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)^7.
__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.


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


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


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


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


[[Badness]]: 0.031181
Badness: 0.0312


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


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


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


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


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


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


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


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


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


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


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


=== Ananta ===
POTE generator: ~25/24 = 71.1170
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}}]
Map: [<2 4 5 10 10 1|, <0 -7 -3 -37 -26 54|]


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


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


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


=== Acyuta ===
POTE generator: ~25/24 = 71.1001
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}}]
Map: [<2 4 5 10 10 17|, <0 -7 -3 -37 -26 -81|]


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


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


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


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


[[Mapping]]: [{{val|2 4 5 6}}, {{val|0 -28 -12 -13}}]
Map: [<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
EDOs: 68, 134, 202, 270, 742, 1012


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


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

Revision as of 03:17, 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.

Comma: 6115295232/6103515625

POTE generator: ~25/24 = 71.1432

Map: [<2 4 5|, <0 -7 -3|]

EDOs: 16, 18, 34, 50, 84, 118, 152, 270, 380, 422, 506, 894, 1400

Badness: 0.0312

Vishnu

Commas: 4375/4374, 29360128/29296875

POTE generator: ~25/24 = 71.1075

Map: [<2 4 5 10|, <0 -7 -3 -37|]

EDOs: 118, 152, 270, 1232, 1502

Badness: 0.0419

11-limit

Commas: 3025/3024, 4375/4374, 5632/5625

POTE generator: ~25/24 = 71.1048

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

EDOs: 118, 152, 270, 422, 962, 1232, 1502

Badness: 0.0142

Ananta

Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374

POTE generator: ~25/24 = 71.1170

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

EDOs: 118, 152, 270, 928, 1198, 1468

Badness: 0.0237

Acyuta

Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625

POTE generator: ~25/24 = 71.1001

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

EDOs: 270, 692, 962

Badness: 0.0158

Quarvish

Commas: 2401/2400, 6115295232/6103515625

POTE generator: ~7/5 = 582.2134

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

EDOs: 68, 134, 202, 270, 742, 1012

Badness: 0.0450

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