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. More information on that can be found [http://tech.groups.yahoo.com/group/tuning-math/message/12793 here].
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. More information on that can be found [http://tech.groups.yahoo.com/group/tuning-math/message/12793 here].


=Wesley=
= Wesley =
Comma: 78125/73728
[[Comma]]: 78125/73728


POTE generator: ~125/96 = 414.509
[[Mapping]]: [<1 4 3|, <0 -7 -2|]


Map: [<1 4 3|, <0 -7 -2|]
[[POTE tuning|POTE generator]]: ~125/96 = 414.509


EDOs: 23, 26, 29, 55c
[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}


Badness: 0.2477
[[Badness]]: 0.247718


==7-limit==
== 7-limit ==
Commas: 405/392, 875/864
[[Comma list]]: 405/392, 875/864


POTE generator: ~9/7 = 415.519
[[Mapping]]: [<1 4 3 8|, <0 -7 -2 -15|]


Map: [<1 4 3 8|, <0 -7 -2 -15|]
[[Wedgie]]: <<7 2 15 -13 4 29||


Wedgie: <<7 2 15 -13 4 29||
[[POTE tuning|POTE generator]]: ~9/7 = 415.519


EDOs: 26
[[EDO|Vals]]: {{Val list| 3d, 23d, 26 }}


Badness: 0.0953
[[Badness]]: 0.095344


==11-limit==
== 11-limit ==
Commas: 45/44, 99/98, 875/864
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
POTE generator: ~9/7 = 415.769


Map: [<1 4 3 8 9|, <0 -7 -2 -15 -16|]
Vals: {{Val list| 3de, 23de, 26, 75bcd }}


EDOs: 23de, 26, 75bcd
Badness: 0.049066


Badness: 0.0491
== 13-limit ==
Comma list: 45/44, 78/77, 99/98, 325/324


==13-limit==
Mapping: [<1 4 3 8 9 12|, <0 -7 -2 -15 -16 -24|]
Commas: 45/44, 78/77, 99/98, 325/324


POTE generator: ~9/7 = 415.645
POTE generator: ~9/7 = 415.645


Map: [<1 4 3 8 9 12|, <0 -7 -2 -15 -16 -24|]
Vals: {{Val list| 3def, 26 }}
 
Badness: 0.038402
 
= Snipes =
[[Comma list]]: 225/224, 6125/5832
 
[[Mapping]]: [<1 4 3 9|, <0 -7 -2 -18|]
 
[[Wedgie]]: <<7 2 18 -13 9 36||
 
[[POTE tuning|POTE generator]]: ~35/27 = 413.513
 
[[EDO|Vals]]: {{Val list| 29, 90cd, 119cd }}
 
[[Badness]]: 0.117943
 
= Crusher =
This temperament is also known as ''roman temperament''.
 
[[Comma list]]: 525/512, 3125/3024
 
[[Mapping]]: [<1 4 3 -1|, <0 -7 -2 11|]
 
[[Wedgie]]: <<7 2 -11 -13 -37 -31||


EDOs: 26
[[POTE tuning|POTE generator]]: ~63/50 = 414.552


Badness: 0.0384
[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}


==Snipes==
[[Badness]]: 0.113386
Commas: 225/224, 6125/5832


POTE generator: ~35/27 = 413.513
== 11-limit ==
Comma list: 100/99, 245/242, 525/512


Map: [<1 4 3 9|, <0 -7 -2 -18|]
Mapping: [<1 4 3 -1 0|, <0 -7 -2 11 10|]


Wedgie: <<7 2 18 -13 9 36||
POTE generator: ~14/11 = 414.471


EDOs: 29, 90cd, 119cd
Vals: {{Val list| 3, 23, 26, 29, 55c }}


Badness: 0.1179
Badness: 0.052841


==Crusher==
== 13-limit ==
Commas: 525/512, 3125/3024
Comma list: 65/64, 100/99, 105/104, 245/242


POTE generator: ~63/50 = 414.552
Mapping: [<1 4 3 -1 0 3|, <0 -7 -2 11 10 2|]


Map: [<1 4 3 -1|, <0 -7 -2 11|]
POTE generator: ~14/11 = 414.472


Wedgie: <<7 2 -11 -13 -37 -31||
Vals: {{Val list| 3, 23, 26, 29, 55cf }}


EDOs: 23, 26, 29, 55c
Badness: 0.030043


Badness: 0.1134
= Dubbla =
[[Comma list]]: 50/49, 78125/73728


=Dubbla=
[[Mapping]]: [<2 1 4 5|, <0 7 2 2|]
Commas: 50/49, 78125/73728


POTE generator: ~192/175 = 185.738
[[Wedgie]]: <<14 4 4 -26 -33 -2||


Map: [<2 1 4 5|, <0 7 2 2|]
[[POTE tuning|POTE generator]]: ~192/175 = 185.738


Wedgie: <<14 4 4 -26 -33 -2||
[[EDO|Vals]]: {{Val list| 6, 26, 58c, 84c }}


EDOs: 6, 26, 58c, 84c
[[Badness]]: 0.181726


Badness: 0.1817
== 11-limit ==
Comma list: 50/49, 125/121, 1344/1331


==11-limit==
Mapping: [<2 1 4 5 6|, <0 7 2 2 3|]
Commas: 50/49, 125/121, 1344/1331


POTE generator: ~11/10 = 185.879
POTE generator: ~11/10 = 185.879


Map: [<2 1 4 5 6|, <0 7 2 2 3|]
Vals: {{Val list| 6, 26, 58c, 84c }}


EDOs: 6, 26, 58c, 84c
Badness: 0.075842


Badness: 0.0758
== 13-limit ==
Comma list: 50/49, 105/104, 125/121, 144/143


==13-limit==
Mapping: [<2 1 4 5 6 4|, <0 7 2 2 3 11|]
Commas: 50/49, 105/104, 125/121, 144/143


POTE generator: ~11/10 = 185.702
POTE generator: ~11/10 = 185.702


Map: [<2 1 4 5 6 4|, <0 7 2 2 3 11|]
Vals: {{Val list| 26, 58c, 84c }}


EDOs: 26, 58c, 84c
Badness: 0.049603


Badness: 0.0496
[[Category:Temperament]]

Revision as of 14:20, 20 April 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. More information on that can be found here.

Wesley

Comma: 78125/73728

Mapping: [<1 4 3|, <0 -7 -2|]

POTE generator: ~125/96 = 414.509

Vals: Template:Val list

Badness: 0.247718

7-limit

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

Vals: Template:Val list

Badness: 0.095344

11-limit

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

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

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

Vals: Template:Val list

Badness: 0.117943

Crusher

This temperament is also known as roman temperament.

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

Vals: Template:Val list

Badness: 0.113386

11-limit

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

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

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

Vals: Template:Val list

Badness: 0.181726

11-limit

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

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

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