Wesley family: Difference between revisions
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{{Mapping|legend=1| 1 4 3 | 0 -7 -2 }} | {{Mapping|legend=1| 1 4 3 | 0 -7 -2 }} | ||
: mapping generators: ~2, ~125/96 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509 | ||
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }} | {{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }} | ||
[[Badness]]: 0.247718 | [[Badness]]: 0.247718 | ||
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[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519 | ||
{{Optimal ET sequence|legend=1| 3d, 23d, 26 }} | {{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }} | ||
[[Badness]]: 0.095344 | [[Badness]]: 0.095344 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769 | Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769 | ||
{{Optimal ET sequence|legend=1| 3de, 23de, 26 | {{Optimal ET sequence|legend=1| 3de, …, 23de, 26 }} | ||
Badness: 0.049066 | Badness: 0.049066 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645 | Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645 | ||
{{Optimal ET sequence|legend=1| 3def, 26 }} | {{Optimal ET sequence|legend=1| 3def, 23deff, 26 }} | ||
Badness: 0.038402 | Badness: 0.038402 | ||
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[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }} | ||
[[Badness]]: 0.117943 | [[Badness]]: 0.117943 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490 | Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 3de, …, 26de, 29 }} | ||
Badness: 0.054296 | Badness: 0.054296 | ||
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[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738 | ||
{{Optimal ET sequence|legend=1| 6, 26, 58c | {{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }} | ||
[[Badness]]: 0.181726 | [[Badness]]: 0.181726 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879 | Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879 | ||
{{Optimal ET sequence|legend=1| 6, 26 | {{Optimal ET sequence|legend=1| 6, 20b, 26 }} | ||
Badness: 0.075842 | Badness: 0.075842 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702 | Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 6f, 20bff, 26 }} | ||
Badness: 0.049603 | Badness: 0.049603 | ||
Revision as of 08:41, 21 September 2023
The wesley family of rank-2 temperaments tempers out the wesley comma, 78125/73728. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone – it is an eigenmonzo (i.e. unchanged-interval). Here is a talk by Gene Ward Smith.
Wesley
Subgroup: 2.3.5
Comma list: 78125/73728
Mapping: [⟨1 4 3], ⟨0 -7 -2]]
- mapping generators: ~2, ~125/96
Optimal tuning (POTE): ~2 = 1\1, ~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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~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]]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769
Optimal ET sequence: 3de, …, 23de, 26
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]]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645
Optimal ET sequence: 3def, 23deff, 26
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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~35/27 = 413.513
Optimal ET sequence: 3d, …, 26d, 29
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]]
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490
Optimal ET sequence: 3de, …, 26de, 29
Badness: 0.054296
Roman
7-limit a.k.a. 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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~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]]
Optimal tuning (POTE): ~2 = 1\1, ~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]]
Optimal tuning (POTE): ~2 = 1\1, ~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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~192/175 = 185.738
Optimal ET sequence: 6, 20b, 26, 58c
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]]
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879
Optimal ET sequence: 6, 20b, 26
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]]
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702
Optimal ET sequence: 6f, 20bff, 26
Badness: 0.049603