Vishnuzmic family: Difference between revisions
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== Vishnuzmic == | == Vishnuzmic == | ||
Subgroup: 2.3.5 | |||
[[Comma]]: 6115295232/6103515625 | [[Comma]]: 6115295232/6103515625 | ||
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== Vishnu == | == Vishnu == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4375/4374, 29360128/29296875 | [[Comma list]]: 4375/4374, 29360128/29296875 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 4375/4374, 5632/5625 | Comma list: 3025/3024, 4375/4374, 5632/5625 | ||
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=== Ananta === | === Ananta === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374 | Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374 | ||
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=== Acyuta === | === Acyuta === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625 | Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625 | ||
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== Quarvish == | == Quarvish == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 2401/2400, 6115295232/6103515625 | [[Comma list]]: 2401/2400, 6115295232/6103515625 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 2401/2400, 9801/9800, 172032/171875 | Comma list: 2401/2400, 9801/9800, 172032/171875 | ||
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== Decavish == | == Decavish == | ||
The ''decavish'' temperament (50&270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}} = 578509309952/576650390625. | The ''decavish'' temperament (50&270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}} = 578509309952/576650390625. | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 420175/419904, 2202927104/2197265625 | [[Comma list]]: 420175/419904, 2202927104/2197265625 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, 41503/41472, 172032/171875 | Comma list: 9801/9800, 41503/41472, 172032/171875 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655 | Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655 | ||
Revision as of 01:52, 6 June 2021
The vishnuzmic family of temperaments tempers out the vishnuzma, [23 6 -14⟩ = 6115295232/6103515625, a 5-limit comma of about 3 cents. It is the amount by which seven just chromatic semitones of 25/24 fall short of a just perfect fourth of 4/3, or in other words (4/3)/(25/24)^7.
Vishnuzmic
Subgroup: 2.3.5
Comma: 6115295232/6103515625
Mapping: [⟨2 4 5], ⟨0 -7 -3]]
POTE generator: ~25/24 = 71.143
Badness: 0.031181
Vishnu
Subgroup: 2.3.5.7
Comma list: 4375/4374, 29360128/29296875
Mapping: [⟨2 4 5 10], ⟨0 -7 -3 -37]]
Wedgie: ⟨⟨ 14 6 74 -23 78 155 ]]
POTE generator: ~25/24 = 71.107
Badness: 0.041912
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5632/5625
Mapping: [⟨2 4 5 10 10], ⟨0 -7 -3 -37 -26]]
POTE generator: ~25/24 = 71.105
Vals: Template:Val list
Badness: 0.014180
Ananta
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Mapping: [⟨2 4 5 10 10 1], ⟨0 -7 -3 -37 -26 54]]
POTE generator: ~25/24 = 71.117
Vals: Template:Val list
Badness: 0.023678
Acyuta
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
Mapping: [⟨2 4 5 10 10 17], ⟨0 -7 -3 -37 -26 -81]]
POTE generator: ~25/24 = 71.101
Vals: Template:Val list
Badness: 0.015805
Quarvish
Subgroup: 2.3.5.7
Comma list: 2401/2400, 6115295232/6103515625
Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]
Wedgie: ⟨⟨ 56 24 26 -92 -116 -7 ]]
POTE generator: ~7/5 = 582.213
Badness: 0.045029
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 172032/171875
Mapping: [⟨2 4 5 6 6], ⟨0 -28 -12 -13 31]]
POTE generator: ~7/5 = 582.213
Vals: Template:Val list
Badness: 0.019868
Decavish
The decavish temperament (50&270) tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904 and the linus comma, [11 -10 -10 10⟩ = 578509309952/576650390625.
Subgroup: 2.3.5.7
Comma list: 420175/419904, 2202927104/2197265625
Mapping: [⟨10 13 22 24], ⟨0 7 3 10]]
Wedgie: ⟨⟨ 70 30 100 -115 -38 148 ]]
POTE generator: ~25/24 = 71.129
Badness: 0.114531
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472, 172032/171875
Mapping: [⟨10 13 22 24 35], ⟨0 7 3 10 -1]]
POTE generator: ~25/24 = 71.141
Vals: Template:Val list
Badness: 0.036938
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
Mapping: [⟨10 13 22 24 35 37], ⟨0 7 3 10 -1 0]]
POTE generator: ~25/24 = 71.151
Vals: Template:Val list
Badness: 0.021906