Vishnuzmic family: Difference between revisions

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__FORCETOC__
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)^7.


Comma: 6115295232/6103515625
= Vishnuzmic =
[[Comma]]: 6115295232/6103515625


POTE generator: ~25/24 = 71.1432
[[Mapping]]: [{{val|2 4 5}}, {{val|0 -7 -3}}]


Map: [<2 4 5|, <0 -7 -3|]
[[POTE generator]]: ~25/24 = 71.143


EDOs: [[16edo|16]], [[18edo|18]], [[34edo|34]], [[50edo|50]], [[84edo|84]], [[118edo|118]], [[152edo|152]], [[270edo|270]], [[388edo|380]], [[422edo|422]], 506, 894, 1400
{{Val list|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}


Badness: 0.0312
[[Badness]]: 0.031181


=Vishnu=
= Vishnu =
Commas: 4375/4374, 29360128/29296875
[[Comma list]]: 4375/4374, 29360128/29296875


POTE generator: ~25/24 = 71.1075
[[Mapping]]: [{{val|2 4 5 10}}, {{val|0 -7 -3 -37}}]


Map: [<2 4 5 10|, <0 -7 -3 -37|]
{{Multival|legend=1|14 6 74 -23 78 155}}


EDOs: 118, 152, 270, [[1232edo|1232]], [[1502edo|1502]]
[[POTE generator]]: ~25/24 = 71.107


Badness: 0.0419
{{Val list|legend=1| 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc }}


==11-limit==
[[Badness]]: 0.041912
Commas: 3025/3024, 4375/4374, 5632/5625


POTE generator: ~25/24 = 71.1048
== 11-limit ==
Comma list: 3025/3024, 4375/4374, 5632/5625


Map: [<2 4 5 10 10|, <0 -7 -3 -37 -26|]
Mapping: [{{val|2 4 5 10 10}}, {{val|0 -7 -3 -37 -26}}]


EDOs: 118, 152, 270, [[422edo|422]], [[962edo|962]], 1232, 1502
POTE generator: ~25/24 = 71.105


Badness: 0.0142
Vals: {{Val list| 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}


==Ananta==
Badness: 0.014180
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374


POTE generator: ~25/24 = 71.1170
=== Ananta ===
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374


Map: [<2 4 5 10 10 1|, <0 -7 -3 -37 -26 54|]
Mapping: [{{val|2 4 5 10 10 1}}, {{val|0 -7 -3 -37 -26 54}}]


EDOs: 118, 152, 270, 928, 1198, 1468
POTE generator: ~25/24 = 71.117


Badness: 0.0237
Vals: {{Val list| 118, 152, 270, 928, 1198, 1468 }}


==Acyuta==
Badness: 0.023678
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625


POTE generator: ~25/24 = 71.1001
=== Acyuta ===
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625


Map: [<2 4 5 10 10 17|, <0 -7 -3 -37 -26 -81|]
Mapping: [{{val|2 4 5 10 10 17}}, {{val|0 -7 -3 -37 -26 -81}}]


EDOs: 270, 692, 962
POTE generator: ~25/24 = 71.101


Badness: 0.0158
Vals: {{Val list| 270, 692, 962, 1654cd, 2616bcdf }}


=Quarvish=
Badness: 0.015805
Commas: 2401/2400, 6115295232/6103515625


POTE generator: ~7/5 = 582.2134
= Quarvish =
[[Comma list]]: 2401/2400, 6115295232/6103515625


Map: [<2 4 5 6|, <0 -28 -12 -13|]
[[Mapping]]: [{{val|2 4 5 6}}, {{val|0 -28 -12 -13}}]


EDOs: 68, 134, 202, 270, 742, 1012
[[POTE generator]]: ~7/5 = 582.213 (2|33,1,2,1,2,1) - 66,68,202,270,742,1012


Badness: 0.0450
{{Val list|legend=1| 68, 134, 202, 270, 742, 1012 }}
 
Badness: 0.045029


[[Category:Theory]]
[[Category:Theory]]

Revision as of 03:15, 4 May 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

Comma: 6115295232/6103515625

Mapping: [⟨2 4 5], ⟨0 -7 -3]]

POTE generator: ~25/24 = 71.143

Template:Val list

Badness: 0.031181

Vishnu

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

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

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

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

Comma list: 2401/2400, 6115295232/6103515625

Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]

POTE generator: ~7/5 = 582.213 (2|33,1,2,1,2,1) - 66,68,202,270,742,1012

Template:Val list

Badness: 0.045029

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