Avicennmic temperaments

Revision as of 14:01, 7 July 2023 by Xenllium (talk | contribs)

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

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 sequence3, 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 sequence3, 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 sequence3, 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 sequence3, 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 sequence3, 26g, 29

Badness: 0.033730

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 sequence9, 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