{{ | {{Optimal ET sequence|legend=1| 14c, 21, 35 }} | ||
[[Badness]]: 0.121752 | [[Badness]]: 0.121752 | ||
| Line 29: | Line 29: | ||
POTE generator: ~8/7 = 242.711 | POTE generator: ~8/7 = 242.711 | ||
Vals: {{ | Vals: {{Optimal ET sequence| 14c, 21, 35, 49bcde, 84bbccde }} | ||
Badness: 0.057471 | Badness: 0.057471 | ||
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POTE generator: ~8/7 = 238.607 | POTE generator: ~8/7 = 238.607 | ||
Vals: {{ | Vals: {{Optimal ET sequence| 14c, 21, 35 }} | ||
Badness: 0.054009 | Badness: 0.054009 | ||
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[[POTE generator]]: ~16/15 = 137.958 | [[POTE generator]]: ~16/15 = 137.958 | ||
{{ | {{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }} | ||
[[Badness]]: 0.089840 | [[Badness]]: 0.089840 | ||
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POTE generator: ~12/11 = 137.900 | POTE generator: ~12/11 = 137.900 | ||
Vals: {{ | Vals: {{Optimal ET sequence| 9, 17, 26, 61bc, 87bcc }} | ||
Badness: 0.042562 | Badness: 0.042562 | ||
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POTE generator: ~12/11 = 136.937 | POTE generator: ~12/11 = 136.937 | ||
Vals: {{ | Vals: {{Optimal ET sequence| 9, 26f, 35 }} | ||
Badness: 0.049684 | Badness: 0.049684 | ||
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POTE generator: ~12/11 = 137.917 | POTE generator: ~12/11 = 137.917 | ||
Vals: {{ | Vals: {{Optimal ET sequence| 9, 17, 26, 61bcf, 87bccf }} | ||
Badness: 0.026212 | Badness: 0.026212 | ||
Revision as of 18:13, 7 May 2023
These temperament temper out the greenwoodma, [-3 4 1 -2⟩ = 405/392.
Temperaments discussed elsewhere include august, injera, schism, sidi, and superpelog.
Greenwood
Subgroup: 2.3.5.7
Comma list: 405/392, 1323/1280
Mapping: [⟨7 11 1 12], ⟨0 0 2 1]]
Wedgie: ⟨⟨ 0 14 7 22 11 -23 ]]
POTE generator: ~8/7 = 241.490
Optimal ET sequence: 14c, 21, 35
Badness: 0.121752
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 1323/1280
Mapping: [⟨7 11 1 12 9], ⟨0 0 2 1 2]]
POTE generator: ~8/7 = 242.711
Vals: 14c, 21, 35, 49bcde, 84bbccde
Badness: 0.057471
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 640/637
Mapping: [⟨7 11 1 12 9 26], ⟨0 0 2 1 2 0]]
POTE generator: ~8/7 = 238.607
Badness: 0.054009
Secund
Subgroup: 2.3.5.7
Comma list: 405/392, 525/512
Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]
Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]
POTE generator: ~16/15 = 137.958
Optimal ET sequence: 9, 17, 26, 61bc, 87bcc
Badness: 0.089840
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 385/384
Mapping: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]
POTE generator: ~12/11 = 137.900
Badness: 0.042562
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 385/384
Mapping: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]
POTE generator: ~12/11 = 136.937
Badness: 0.049684
Secundly
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 65/64, 78/77, 99/98
Mapping: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]
POTE generator: ~12/11 = 137.917
Vals: 9, 17, 26, 61bcf, 87bccf
Badness: 0.026212