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__FORCETOC__
{{Technical data page}}
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 [[temperament]]s [[Tempering out|tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} = 6115295232/6103515625, a [[5-limit]] comma of about 3 [[cent]]s. 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>.


Comma: 6115295232/6103515625
== Vishnu ==
[[Subgroup]]: 2.3.5


POTE generator: ~25/24 = 71.1432
[[Comma list]]: 6115295232/6103515625


Map: [&lt;2 4 5|, &lt;0 -7 -3|]
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}


EDOs: [[16edo|16]], [[18edo|18]], [[34edo|34]], [[50edo|50]], [[84edo|84]], [[118edo|118]], [[152edo|152]], [[270edo|270]], [[388edo|380]], [[422edo|422]], 506, 894, 1400
: mapping generators: ~78125/55296, ~25/24


Badness: 0.0312
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143


=Vishnu=
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}
Commas: 4375/4374, 29360128/29296875


POTE generator: ~25/24 = 71.1075
[[Badness]]: 0.031181


Map: [&lt;2 4 5 10|, &lt;0 -7 -3 -37|]
== Septimal vishnu ==
[[Subgroup]]: 2.3.5.7


EDOs: 118, 152, 270, [[1232edo|1232]], [[1502edo|1502]]
[[Comma list]]: 4375/4374, 29360128/29296875


Badness: 0.0419
{{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}


==11-limit==
[[Optimal tuning]]s:
Commas: 3025/3024, 4375/4374, 5632/5625
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107


POTE generator: ~25/24 = 71.1048
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}


Map: [&lt;2 4 5 10 10|, &lt;0 -7 -3 -37 -26|]
[[Badness]]: 0.041912


EDOs: 118, 152, 270, [[422edo|422]], [[962edo|962]], 1232, 1502
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0142
Comma list: 3025/3024, 4375/4374, 5632/5625


==Ananta==
Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374


POTE generator: ~25/24 = 71.1170
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1142
* POTE: ~99/70 = 1\2, ~25/24 = 71.105


Map: [&lt;2 4 5 10 10 1|, &lt;0 -7 -3 -37 -26 54|]
Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}


EDOs: 118, 152, 270, 928, 1198, 1468
Badness: 0.014180


Badness: 0.0237
==== Ananta ====
Subgroup: 2.3.5.7.11.13


==Acyuta==
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625


POTE generator: ~25/24 = 71.1001
Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}


Map: [&lt;2 4 5 10 10 17|, &lt;0 -7 -3 -37 -26 -81|]
Optimal tuning:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
* POTE: ~99/70 = 1\2, ~25/24 = 71.117


EDOs: 270, 692, 962
Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}


Badness: 0.0158
Badness: 0.023678


=Quarvish=
==== Acyuta ====
Commas: 2401/2400, 6115295232/6103515625
Subgroup: 2.3.5.7.11.13


POTE generator: ~7/5 = 582.2134
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625


Map: [&lt;2 4 5 6|, &lt;0 -28 -12 -13|]
Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}


EDOs: 68, 134, 202, 270, 742, 1012
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
* POTE: ~99/70 = 1\2, ~25/24 = 71.101


Badness: 0.0450
Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}


[[Category:Theory]]
Badness: 0.015805
[[Category:Temperament family]]
 
[[Category:Vishnuzmic]]
== Vishnean ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 540225/524288
 
{{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779
 
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}
 
[[Badness]]: 0.161398
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 385/384, 1350/1331
 
Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}
 
Optimal tunings:
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* POTE: ~63/44 = 1\2, ~25/24 = 71.924
 
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
 
Badness: 0.071990
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 126/125, 144/143, 847/845
 
Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}
 
Optimal tunings:
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* POTE: ~55/39 = 1\2, ~25/24 = 71.926
 
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
 
Badness: 0.040739
 
== Narayana ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 65625/65536, 321489/320000
 
{{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~567/400 = 1\2, ~25/24 = 71.2706
* [[POTE]]: ~567/400 = 1\2, ~25/24 = 71.265
 
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
 
[[Badness]]: 0.094295
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 8019/8000, 65625/65536
 
Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}
 
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.2609
* POTE: ~99/70 = 1\2, ~25/24 = 71.248
 
Optimal ET sequence: {{Optimal ET sequence| 34e, 84, 118, 202, 320 }}
 
Badness: 0.045908
 
== Quarvish ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 6115295232/6103515625
 
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
* [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)
 
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
 
[[Badness]]: 0.045029
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 9801/9800, 172032/171875
 
Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}
 
Optimal tunings:
* CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)
* POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)
 
Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}
 
Badness: 0.019868
 
== Decavish ==
The decavish temperament (50 &amp; 270) tempers out the wizma, {{monzo| -6 -8 2 5 }} = 420175/419904 and the [[linus comma]], {{monzo| 11 -10 -10 10 }} = 578509309952/576650390625.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 420175/419904, 2202927104/2197265625
 
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
 
: mapping generators: ~15/14, ~54/49
 
[[Optimal tuning]]s:
* [[CTE]]: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)
* [[POTE]]: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)
 
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}
 
[[Badness]]: 0.114531
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 41503/41472, 172032/171875
 
Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}
 
Optimal tunings:
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)
 
Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}
 
Badness: 0.036938
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
 
Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}
 
Optimal tunings:
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)
 
Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}
 
Badness: 0.021906
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]
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