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]{{dead link}}.
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.


== Wesley ==
== Wesley ==
Subgroup: 2.3.5
[[Comma]]: 78125/73728
[[Comma]]: 78125/73728


Line 13: Line 15:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 405/392, 875/864
[[Comma list]]: 405/392, 875/864


Line 26: Line 30:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 875/864
Comma list: 45/44, 99/98, 875/864


Line 37: Line 43:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 78/77, 99/98, 325/324
Comma list: 45/44, 78/77, 99/98, 325/324


Line 48: Line 56:


== Snipes ==
== Snipes ==
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 6125/5832
[[Comma list]]: 225/224, 6125/5832


Line 60: Line 70:
[[Badness]]: 0.117943
[[Badness]]: 0.117943


== Crusher ==
== Roman ==
This temperament is also known as ''[[Avicennmic temperaments #Roman|roman temperament]]''.
{{see also|Avicennmic temperaments #Roman}}
 
=== 7-limit (Crusher) ===
Subgroup: 2.3.5.7


[[Comma list]]: 525/512, 3125/3024
[[Comma list]]: 525/512, 3125/3024
Line 76: Line 89:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 525/512
Comma list: 100/99, 245/242, 525/512


Line 87: Line 102:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 100/99, 105/104, 245/242
Comma list: 65/64, 100/99, 105/104, 245/242


Line 98: Line 115:


== Dubbla ==
== Dubbla ==
Subgroup: 2.3.5.7
[[Comma list]]: 50/49, 78125/73728
[[Comma list]]: 50/49, 78125/73728


Line 111: Line 130:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 50/49, 125/121, 1344/1331
Comma list: 50/49, 125/121, 1344/1331


Line 122: Line 143:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 105/104, 125/121, 144/143
Comma list: 50/49, 105/104, 125/121, 144/143


Revision as of 01:38, 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.

Wesley

Subgroup: 2.3.5

Comma: 78125/73728

Mapping: [⟨1 4 3], ⟨0 -7 -2]]

POTE generator: ~125/96 = 414.509

Template:Val list

Badness: 0.247718

7-limit

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

Template:Val list

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

Template:Val list

Badness: 0.117943

Roman

See also: Avicennmic temperaments § 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

Template:Val list

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

Template:Val list

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

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