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.
{{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>.


== Vishnuzmic ==
== Vishnu ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 6115295232/6103515625
[[Comma list]]: 6115295232/6103515625


[[Mapping]]: [{{val|2 4 5}}, {{val|0 -7 -3}}]
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}


[[POTE generator]]: ~25/24 = 71.143
: mapping generators: ~78125/55296, ~25/24


{{Val list|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}
[[Optimal tuning]]s:
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143
 
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}


[[Badness]]: 0.031181
[[Badness]]: 0.031181


== Vishnu ==
== Septimal vishnu ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 29360128/29296875
[[Comma list]]: 4375/4374, 29360128/29296875


[[Mapping]]: [{{val|2 4 5 10}}, {{val|0 -7 -3 -37}}]
{{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}


{{Multival|legend=1|14 6 74 -23 78 155}}
[[Optimal tuning]]s:
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107


[[POTE generator]]: ~25/24 = 71.107
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}
 
{{Val list|legend=1| 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc }}


[[Badness]]: 0.041912
[[Badness]]: 0.041912
Line 34: Line 39:
Comma list: 3025/3024, 4375/4374, 5632/5625
Comma list: 3025/3024, 4375/4374, 5632/5625


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


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


Vals: {{Val list| 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}


Badness: 0.014180
Badness: 0.014180


=== Ananta ===
==== Ananta ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
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: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}


POTE generator: ~25/24 = 71.117
Optimal tuning:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
* POTE: ~99/70 = 1\2, ~25/24 = 71.117


Vals: {{Val list| 118, 152, 270, 928, 1198, 1468 }}
Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}


Badness: 0.023678
Badness: 0.023678


=== Acyuta ===
==== Acyuta ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
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: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}


POTE generator: ~25/24 = 71.101
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
* POTE: ~99/70 = 1\2, ~25/24 = 71.101


Vals: {{Val list| 270, 692, 962, 1654cd, 2616bcdf }}
Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}


Badness: 0.015805
Badness: 0.015805


== Vishnean ==
== Vishnean ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 540225/524288
[[Comma list]]: 126/125, 540225/524288


[[Mapping]]: [{{val|2 4 5 5}}, {{val|0 -7 -3 5}}]
{{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}
 
{{Multival|legend=1|14 6 -10 -23 -55 -40}}


[[POTE generator]]: ~25/24 = 71.779
[[Optimal tuning]]s:
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779


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


[[Badness]]: 0.161398
[[Badness]]: 0.161398
Line 88: Line 99:
Comma list: 126/125, 385/384, 1350/1331
Comma list: 126/125, 385/384, 1350/1331


Mapping: [{{val|2 4 5 5 8}}, {{val|0 -7 -3 5 -9}}]
Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}


POTE generator: ~25/24 = 71.924
Optimal tunings:
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* POTE: ~63/44 = 1\2, ~25/24 = 71.924


Vals: {{Val list| 16, 34, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}


Badness: 0.071990
Badness: 0.071990
Line 101: Line 114:
Comma list: 105/104, 126/125, 144/143, 847/845
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: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}


POTE generator: ~25/24 = 71.926
Optimal tunings:
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* POTE: ~55/39 = 1\2, ~25/24 = 71.926


Vals: {{Val list| 16, 34, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}


Badness: 0.040739
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 ==
== Quarvish ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400, 6115295232/6103515625
[[Comma list]]: 2401/2400, 6115295232/6103515625


[[Mapping]]: [{{val|2 4 5 6}}, {{val|0 -28 -12 -13}}]
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
 
{{Multival|legend=1|56 24 26 -92 -116 -7}}


[[POTE generator]]: ~7/5 = 582.213
[[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)


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


Badness: 0.045029
[[Badness]]: 0.045029


=== 11-limit ===
=== 11-limit ===
Line 129: Line 174:
Comma list: 2401/2400, 9801/9800, 172032/171875
Comma list: 2401/2400, 9801/9800, 172032/171875


Mapping: [{{val|2 4 5 6 6}}, {{val|0 -28 -12 -13 31}}]
Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}


POTE generator: ~7/5 = 582.213
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)


Vals: {{Val list| 68, 134, 202, 270, 742, 1012 }}
Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}


Badness: 0.019868
Badness: 0.019868


== Decavish ==
== Decavish ==
The ''decavish'' temperament (50&amp;270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}} = 578509309952/576650390625.
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 2202927104/2197265625
[[Comma list]]: 420175/419904, 2202927104/2197265625


[[Mapping]]: [{{val|10 13 22 24}}, {{val|0 7 3 10}}]
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}


{{Multival|legend=1|70 30 100 -115 -38 148}}
: mapping generators: ~15/14, ~54/49


[[POTE generator]]: ~25/24 = 71.129
[[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)


{{Val list|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]]: 0.114531
Line 159: Line 208:
Comma list: 9801/9800, 41503/41472, 172032/171875
Comma list: 9801/9800, 41503/41472, 172032/171875


Mapping: [{{val|10 13 22 24 35}}, {{val|0 7 3 10 -1}}]
Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}


POTE generator: ~25/24 = 71.141
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)


Vals: {{Val list| 50, 220, 270, 860, 1130, 1400, 3070cd, 4470cde }}
Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}


Badness: 0.036938
Badness: 0.036938
Line 172: Line 223:
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
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: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}


POTE generator: ~25/24 = 71.151
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)


Vals: {{Val list| 50, 220, 270, 590, 860, 1130 }}
Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}


Badness: 0.021906
Badness: 0.021906


[[Category:Theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Vishnuzmic]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:38, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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.

Vishnu

Subgroup: 2.3.5

Comma list: 6115295232/6103515625

Mapping: [⟨2 4 5], ⟨0 -7 -3]]

mapping generators: ~78125/55296, ~25/24

Optimal tunings:

  • CTE: ~78125/55296 = 1\2, ~25/24 = 71.1556
  • POTE: ~78125/55296 = 1\2, ~25/24 = 71.143

Optimal ET sequence: 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc

Badness: 0.031181

Septimal vishnu

Subgroup: 2.3.5.7

Comma list: 4375/4374, 29360128/29296875

Mapping: [⟨2 4 5 10], ⟨0 -7 -3 -37]]

Optimal tunings:

  • CTE: ~10125/7168 = 1\2, ~25/24 = 71.1175
  • POTE: ~10125/7168 = 1\2, ~25/24 = 71.107

Optimal ET sequence: 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd

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]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1142
  • POTE: ~99/70 = 1\2, ~25/24 = 71.105

Optimal ET sequence: 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd

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]]

Optimal tuning:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1173
  • POTE: ~99/70 = 1\2, ~25/24 = 71.117

Optimal ET sequence: 118, 152, 270, 928, 1198, 1468

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]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1079
  • POTE: ~99/70 = 1\2, ~25/24 = 71.101

Optimal ET sequence: 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf

Badness: 0.015805

Vishnean

Subgroup: 2.3.5.7

Comma list: 126/125, 540225/524288

Mapping: [⟨2 4 5 5], ⟨0 -7 -3 5]]

Optimal tunings:

  • CTE: ~735/512 = 1\2, ~25/24 = 71.4956
  • POTE: ~735/512 = 1\2, ~25/24 = 71.779

Optimal ET sequence: 16, 34, 50, 134dd

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]]

Optimal tunings:

  • CTE: ~63/44 = 1\2, ~25/24 = 71.6218
  • POTE: ~63/44 = 1\2, ~25/24 = 71.924

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: [⟨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: 16, 34, 50

Badness: 0.040739

Narayana

Subgroup: 2.3.5.7

Comma list: 65625/65536, 321489/320000

Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]

Optimal tunings:

  • CTE: ~567/400 = 1\2, ~25/24 = 71.2706
  • POTE: ~567/400 = 1\2, ~25/24 = 71.265

Optimal ET sequence: 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: [⟨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: 34e, 84, 118, 202, 320

Badness: 0.045908

Quarvish

Subgroup: 2.3.5.7

Comma list: 2401/2400, 6115295232/6103515625

Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]

Optimal tunings:

  • 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: 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: [⟨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: 68, 134, 202, 270, 742, 1012

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 6 19 14], ⟨0 7 3 10]]

mapping generators: ~15/14, ~54/49

Optimal tunings:

  • 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: 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: [⟨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: 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: [⟨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: 50, 220, 270, 590, 860, 1130

Badness: 0.021906

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