Wesley family: Difference between revisions
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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, in other words. | 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, in other words. Here is [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12793.html a talk by Gene Ward Smith]. | ||
== Wesley == | == Wesley == | ||
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[[Comma]]: 78125/73728 | [[Comma]]: 78125/73728 | ||
[[Mapping]]: [{{ | [[Mapping]]: [{{val| 1 4 3 }}, {{val| 0 -7 -2 }}] | ||
[[POTE generator]]: ~125/96 = 414.509 | [[POTE generator]]: ~125/96 = 414.509 | ||
| Line 14: | Line 14: | ||
[[Badness]]: 0.247718 | [[Badness]]: 0.247718 | ||
== | == Septimal wesley == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: 405/392, 875/864 | [[Comma list]]: 405/392, 875/864 | ||
[[Mapping]]: [{{ | [[Mapping]]: [{{val| 1 4 3 8 }}, {{val| 0 -7 -2 -15 }}] | ||
{{Multival|legend=1|7 2 15 -13 4 29}} | {{Multival|legend=1|7 2 15 -13 4 29}} | ||
| Line 34: | Line 34: | ||
Comma list: 45/44, 99/98, 875/864 | Comma list: 45/44, 99/98, 875/864 | ||
Mapping: [{{ | Mapping: [{{val| 1 4 3 8 9 }}, {{val| 0 -7 -2 -15 -16 }}] | ||
POTE generator: ~9/7 = 415.769 | POTE generator: ~9/7 = 415.769 | ||
| Line 47: | Line 47: | ||
Comma list: 45/44, 78/77, 99/98, 325/324 | Comma list: 45/44, 78/77, 99/98, 325/324 | ||
Mapping: [{{ | Mapping: [{{val| 1 4 3 8 9 12 }}, {{val| 0 -7 -2 -15 -16 -24 }}] | ||
POTE generator: ~9/7 = 415.645 | POTE generator: ~9/7 = 415.645 | ||
| Line 60: | Line 60: | ||
[[Comma list]]: 225/224, 6125/5832 | [[Comma list]]: 225/224, 6125/5832 | ||
[[Mapping]]: [{{ | [[Mapping]]: [{{val| 1 4 3 9 }}, {{val| 0 -7 -2 -18 }}] | ||
{{Multival|legend=1|7 2 18 -13 9 36}} | {{Multival|legend=1|7 2 18 -13 9 36}} | ||
| Line 78: | Line 78: | ||
[[Comma list]]: 525/512, 3125/3024 | [[Comma list]]: 525/512, 3125/3024 | ||
[[Mapping]]: [{{ | [[Mapping]]: [{{val| 1 4 3 -1 }}, {{val| 0 -7 -2 11 }}] | ||
{{Multival|legend=1|7 2 -11 -13 -37 -31}} | {{Multival|legend=1|7 2 -11 -13 -37 -31}} | ||
| Line 93: | Line 93: | ||
Comma list: 100/99, 245/242, 525/512 | Comma list: 100/99, 245/242, 525/512 | ||
Mapping: [{{ | Mapping: [{{val| 1 4 3 -1 0 }}, {{val| 0 -7 -2 11 10 }}] | ||
POTE generator: ~14/11 = 414.471 | POTE generator: ~14/11 = 414.471 | ||
| Line 106: | Line 106: | ||
Comma list: 65/64, 100/99, 105/104, 245/242 | Comma list: 65/64, 100/99, 105/104, 245/242 | ||
Mapping: [{{ | Mapping: [{{val| 1 4 3 -1 0 3 }}, {{val| 0 -7 -2 11 10 2 }}] | ||
POTE generator: ~14/11 = 414.472 | POTE generator: ~14/11 = 414.472 | ||
| Line 119: | Line 119: | ||
[[Comma list]]: 50/49, 78125/73728 | [[Comma list]]: 50/49, 78125/73728 | ||
[[Mapping]]: [{{ | [[Mapping]]: [{{val| 2 1 4 5 }}, {{val| 0 7 2 2 }}] | ||
{{Multival|legend=1|14 4 4 -26 -33 -2}} | {{Multival|legend=1|14 4 4 -26 -33 -2}} | ||
| Line 134: | Line 134: | ||
Comma list: 50/49, 125/121, 1344/1331 | Comma list: 50/49, 125/121, 1344/1331 | ||
Mapping: [{{ | Mapping: [{{val| 2 1 4 5 6 }}, {{val| 0 7 2 2 3 }}] | ||
POTE generator: ~11/10 = 185.879 | POTE generator: ~11/10 = 185.879 | ||
| Line 147: | Line 147: | ||
Comma list: 50/49, 105/104, 125/121, 144/143 | Comma list: 50/49, 105/104, 125/121, 144/143 | ||
Mapping: [{{ | Mapping: [{{val| 2 1 4 5 6 4 }}, {{val| 0 7 2 2 3 11 }}] | ||
POTE generator: ~11/10 = 185.702 | POTE generator: ~11/10 = 185.702 | ||
| Line 155: | Line 155: | ||
Badness: 0.049603 | Badness: 0.049603 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Wesley family| ]] <!-- main article --> | |||
[[Category:Rank 2]] | |||
Revision as of 06:03, 2 August 2021
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, 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
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Badness: 0.117943
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.049603