Vishnuzmic family: Difference between revisions

Revision as of 10:23, 24 July 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

Template:Val list

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

Template:Val list

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

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

Template:Val list

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

Vals: 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

Vals: Template:Val list

Badness: 0.040739

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

Template:Val list

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

Template:Val list

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

@@ Line 1: / Line 1: @@
-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)^7.
+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 ==
@@ Line 6: / Line 6: @@
 [[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
@@ Line 19: / Line 19: @@
 [[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}}
@@ Line 34: / Line 34: @@
 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
@@ Line 47: / Line 47: @@
 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
@@ Line 60: / Line 60: @@
 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
-Vals: {{Val list| 270, 692, 962, 1654cd, 2616bcdf }}
+Vals: {{Val list| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
 Badness: 0.015805
@@ Line 73: / Line 73: @@
 [[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}}
@@ Line 88: / Line 88: @@
 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
@@ Line 101: / Line 101: @@
 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
@@ Line 114: / Line 114: @@
 [[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}}
@@ Line 129: / Line 129: @@
 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
@@ Line 144: / Line 144: @@
 [[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}}
@@ Line 159: / Line 159: @@
 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
@@ Line 172: / Line 172: @@
 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
@@ Line 180: / Line 180: @@
 Badness: 0.021906
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
 [[Category:Vishnuzmic]]
 [[Category:Vishnuzmic family| ]] <!-- main article -->
+[[Category:Rank 2]]

Vishnuzmic family: Difference between revisions

Revision as of 10:23, 24 July 2021

Contents

Vishnuzmic

Vishnu

11-limit

Ananta

Acyuta

Vishnean

11-limit

13-limit

Quarvish

11-limit

Decavish

11-limit

13-limit

Navigation menu

Vishnuzmic family: Difference between revisions

Revision as of 10:23, 24 July 2021

Vishnuzmic

Vishnu

11-limit

Ananta

Acyuta

Vishnean

11-limit

13-limit

Quarvish

11-limit

Decavish

11-limit

13-limit

Navigation menu

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