Vishnuzmic family: Difference between revisions
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The '''vishnuzmic family''' of temperaments tempers out the [[vishnuzma]], {{Monzo| 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) | The '''vishnuzmic family''' of temperaments tempers out the [[vishnuzma]], {{Monzo| 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)<sup>7</sup>. | ||
== Vishnuzmic == | == Vishnuzmic == | ||
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[[Comma]]: 6115295232/6103515625 | [[Comma]]: 6115295232/6103515625 | ||
[[Mapping]]: [{{val|2 4 5}}, {{val|0 -7 -3}}] | [[Mapping]]: [{{val| 2 4 5 }}, {{val| 0 -7 -3 }}] | ||
[[POTE generator]]: ~25/24 = 71.143 | [[POTE generator]]: ~25/24 = 71.143 | ||
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[[Comma list]]: 4375/4374, 29360128/29296875 | [[Comma list]]: 4375/4374, 29360128/29296875 | ||
[[Mapping]]: [{{val|2 4 5 10}}, {{val|0 -7 -3 -37}}] | [[Mapping]]: [{{val| 2 4 5 10 }}, {{val| 0 -7 -3 -37 }}] | ||
{{Multival|legend=1|14 6 74 -23 78 155}} | {{Multival|legend=1|14 6 74 -23 78 155}} | ||
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Comma list: 3025/3024, 4375/4374, 5632/5625 | Comma list: 3025/3024, 4375/4374, 5632/5625 | ||
Mapping: [{{val|2 4 5 10 10}}, {{val|0 -7 -3 -37 -26}}] | Mapping: [{{val| 2 4 5 10 10 }}, {{val| 0 -7 -3 -37 -26 }}] | ||
POTE generator: ~25/24 = 71.105 | POTE generator: ~25/24 = 71.105 | ||
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Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374 | Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374 | ||
Mapping: [{{val|2 4 5 10 10 1}}, {{val|0 -7 -3 -37 -26 54}}] | Mapping: [{{val| 2 4 5 10 10 1 }}, {{val| 0 -7 -3 -37 -26 54 }}] | ||
POTE generator: ~25/24 = 71.117 | POTE generator: ~25/24 = 71.117 | ||
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Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625 | Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625 | ||
Mapping: [{{val|2 4 5 10 10 17}}, {{val|0 -7 -3 -37 -26 -81}}] | Mapping: [{{val| 2 4 5 10 10 17 }}, {{val| 0 -7 -3 -37 -26 -81 }}] | ||
POTE generator: ~25/24 = 71.101 | POTE generator: ~25/24 = 71.101 | ||
Vals: {{Val list| 270, 692, 962, 1654cd, 2616bcdf }} | Vals: {{Val list| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }} | ||
Badness: 0.015805 | Badness: 0.015805 | ||
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[[Comma list]]: 126/125, 540225/524288 | [[Comma list]]: 126/125, 540225/524288 | ||
[[Mapping]]: [{{val|2 4 5 5}}, {{val|0 -7 -3 5}}] | [[Mapping]]: [{{val| 2 4 5 5 }}, {{val| 0 -7 -3 5 }}] | ||
{{Multival|legend=1|14 6 -10 -23 -55 -40}} | {{Multival|legend=1|14 6 -10 -23 -55 -40}} | ||
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Comma list: 126/125, 385/384, 1350/1331 | Comma list: 126/125, 385/384, 1350/1331 | ||
Mapping: [{{val|2 4 5 5 8}}, {{val|0 -7 -3 5 -9}}] | Mapping: [{{val| 2 4 5 5 8 }}, {{val| 0 -7 -3 5 -9 }}] | ||
POTE generator: ~25/24 = 71.924 | POTE generator: ~25/24 = 71.924 | ||
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Comma list: 105/104, 126/125, 144/143, 847/845 | Comma list: 105/104, 126/125, 144/143, 847/845 | ||
Mapping: [{{val|2 4 5 5 8 8}}, {{val|0 -7 -3 5 -9 -5}}] | Mapping: [{{val| 2 4 5 5 8 8 }}, {{val| 0 -7 -3 5 -9 -5 }}] | ||
POTE generator: ~25/24 = 71.926 | POTE generator: ~25/24 = 71.926 | ||
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[[Comma list]]: 2401/2400, 6115295232/6103515625 | [[Comma list]]: 2401/2400, 6115295232/6103515625 | ||
[[Mapping]]: [{{val|2 4 5 6}}, {{val|0 -28 -12 -13}}] | [[Mapping]]: [{{val| 2 4 5 6 }}, {{val| 0 -28 -12 -13 }}] | ||
{{Multival|legend=1|56 24 26 -92 -116 -7}} | {{Multival|legend=1|56 24 26 -92 -116 -7}} | ||
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Comma list: 2401/2400, 9801/9800, 172032/171875 | Comma list: 2401/2400, 9801/9800, 172032/171875 | ||
Mapping: [{{val|2 4 5 6 6}}, {{val|0 -28 -12 -13 31}}] | Mapping: [{{val| 2 4 5 6 6 }}, {{val| 0 -28 -12 -13 31 }}] | ||
POTE generator: ~7/5 = 582.213 | POTE generator: ~7/5 = 582.213 | ||
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[[Comma list]]: 420175/419904, 2202927104/2197265625 | [[Comma list]]: 420175/419904, 2202927104/2197265625 | ||
[[Mapping]]: [{{val|10 13 22 24}}, {{val|0 7 3 10}}] | [[Mapping]]: [{{val| 10 13 22 24 }}, {{val| 0 7 3 10 }}] | ||
{{Multival|legend=1|70 30 100 -115 -38 148}} | {{Multival|legend=1|70 30 100 -115 -38 148}} | ||
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Comma list: 9801/9800, 41503/41472, 172032/171875 | Comma list: 9801/9800, 41503/41472, 172032/171875 | ||
Mapping: [{{val|10 13 22 24 35}}, {{val|0 7 3 10 -1}}] | Mapping: [{{val| 10 13 22 24 35 }}, {{val| 0 7 3 10 -1 }}] | ||
POTE generator: ~25/24 = 71.141 | POTE generator: ~25/24 = 71.141 | ||
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Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655 | Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655 | ||
Mapping: [{{val|10 13 22 24 35 37}}, {{val|0 7 3 10 -1 0}}] | Mapping: [{{val| 10 13 22 24 35 37 }}, {{val| 0 7 3 10 -1 0 }}] | ||
POTE generator: ~25/24 = 71.151 | POTE generator: ~25/24 = 71.151 | ||
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Badness: 0.021906 | Badness: 0.021906 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Vishnuzmic]] | [[Category:Vishnuzmic]] | ||
[[Category:Vishnuzmic family| ]] <!-- main article --> | [[Category:Vishnuzmic family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | |||