Wesley family: Difference between revisions
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Comma list: 45/44, 99/98, 875/864 | Comma list: 45/44, 99/98, 875/864 | ||
{{Mapping|legend=0| 1 -3 1 -7 -7 | 0 7 2 15 16 }} | |||
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Comma list: 45/44, 78/77, 99/98, 325/324 | Comma list: 45/44, 78/77, 99/98, 325/324 | ||
{{Mapping|legend=0| 1 -3 1 -7 -7 -12 | 0 7 2 15 16 24 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 55/54, 225/224, 245/242 | Comma list: 55/54, 225/224, 245/242 | ||
{{Mapping|legend=0| 1 -3 1 -9 -9 | 0 7 2 18 19 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 100/99, 245/242, 525/512 | Comma list: 100/99, 245/242, 525/512 | ||
{{Mapping|legend=0| 1 -3 1 10 10 | 0 7 2 -11 -10 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 65/64, 100/99, 105/104, 245/242 | Comma list: 65/64, 100/99, 105/104, 245/242 | ||
{{Mapping|legend=0| 1 -3 1 10 10 5 | 0 7 2 -11 -10 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 50/49, 125/121, 1344/1331 | Comma list: 50/49, 125/121, 1344/1331 | ||
{{Mapping|legend=0| 2 1 4 5 6 | 0 7 2 2 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 50/49, 105/104, 125/121, 144/143 | Comma list: 50/49, 105/104, 125/121, 144/143 | ||
{{Mapping|legend=0| 2 1 4 5 6 4 | 0 7 2 2 3 11 }} | |||
Optimal tunings: | Optimal tunings: | ||
Latest revision as of 12:33, 24 September 2026
- 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
The generator of wesley is one half of a ~5/2, around 786 cents, seven of which after octave reduction reach the perfect fifth. The ploidacot signature of this temperament is delta-heptacot. A good tuning for the generator may be found between 17\26 and 19\29.
Subgroup: 2.3.5
Comma list: 78125/73728
Mapping: [⟨1 -3 1], ⟨0 7 2]]
- mapping generators: ~2, ~192/125
- WE ~2 = 1202.9225 ¢, ~192/125 = 787.4042 ¢
- error map: ⟨+2.922 +1.107 -8.583]
- CWE ~2 = 1200.0000 ¢, ~192/125 = 785.7808 ¢
- error map: ⟨0.000 -1.490 -14.752]
Optimal ET sequence: 3, …, 23, 26, 29, 55c
Badness (Sintel): 5.81
Septimal wesley
Subgroup: 2.3.5.7
Comma list: 405/392, 875/864
Mapping: [⟨1 -3 1 -7], ⟨0 7 2 15]]
- WE: ~2 = 1203.6434 ¢, ~14/9 = 786.8631 ¢
- error map: ⟨+3.634 -4.844 -8.944 +8.617]
- CWE: ~2 = 1200.0000 ¢, ~14/9 = 784.7754 ¢
- error map: ⟨0.000 -8.527 -16.763 +2.805]
Optimal ET sequence: 3d, …, 23d, 26
Badness (Sintel): 2.41
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 875/864
Mapping: [⟨1 -3 1 -7 -7], ⟨0 7 2 15 16]]
Optimal tunings:
- WE: ~2 = 1203.6405 ¢, ~11/7 = 786.6101 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 784.5242 ¢
Optimal ET sequence: 3de, …, 23de, 26
Badness (Sintel): 1.62
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 78/77, 99/98, 325/324
Mapping: [⟨1 -3 1 -7 -7 -12], ⟨0 7 2 15 16 24]]
Optimal tunings:
- WE: ~2 = 1200.0000 ¢, ~11/7 = 786.5973 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 784.5923 ¢
Optimal ET sequence: 3def, 23deff, 26
Badness (Sintel): 1.59
Snipes
Subgroup: 2.3.5.7
Comma list: 225/224, 6125/5832
Mapping: [⟨1 -3 1 -9], ⟨0 7 2 18]]
- WE: ~2 = 1201.9268 ¢, ~54/35 = 787.7496 ¢
- error map: ⟨+1.927 +6.511 -8.888 -6.675]
- CWE: ~2 = 1200.0000 ¢, ~54/35 = 786.6189 ¢
- error map: ⟨0.000 +4.377 -13.076 -9.686]
Optimal ET sequence: 3d, …, 26d, 29
Badness (Sintel): 2.98
11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 225/224, 245/242
Mapping: [⟨1 -3 1 -9 -9], ⟨0 7 2 18 19]]
Optimal tunings:
- WE: ~2 = 1201.9201 ¢, ~11/7 = 787.7690 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 786.6402 ¢
Optimal ET sequence: 3de, …, 26de, 29
Badness (Sintel): 1.79
Roman
Roman tempers out 525/512, the avicennma. The 7-limit version has also been proposed as crusher.
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3024
Mapping: [⟨1 -3 1 10], ⟨0 7 2 -11]]
- WE: ~2 = 1203.0258 ¢, ~63/40 = 787.4289 ¢
- error map: ⟨+3.026 +0.970 -8.430 -0.286]
- CWE: ~2 = 1200.0000 ¢, ~63/40 = 785.4717 ¢
- error map: ⟨0.000 -3.653 -15.370 -9.0145]
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness (Sintel): 2.87
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 525/512
Mapping: [⟨1 -3 1 10 10], ⟨0 7 2 -11 -10]]
Optimal tunings:
- WE: ~2 = 1202.7762 ¢, ~11/7 = 787.3465 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 785.5130 ¢
Optimal ET sequence: 3, 23, 26, 29, 55c
Badness (Sintel): 1.75
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 100/99, 105/104, 245/242
Mapping: [⟨1 -3 1 10 10 5], ⟨0 7 2 -11 -10 -2]]
Optimal tunings:
- WE: ~2 = 1202.8327 ¢, ~11/7 = 787.3820 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 785.5085 ¢
Optimal ET sequence: 3, 23, 26, 29, 55cf
Badness (Sintel): 1.24
Dubbla
Subgroup: 2.3.5.7
Comma list: 50/49, 78125/73728
Mapping: [⟨2 1 4 5], ⟨0 7 2 2]]
- mapping generators: ~7/5, ~192/175
Optimal ET sequence: 6, 20b, 26, 58c
Badness (Sintel): 4.60
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 tunings:
- WE: ~7/5 = 600.3702 ¢, ~11/10 = 185.9936 ¢
- CWE: ~7/5 = 600.0000 ¢, ~11/10 = 185.9408 ¢
Optimal ET sequence: 6, 20b, 26
Badness (Sintel): 2.51
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 tunings:
- WE: ~7/5 = 600.3563 ¢, ~11/10 = 185.8121 ¢
- CWE: ~7/5 = 600.0000 ¢, ~11/10 = 185.7623 ¢
Optimal ET sequence: 6f, 20bff, 26
Badness (Sintel): 2.05