Avicennmic temperaments: Difference between revisions
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=== 7-limit (Crusher) === | === 7-limit (Crusher) === | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 525/512, 3125/3024 | [[Comma list]]: 525/512, 3125/3024 | ||
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=== 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 | ||
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=== 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 | ||
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=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 35/34, 52/51, 65/64, 100/99, 121/119 | Comma list: 35/34, 52/51, 65/64, 100/99, 121/119 | ||
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=== 19-limit === | === 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 | Comma list: 35/34, 52/51, 65/64, 100/99, 121/119, 133/132 | ||
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== Secund == | == Secund == | ||
{{see also|Greenwoodmic temperaments #Secund}} | {{see also|Greenwoodmic temperaments #Secund}} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 405/392, 525/512 | [[Comma list]]: 405/392, 525/512 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 45/44, 99/98, 385/384 | Comma list: 45/44, 99/98, 385/384 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 27/26, 45/44, 99/98, 385/384 | Comma list: 27/26, 45/44, 99/98, 385/384 | ||
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=== Secundly === | === Secundly === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 45/44, 65/64, 78/77, 99/98 | Comma list: 45/44, 65/64, 78/77, 99/98 | ||
Revision as of 01:29, 2 August 2021
These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.
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
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.026212