Avicennmic temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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POTE generator: ~12/11 = 137.900 | POTE generator: ~12/11 = 137.900 | ||
{{Optimal ET sequence | Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bc, 87bcc }} | ||
Badness: 0.042562 | Badness: 0.042562 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~12/11 = 136.937 | POTE generator: ~12/11 = 136.937 | ||
{{Optimal ET sequence | Optimal ET sequence: {{Optimal ET sequence| 9, 26f, 35 }} | ||
Badness: 0.049684 | Badness: 0.049684 | ||
=== Secundly === | ==== Secundly ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 123: | Line 123: | ||
POTE generator: ~12/11 = 137.917 | POTE generator: ~12/11 = 137.917 | ||
{{Optimal ET sequence | Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bcf, 87bccf }} | ||
Badness: 0.026212 | Badness: 0.026212 | ||
Revision as of 14:01, 7 July 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
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
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