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Vishnu family: Difference between revisions

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m FloraC moved page Vishnuzmic family to Vishnu family: The temp's name is *vishnu*
m Units, misc. cleanup, - redundant category
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{{Technical data page}}
{{Technical data page}}
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>.
The '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), 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>.


== Vishnu ==
== Vishnu ==
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{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}
: mapping generators: ~78125/55296, ~25/24
: mapping generators: ~78125/55296, ~25/24


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1556{{c}}
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~25/24 = 71.143{{c}}


{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}


[[Badness]]: 0.031181
[[Badness]] (Smith): 0.031181


== Septimal vishnu ==
== Septimal vishnu ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[CTE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1175{{c}}
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107
* [[POTE]]: ~10125/7168 = 600.000{{c}}, ~25/24 = 71.107{{c}}


{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}


[[Badness]]: 0.041912
[[Badness]] (Smith): 0.041912


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1142
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1142{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.105
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.105{{c}}


Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}
{{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}


Badness: 0.014180
Badness (Smith): 0.014180


==== Ananta ====
==== Ananta ====
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Optimal tuning:  
Optimal tuning:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1173{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.117
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.117{{c}}


Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}
{{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}


Badness: 0.023678
Badness (Smith): 0.023678


==== Acyuta ====
==== Acyuta ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1079{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.101
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.101{{c}}


Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
{{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}


Badness: 0.015805
Badness (Smith): 0.015805


== Vishnean ==
== Vishnean ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
* [[CTE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.4956{{c}}
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779
* [[POTE]]: ~735/512 = 600.000{{c}}, ~25/24 = 71.779{{c}}


{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}


[[Badness]]: 0.161398
[[Badness]] (Smith): 0.161398


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* CTE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.6218{{c}}
* POTE: ~63/44 = 1\2, ~25/24 = 71.924
* POTE: ~63/44 = 600.000{{c}}, ~25/24 = 71.924{{c}}


Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
{{Optimal ET sequence|legend=0| 16, 34, 50 }}


Badness: 0.071990
Badness (Smith): 0.071990


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* CTE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.6369{{c}}
* POTE: ~55/39 = 1\2, ~25/24 = 71.926
* POTE: ~55/39 = 600.000{{c}}, ~25/24 = 71.926{{c}}


Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
{{Optimal ET sequence|legend=0| 16, 34, 50 }}


Badness: 0.040739
Badness (Smith): 0.040739


== Narayana ==
== Narayana ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~567/400 = 1\2, ~25/24 = 71.2706
* [[CTE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2706{{c}}
* [[POTE]]: ~567/400 = 1\2, ~25/24 = 71.265
* [[POTE]]: ~567/400 = 600.000{{c}}, ~25/24 = 71.265{{c}}


{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}


[[Badness]]: 0.094295
[[Badness]] (Smith): 0.094295


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.2609
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2609{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.248
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.248{{c}}


Optimal ET sequence: {{Optimal ET sequence| 34e, 84, 118, 202, 320 }}
{{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}


Badness: 0.045908
Badness (Smith): 0.045908


== Quarvish ==
== Quarvish ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~7/5 = 582.2115{{c}} (~110592/109375 = 17.7885{{c}})
* [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~110592/109375 = 17.787{{c}})


{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}


[[Badness]]: 0.045029
[[Badness]] (Smith): 0.045029


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)
* CTE: ~99/70 = 600.0000{{c}}, ~7/5 = 582.2122{{c}} (~99/98 = 17.7878{{c}})
* POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)
* POTE: ~99/70 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~99/98 = 17.787{{c}})


Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}
{{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}


Badness: 0.019868
Badness (Smith): 0.019868


== Decavish ==
== 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.
The decavish temperament (50 & 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
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
: mapping generators: ~15/14, ~54/49
: mapping generators: ~15/14, ~54/49


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)
* [[CTE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8587{{c}} (~25/24 = 71.1413{{c}}, or ~36/35 = 48.8587{{c}})
* [[POTE]]: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)
* [[POTE]]: ~15/14 = 120.000{{c}}, ~54/49 = 168.871{{c}} (~25/24 = 71.129{{c}}, or ~36/35 = 48.871{{c}})


{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}


[[Badness]]: 0.114531
[[Badness]] (Smith): 0.114531


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.141{{c}}, or ~36/35 = 48.859{{c}})


Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}


Badness: 0.036938
Badness (Smith): 0.036938


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.151{{c}}, or ~36/35 = 48.859{{c}})


Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}
{{Optimal ET sequence|legend=0| 50, 220, 270, 590, 860, 1130 }}


Badness: 0.021906
Badness (Smith): 0.021906


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Vishnu_family"