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]{{dead link}}.


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


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


[[POTE tuning|POTE generator]]: ~125/96 = 414.509
[[POTE generator]]: ~125/96 = 414.509


[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}
{{Val list|legend=1| 3, 23, 26, 29, 55c }}


[[Badness]]: 0.247718
[[Badness]]: 0.247718


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


[[Mapping]]: [<1 4 3 8|, <0 -7 -2 -15|]
[[Mapping]]: [{{Val|1 4 3 8}}, {{Val|0 -7 -2 -15}}]


[[Wedgie]]: <<7 2 15 -13 4 29||
{{Multival|legend=1|7 2 15 -13 4 29}}


[[POTE tuning|POTE generator]]: ~9/7 = 415.519
[[POTE generator]]: ~9/7 = 415.519


[[EDO|Vals]]: {{Val list| 3d, 23d, 26 }}
{{Val list|legend=1| 3d, 23d, 26 }}


[[Badness]]: 0.095344
[[Badness]]: 0.095344


== 11-limit ==
=== 11-limit ===
Comma list: 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|]
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 36: Line 36:
Badness: 0.049066
Badness: 0.049066


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


Mapping: [<1 4 3 8 9 12|, <0 -7 -2 -15 -16 -24|]
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 47: Line 47:
Badness: 0.038402
Badness: 0.038402


= Snipes =
== Snipes ==
[[Comma list]]: 225/224, 6125/5832
[[Comma list]]: 225/224, 6125/5832


[[Mapping]]: [<1 4 3 9|, <0 -7 -2 -18|]
[[Mapping]]: [{{Val|1 4 3 9}}, {{Val|0 -7 -2 -18}}]


[[Wedgie]]: <<7 2 18 -13 9 36||
{{Multival|legend=1|7 2 18 -13 9 36}}


[[POTE tuning|POTE generator]]: ~35/27 = 413.513
[[POTE generator]]: ~35/27 = 413.513


[[EDO|Vals]]: {{Val list| 29, 90cd, 119cd }}
{{Val list|legend=1| 29, 90cd, 119cd }}


[[Badness]]: 0.117943
[[Badness]]: 0.117943


= Crusher =
== Crusher ==
This temperament is also known as ''roman temperament''.
This temperament is also known as ''roman temperament''.


[[Comma list]]: 525/512, 3125/3024
[[Comma list]]: 525/512, 3125/3024


[[Mapping]]: [<1 4 3 -1|, <0 -7 -2 11|]
[[Mapping]]: [{{Val|1 4 3 -1}}, {{Val|0 -7 -2 11}}]


[[Wedgie]]: <<7 2 -11 -13 -37 -31||
{{Multival|legend=1|7 2 -11 -13 -37 -31}}


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


[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}
{{Val list|legend=1| 3, 23, 26, 29, 55c }}


[[Badness]]: 0.113386
[[Badness]]: 0.113386


== 11-limit ==
=== 11-limit ===
Comma list: 100/99, 245/242, 525/512
Comma list: 100/99, 245/242, 525/512


Mapping: [<1 4 3 -1 0|, <0 -7 -2 11 10|]
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 86: Line 86:
Badness: 0.052841
Badness: 0.052841


== 13-limit ==
=== 13-limit ===
Comma list: 65/64, 100/99, 105/104, 245/242
Comma list: 65/64, 100/99, 105/104, 245/242


Mapping: [<1 4 3 -1 0 3|, <0 -7 -2 11 10 2|]
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 97: Line 97:
Badness: 0.030043
Badness: 0.030043


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


[[Mapping]]: [<2 1 4 5|, <0 7 2 2|]
[[Mapping]]: [{{Val|2 1 4 5}}, {{Val|0 7 2 2}}]


[[Wedgie]]: <<14 4 4 -26 -33 -2||
{{Multival|legend=1|14 4 4 -26 -33 -2}}


[[POTE tuning|POTE generator]]: ~192/175 = 185.738
[[POTE generator]]: ~192/175 = 185.738


[[EDO|Vals]]: {{Val list| 6, 26, 58c, 84c }}
{{Val list|legend=1| 6, 26, 58c, 84c }}


[[Badness]]: 0.181726
[[Badness]]: 0.181726


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


Mapping: [<2 1 4 5 6|, <0 7 2 2 3|]
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 121: Line 121:
Badness: 0.075842
Badness: 0.075842


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


Mapping: [<2 1 4 5 6 4|, <0 7 2 2 3 11|]
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 133: Line 133:


[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Temperament family]]

Revision as of 03:19, 10 June 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[dead link].

Wesley

Comma: 78125/73728

Mapping: [⟨1 4 3], ⟨0 -7 -2]]

POTE generator: ~125/96 = 414.509

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

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

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

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

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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