Wesley family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The wesley family of temperaments tempers out 78125/73728, the wesley comma. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone – it is an eigenmonzo (i.e. unchanged-interval), which Gene Ward Smith has talked about[1].
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 = 1200.000 ¢, ~125/96 = 414.509 ¢
Optimal ET sequence: 3, …, 23, 26, 29, 55c
Badness (Smith): 0.247718
Septimal wesley
Subgroup: 2.3.5.7
Comma list: 405/392, 875/864
Mapping: [⟨1 4 3 8], ⟨0 -7 -2 -15]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 415.519 ¢
Optimal ET sequence: 3d, …, 23d, 26
Badness (Smith): 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 = 1200.000 ¢, ~9/7 = 415.769 ¢
Optimal ET sequence: 3de, …, 23de, 26
Badness (Smith): 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 = 1200.000 ¢, ~9/7 = 415.645 ¢
Optimal ET sequence: 3def, 23deff, 26
Badness (Smith): 0.038402
Snipes
Subgroup: 2.3.5.7
Comma list: 225/224, 6125/5832
Mapping: [⟨1 4 3 9], ⟨0 -7 -2 -18]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~35/27 = 413.513 ¢
Optimal ET sequence: 3d, …, 26d, 29
Badness (Smith): 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 = 1200.000 ¢, ~14/11 = 413.490 ¢
Optimal ET sequence: 3de, …, 26de, 29
Badness (Smith): 0.054296
Roman
7-limit Roman is also known as "crusher".
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3024
Mapping: [⟨1 4 3 -1], ⟨0 -7 -2 11]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~63/50 = 414.552 ¢
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness (Smith): 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 = 1200.000 ¢, ~14/11 = 414.471 ¢
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness (Smith): 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 = 1200.000 ¢, ~14/11 = 414.472 ¢
Optimal ET sequence: 3, 23, 26, 29, 55cf
Badness (Smith): 0.030043
Dubbla
Subgroup: 2.3.5.7
Comma list: 50/49, 78125/73728
Mapping: [⟨2 1 4 5], ⟨0 7 2 2]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~192/175 = 185.738 ¢
Optimal ET sequence: 6, 20b, 26, 58c
Badness (Smith): 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 = 1200.000 ¢, ~11/10 = 185.879 ¢
Optimal ET sequence: 6, 20b, 26
Badness (Smith): 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 = 1200.000 ¢, ~11/10 = 185.702 ¢
Optimal ET sequence: 6f, 20bff, 26
Badness (Smith): 0.049603