Wesley family: Difference between revisions
Cmloegcmluin (talk | contribs) add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~125/96 = 414.509 | [[POTE generator]]: ~125/96 = 414.509 | ||
{{ | {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }} | ||
[[Badness]]: 0.247718 | [[Badness]]: 0.247718 | ||
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[[POTE generator]]: ~9/7 = 415.519 | [[POTE generator]]: ~9/7 = 415.519 | ||
{{ | {{Optimal ET sequence|legend=1| 3d, 23d, 26 }} | ||
[[Badness]]: 0.095344 | [[Badness]]: 0.095344 | ||
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POTE generator: ~9/7 = 415.769 | POTE generator: ~9/7 = 415.769 | ||
Optimal | {{Optimal ET sequence|legend=1| 3de, 23de, 26, 75bcd }} | ||
Badness: 0.049066 | Badness: 0.049066 | ||
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POTE generator: ~9/7 = 415.645 | POTE generator: ~9/7 = 415.645 | ||
Optimal | {{Optimal ET sequence|legend=1| 3def, 26 }} | ||
Badness: 0.038402 | Badness: 0.038402 | ||
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[[POTE generator]]: ~35/27 = 413.513 | [[POTE generator]]: ~35/27 = 413.513 | ||
{{ | {{Optimal ET sequence|legend=1| 29, 90cd, 119ccdd }} | ||
[[Badness]]: 0.117943 | [[Badness]]: 0.117943 | ||
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POTE generator: ~14/11 = 413.490 | POTE generator: ~14/11 = 413.490 | ||
Optimal | {{Optimal ET sequence|legend=1| 29, 90cd, 119ccdde }} | ||
Badness: 0.054296 | Badness: 0.054296 | ||
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[[POTE generator]]: ~63/50 = 414.552 | [[POTE generator]]: ~63/50 = 414.552 | ||
{{ | {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }} | ||
[[Badness]]: 0.113386 | [[Badness]]: 0.113386 | ||
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POTE generator: ~14/11 = 414.471 | POTE generator: ~14/11 = 414.471 | ||
Optimal | {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }} | ||
Badness: 0.052841 | Badness: 0.052841 | ||
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POTE generator: ~14/11 = 414.472 | POTE generator: ~14/11 = 414.472 | ||
Optimal | {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }} | ||
Badness: 0.030043 | Badness: 0.030043 | ||
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[[POTE generator]]: ~192/175 = 185.738 | [[POTE generator]]: ~192/175 = 185.738 | ||
{{ | {{Optimal ET sequence|legend=1| 6, 26, 58c, 84c }} | ||
[[Badness]]: 0.181726 | [[Badness]]: 0.181726 | ||
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POTE generator: ~11/10 = 185.879 | POTE generator: ~11/10 = 185.879 | ||
Optimal | {{Optimal ET sequence|legend=1| 6, 26, 58c, 84c }} | ||
Badness: 0.075842 | Badness: 0.075842 | ||
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POTE generator: ~11/10 = 185.702 | POTE generator: ~11/10 = 185.702 | ||
Optimal | {{Optimal ET sequence|legend=1| 26, 58c, 84c }} | ||
Badness: 0.049603 | Badness: 0.049603 | ||
Revision as of 16:11, 7 May 2023
This tempers out the wesley comma, 78125/73728. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone - it is an eigenmonzo, or unchanged-interval, in other words. Here is a talk by Gene Ward Smith.
Wesley
Subgroup: 2.3.5
Comma: 78125/73728
Mapping: [⟨1 4 3], ⟨0 -7 -2]]
POTE generator: ~125/96 = 414.509
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness: 0.247718
Septimal wesley
Subgroup: 2.3.5.7
Comma list: 405/392, 875/864
Mapping: [⟨1 4 3 8], ⟨0 -7 -2 -15]]
Wedgie: ⟨⟨ 7 2 15 -13 4 29 ]]
POTE generator: ~9/7 = 415.519
Optimal ET sequence: 3d, 23d, 26
Badness: 0.095344
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 875/864
Mapping: [⟨1 4 3 8 9], ⟨0 -7 -2 -15 -16]]
POTE generator: ~9/7 = 415.769
Optimal ET sequence: 3de, 23de, 26, 75bcd
Badness: 0.049066
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 78/77, 99/98, 325/324
Mapping: [⟨1 4 3 8 9 12], ⟨0 -7 -2 -15 -16 -24]]
POTE generator: ~9/7 = 415.645
Badness: 0.038402
Snipes
Subgroup: 2.3.5.7
Comma list: 225/224, 6125/5832
Mapping: [⟨1 4 3 9], ⟨0 -7 -2 -18]]
Wedgie: ⟨⟨ 7 2 18 -13 9 36 ]]
POTE generator: ~35/27 = 413.513
Optimal ET sequence: 29, 90cd, 119ccdd
Badness: 0.117943
11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 225/224, 245/242
Mapping: [⟨1 4 3 9 10], ⟨0 -7 -2 -18 -19]]
POTE generator: ~14/11 = 413.490
Optimal ET sequence: 29, 90cd, 119ccdde
Badness: 0.054296
Roman
7-limit (Crusher)
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3024
Mapping: [⟨1 4 3 -1], ⟨0 -7 -2 11]]
Wedgie: ⟨⟨ 7 2 -11 -13 -37 -31 ]]
POTE generator: ~63/50 = 414.552
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness: 0.113386
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 525/512
Mapping: [⟨1 4 3 -1 0], ⟨0 -7 -2 11 10]]
POTE generator: ~14/11 = 414.471
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness: 0.052841
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 100/99, 105/104, 245/242
Mapping: [⟨1 4 3 -1 0 3], ⟨0 -7 -2 11 10 2]]
POTE generator: ~14/11 = 414.472
Optimal ET sequence: 3, 23, 26, 29, 55cf
Badness: 0.030043
Dubbla
Subgroup: 2.3.5.7
Comma list: 50/49, 78125/73728
Mapping: [⟨2 1 4 5], ⟨0 7 2 2]]
Wedgie: ⟨⟨ 14 4 4 -26 -33 -2 ]]
POTE generator: ~192/175 = 185.738
Optimal ET sequence: 6, 26, 58c, 84c
Badness: 0.181726
11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 125/121, 1344/1331
Mapping: [⟨2 1 4 5 6], ⟨0 7 2 2 3]]
POTE generator: ~11/10 = 185.879
Optimal ET sequence: 6, 26, 58c, 84c
Badness: 0.075842
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 105/104, 125/121, 144/143
Mapping: [⟨2 1 4 5 6 4], ⟨0 7 2 2 3 11]]
POTE generator: ~11/10 = 185.702
Optimal ET sequence: 26, 58c, 84c
Badness: 0.049603