Avicennmic temperaments: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 15: Line 15:
[[POTE generator]]: ~63/50 = 414.552
[[POTE generator]]: ~63/50 = 414.552


{{Val list|legend=1| 3, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}


[[Badness]]: 0.113386
[[Badness]]: 0.113386
Line 28: Line 28:
POTE generator: ~14/11 = 414.471
POTE generator: ~14/11 = 414.471


Vals: {{Val list| 3, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}


Badness: 0.052841
Badness: 0.052841
Line 41: Line 41:
POTE generator: ~14/11 = 414.472
POTE generator: ~14/11 = 414.472


Vals: {{Val list| 3, 23, 26, 29, 55cf }}
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}


Badness: 0.030043
Badness: 0.030043
Line 54: Line 54:
POTE generator: ~14/11 = 414.164
POTE generator: ~14/11 = 414.164


Vals: {{Val list| 3, 26g, 29 }}
{{Optimal ET sequence|legend=1| 3, 26g, 29 }}


Badness: 0.041555
Badness: 0.041555
Line 67: Line 67:
POTE generator: ~14/11 = 414.130
POTE generator: ~14/11 = 414.130


Vals: {{Val list| 3, 26g, 29 }}
{{Optimal ET sequence|legend=1| 3, 26g, 29 }}


Badness: 0.033730
Badness: 0.033730
Line 84: Line 84:
[[POTE generator]]: ~16/15 = 137.958
[[POTE generator]]: ~16/15 = 137.958


{{Val list|legend=1| 9, 17, 26, 61bc, 87bcc }}
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}


[[Badness]]: 0.089840
[[Badness]]: 0.089840
Line 97: Line 97:
POTE generator: ~12/11 = 137.900
POTE generator: ~12/11 = 137.900


Vals: {{Val list| 9, 17, 26, 61bc, 87bcc }}
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}


Badness: 0.042562
Badness: 0.042562
Line 110: Line 110:
POTE generator: ~12/11 = 136.937
POTE generator: ~12/11 = 136.937


Vals: {{Val list| 9, 26f, 35 }}
{{Optimal ET sequence|legend=1| 9, 26f, 35 }}


Badness: 0.049684
Badness: 0.049684
Line 123: Line 123:
POTE generator: ~12/11 = 137.917
POTE generator: ~12/11 = 137.917


Vals: {{Val list| 9, 17, 26, 61bcf, 87bccf }}
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bcf, 87bccf }}


Badness: 0.026212
Badness: 0.026212

Revision as of 18:15, 7 May 2023

These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, dichotic, flattone, hexadecimal, muggles, lemba, deflated, and pycnic.

Roman

See also: Wesley family § 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

Optimal ET sequence: 3, 23, 26, 29, 55c

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

Optimal ET sequence: 3, 23, 26, 29, 55c

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

Optimal ET sequence: 3, 23, 26, 29, 55cf

Badness: 0.030043

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 35/34, 52/51, 65/64, 100/99, 121/119

Mapping: [⟨1 4 3 -1 0 3 1], ⟨0 -7 -2 11 10 2 9]]

POTE generator: ~14/11 = 414.164

Optimal ET sequence: 3, 26g, 29

Badness: 0.041555

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 35/34, 52/51, 65/64, 100/99, 121/119, 133/132

Mapping: [⟨1 4 3 -1 0 3 1 7], ⟨0 -7 -2 11 10 2 9 -8]]

POTE generator: ~14/11 = 414.130

Optimal ET sequence: 3, 26g, 29

Badness: 0.033730

Secund

See also: Greenwoodmic temperaments § Secund

Subgroup: 2.3.5.7

Comma list: 405/392, 525/512

Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]

Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]

POTE generator: ~16/15 = 137.958

Optimal ET sequence: 9, 17, 26, 61bc, 87bcc

Badness: 0.089840

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]

POTE generator: ~12/11 = 137.900

Optimal ET sequence: 9, 17, 26, 61bc, 87bcc

Badness: 0.042562

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]

POTE generator: ~12/11 = 136.937

Optimal ET sequence: 9, 26f, 35

Badness: 0.049684

Secundly

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 65/64, 78/77, 99/98

Mapping: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]

POTE generator: ~12/11 = 137.917

Optimal ET sequence: 9, 17, 26, 61bcf, 87bccf

Badness: 0.026212

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