Vishnu family: Difference between revisions
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POTE generator: ~25/24 = 71.105 | POTE generator: ~25/24 = 71.105 | ||
Optimal GPV sequence: {{Val list| 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }} | |||
Badness: 0.014180 | Badness: 0.014180 | ||
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POTE generator: ~25/24 = 71.117 | POTE generator: ~25/24 = 71.117 | ||
Optimal GPV sequence: {{Val list| 118, 152, 270, 928, 1198, 1468 }} | |||
Badness: 0.023678 | Badness: 0.023678 | ||
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POTE generator: ~25/24 = 71.101 | POTE generator: ~25/24 = 71.101 | ||
Optimal GPV sequence: {{Val list| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }} | |||
Badness: 0.015805 | Badness: 0.015805 | ||
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POTE generator: ~25/24 = 71.924 | POTE generator: ~25/24 = 71.924 | ||
Optimal GPV sequence: {{Val list| 16, 34, 50 }} | |||
Badness: 0.071990 | Badness: 0.071990 | ||
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POTE generator: ~25/24 = 71.926 | POTE generator: ~25/24 = 71.926 | ||
Optimal GPV sequence: {{Val list| 16, 34, 50 }} | |||
Badness: 0.040739 | Badness: 0.040739 | ||
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POTE generator: ~25/24 = 71.248 | POTE generator: ~25/24 = 71.248 | ||
Optimal GPV sequence: {{Val list| 34e, 84, 118, 202, 320 }} | |||
Badness: 0.045908 | Badness: 0.045908 | ||
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{{Val list|legend=1| 68, 134, 202, 270, 742, 1012 }} | {{Val list|legend=1| 68, 134, 202, 270, 742, 1012 }} | ||
Badness: 0.045029 | [[Badness]]: 0.045029 | ||
=== 11-limit === | === 11-limit === | ||
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POTE generator: ~7/5 = 582.213 | POTE generator: ~7/5 = 582.213 | ||
Optimal GPV sequence: {{Val list| 68, 134, 202, 270, 742, 1012 }} | |||
Badness: 0.019868 | Badness: 0.019868 | ||
== Decavish == | == Decavish == | ||
The ''decavish'' temperament (50&270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/ | The ''decavish'' temperament (50&270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/14 equal-step tuning|linus comma]], {{monzo|11 -10 -10 10}} = 578509309952/576650390625. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~25/24 = 71.141 | POTE generator: ~25/24 = 71.141 | ||
Optimal GPV sequence: {{Val list| 50, 220, 270, 860, 1130, 1400, 3070cd, 4470cde }} | |||
Badness: 0.036938 | Badness: 0.036938 | ||
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POTE generator: ~25/24 = 71.151 | POTE generator: ~25/24 = 71.151 | ||
Optimal GPV sequence: {{Val list| 50, 220, 270, 590, 860, 1130 }} | |||
Badness: 0.021906 | Badness: 0.021906 | ||
Revision as of 16:36, 8 January 2022
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.
Vishnu
Subgroup: 2.3.5
Comma list: 6115295232/6103515625
Mapping: [⟨2 4 5], ⟨0 -7 -3]]
POTE generator: ~25/24 = 71.143
Badness: 0.031181
Septimal 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.015805
Vishnean
Subgroup: 2.3.5.7
Comma list: 126/125, 540225/524288
Mapping: [⟨2 4 5 5], ⟨0 -7 -3 5]]
Wedgie: ⟨⟨ 14 6 -10 -23 -55 -40 ]]
POTE generator: ~25/24 = 71.779
Badness: 0.161398
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384, 1350/1331
Mapping: [⟨2 4 5 5 8], ⟨0 -7 -3 5 -9]]
POTE generator: ~25/24 = 71.924
Optimal GPV sequence: Template:Val list
Badness: 0.071990
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 144/143, 847/845
Mapping: [⟨2 4 5 5 8 8], ⟨0 -7 -3 5 -9 -5]]
POTE generator: ~25/24 = 71.926
Optimal GPV sequence: Template:Val list
Badness: 0.040739
Narayana
Subgroup: 2.3.5.7
Comma list: 65625/65536, 321489/320000
Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]
Wedgie: ⟨⟨ 14 6 -44 -23 -109 -119 ]]
POTE generator: ~25/24 = 71.265
Badness: 0.094295
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 65625/65536
Mapping: [⟨2 4 5 3 3], ⟨0 -7 -3 22 33]]
POTE generator: ~25/24 = 71.248
Optimal GPV sequence: Template:Val list
Badness: 0.045908
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.021906