Vishnu family: Difference between revisions

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m Units, misc. cleanup, - redundant category
Switch to Sintel's badness, WE & CWE tunings
Line 11: Line 11:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1556{{c}}
* [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~25/24 = 71.143{{c}}
: [[error map]]: {{val| -0.046 -0.030 +0.150 }}
* [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1482{{c}}
: error map: {{val| 0.000 +0.007 +0.242 }}


{{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]] (Smith): 0.031181
[[Badness]] (Sintel): 0.731


== Septimal vishnu ==
== Septimal vishnu ==
Line 26: Line 28:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1175{{c}}
* [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}
* [[POTE]]: ~10125/7168 = 600.000{{c}}, ~25/24 = 71.107{{c}}
: [[error map]]: {{val| -0.103 +0.129 +0.125 -0.092 }}
* [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1106{{c}}
: error map: {{val| 0.000 +0.271 +0.354 +0.081 }}


{{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]] (Smith): 0.041912
[[Badness]] (Sintel): 1.06


=== 11-limit ===
=== 11-limit ===
Line 41: Line 45:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1142{{c}}
* WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.105{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}


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


Badness (Smith): 0.014180
Badness (Sintel): 0.469


==== Ananta ====
==== Ananta ====
Line 56: Line 60:


Optimal tuning:  
Optimal tuning:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1173{{c}}
* WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.117{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}


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


Badness (Smith): 0.023678
Badness (Sintel): 0.978


==== Acyuta ====
==== Acyuta ====
Line 71: Line 75:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1079{{c}}
* WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.101{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}


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


Badness (Smith): 0.015805
Badness (Sintel): 0.653


== Vishnean ==
== Vishnean ==
Line 86: Line 90:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.4956{{c}}
* [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}
* [[POTE]]: ~735/512 = 600.000{{c}}, ~25/24 = 71.779{{c}}
: [[error map]]: {{val| +1.751 -1.637 +2.413 -5.031 }}
* [[CWE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.7141{{c}}
: error map: {{val| 0.000 -3.954 -1.456 -10.255 }}


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


[[Badness]] (Smith): 0.161398
[[Badness]] (Sintel): 4.08


=== 11-limit ===
=== 11-limit ===
Line 101: Line 107:


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.6218{{c}}
* WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}
* POTE: ~63/44 = 600.000{{c}}, ~25/24 = 71.924{{c}}
* CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}


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


Badness (Smith): 0.071990
Badness (Sintel): 2.38


=== 13-limit ===
=== 13-limit ===
Line 116: Line 122:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.6369{{c}}
* WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~25/24 = 71.926{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}


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


Badness (Smith): 0.040739
Badness (Sintel): 1.68


== Narayana ==
== Narayana ==
Line 131: Line 137:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2706{{c}}
* [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}
* [[POTE]]: ~567/400 = 600.000{{c}}, ~25/24 = 71.265{{c}}
: [[error map]]: {{val| +0.228 -0.447 +0.422 -0.362 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2659{{c}}
: error map: {{val| 0.000 -0.816 -0.111 -0.976 }}


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


[[Badness]] (Smith): 0.094295
[[Badness]] (Sintel): 2.39


=== 11-limit ===
=== 11-limit ===
Line 146: Line 154:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2609{{c}}
* WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.248{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}


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


Badness (Smith): 0.045908
Badness (Sintel): 1.52


== Quarvish ==
== Quarvish ==
Line 159: Line 167:


{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
: mapping generators: ~78125/55296, ~110592/109375


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~7/5 = 582.2115{{c}} (~110592/109375 = 17.7885{{c}})
* [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~110592/109375 = 17.787{{c}})
: [[error map]]: {{val| -0.025 -0.020 +0.189 -0.123 }}
* [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~110592/109375 = 17.7873{{c}}
: error map: {{val| 0.000 +0.002 +0.239 -0.060 }}


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


[[Badness]] (Smith): 0.045029
[[Badness]] (Sintel): 1.14


=== 11-limit ===
=== 11-limit ===
Line 176: Line 187:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~7/5 = 582.2122{{c}} (~99/98 = 17.7878{{c}})
* WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~99/98 = 17.787{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}


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


Badness (Smith): 0.019868
Badness (Sintel): 0.657


== Decavish ==
== Decavish ==
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.
Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 270 }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 194: Line 205:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8587{{c}} (~25/24 = 71.1413{{c}}, or ~36/35 = 48.8587{{c}})
* [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})
* [[POTE]]: ~15/14 = 120.000{{c}}, ~54/49 = 168.871{{c}} (~25/24 = 71.129{{c}}, or ~36/35 = 48.871{{c}})
: [[error map]]: {{val| -0.043 +0.071 +0.197 -0.242 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8658{{c}} (~36/35 = 48.8658{{c}})
: error map: {{val| 0.000 +0.106 +0.284 -0.168 }}


{{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]] (Smith): 0.114531
[[Badness]] (Sintel): 2.90


=== 11-limit ===
=== 11-limit ===
Line 209: Line 222:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.141{{c}}, or ~36/35 = 48.859{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8589{{c}} (~36/35 = 48.8589{{c}})


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


Badness (Smith): 0.036938
Badness (Sintel): 1.22


=== 13-limit ===
=== 13-limit ===
Line 224: Line 237:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.151{{c}}, or ~36/35 = 48.859{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8506{{c}} (~36/35 = 48.8506{{c}})


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


Badness (Smith): 0.021906
Badness (Sintel): 0.905


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 10:05, 19 June 2026

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 vishnu family tempers out the vishnu comma (monzo[23 6 -14, ratio: 6 115 295 232 / 6 103 515 625), 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:

  • WE: ~78125/55296 = 599.9771 ¢, ~25/24 = 71.1405 ¢
error map: -0.046 -0.030 +0.150]
  • CWE: ~78125/55296 = 600.0000 ¢, ~25/24 = 71.1482 ¢
error map: 0.000 +0.007 +0.242]

Optimal ET sequence16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc

Badness (Sintel): 0.731

Septimal vishnu

Subgroup: 2.3.5.7

Comma list: 4375/4374, 29360128/29296875

Mapping[2 4 5 10], 0 -7 -3 -37]]

Optimal tunings:

  • WE: ~10125/7168 = 599.9486 ¢, ~25/24 = 71.1014 ¢
error map: -0.103 +0.129 +0.125 -0.092]
  • CWE: ~10125/7168 = 600.0000 ¢, ~25/24 = 71.1106 ¢
error map: 0.000 +0.271 +0.354 +0.081]

Optimal ET sequence34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd

Badness (Sintel): 1.06

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:

  • WE: ~99/70 = 599.9549 ¢, ~25/24 = 71.0994 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1077 ¢

Optimal ET sequence: 34d, 84de, 118, 152, 270, 962, 1232, 1502

Badness (Sintel): 0.469

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:

  • WE: ~99/70 = 599.9940 ¢, ~25/24 = 71.1163 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1170 ¢

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

Badness (Sintel): 0.978

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:

  • WE: ~99/70 = 599.9475 ¢, ~25/24 = 71.0947 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1028 ¢

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

Badness (Sintel): 0.653

Vishnean

Subgroup: 2.3.5.7

Comma list: 126/125, 540225/524288

Mapping[2 4 5 5], 0 -7 -3 5]]

Optimal tunings:

  • WE: ~735/512 = 600.8754 ¢, ~25/24 = 71.8834 ¢
error map: +1.751 -1.637 +2.413 -5.031]
  • CWE: ~735/512 = 600.0000 ¢, ~25/24 = 71.7141 ¢
error map: 0.000 -3.954 -1.456 -10.255]

Optimal ET sequence16, 34, 50, 134dd

Badness (Sintel): 4.08

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:

  • WE: ~63/44 = 600.7144 ¢, ~25/24 = 72.0091 ¢
  • CWE: ~63/44 = 600.0000 ¢, ~25/24 = 71.8588 ¢

Optimal ET sequence: 16, 34, 50

Badness (Sintel): 2.38

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:

  • WE: ~55/39 = 600.5983 ¢, ~25/24 = 71.9975 ¢
  • CWE: ~55/39 = 600.0000 ¢, ~25/24 = 71.8699 ¢

Optimal ET sequence: 16, 34, 50

Badness (Sintel): 1.68

Narayana

Subgroup: 2.3.5.7

Comma list: 65625/65536, 321489/320000

Mapping[2 4 5 3], 0 -7 -3 22]]

Optimal tunings:

  • WE: ~567/400 = 600.1141 ¢, ~25/24 = 71.2783 ¢
error map: +0.228 -0.447 +0.422 -0.362]
  • CWE: ~567/400 = 600.0000 ¢, ~25/24 = 71.2659 ¢
error map: 0.000 -0.816 -0.111 -0.976]

Optimal ET sequence34, 84, 118, 202, 320, 522

Badness (Sintel): 2.39

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:

  • WE: ~99/70 = 600.0992 ¢, ~25/24 = 71.2593 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.2501 ¢

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

Badness (Sintel): 1.52

Quarvish

Subgroup: 2.3.5.7

Comma list: 2401/2400, 6115295232/6103515625

Mapping[2 4 5 6], 0 -28 -12 -13]]

mapping generators: ~78125/55296, ~110592/109375

Optimal tunings:

  • WE: ~78125/55296 = 599.9874 ¢, ~110592/109375 = 17.7862 ¢
error map: -0.025 -0.020 +0.189 -0.123]
  • CWE: ~78125/55296 = 600.0000 ¢, ~110592/109375 = 17.7873 ¢
error map: 0.000 +0.002 +0.239 -0.060]

Optimal ET sequence68, 134, 202, 270, 742, 1012

Badness (Sintel): 1.14

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:

  • WE: ~99/70 = 599.9884 ¢, ~99/98 = 17.7865 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~99/98 = 17.7870 ¢

Optimal ET sequence: 68, 134, 202, 270, 742, 1012

Badness (Sintel): 0.657

Decavish

Decavish tempers out the wizma as well as the linus comma, and may be described as the 50 & 270 temperament.

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:

  • WE: ~15/14 = 119.9957 ¢, ~54/49 = 168.8645 ¢ (~36/35 = 48.8689 ¢)
error map: -0.043 +0.071 +0.197 -0.242]
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8658 ¢ (~36/35 = 48.8658 ¢)
error map: 0.000 +0.106 +0.284 -0.168]

Optimal ET sequence50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c

Badness (Sintel): 2.90

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:

  • WE: ~15/14 = 119.9997 ¢, ~54/49 = 168.8587 ¢ (~36/35 = 48.8590 ¢)
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8589 ¢ (~36/35 = 48.8589 ¢)

Optimal ET sequence: 50, …, 220, 270, 860, 1130, 1400

Badness (Sintel): 1.22

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:

  • WE: ~15/14 = 120.0037 ¢, ~54/49 = 168.8537 ¢ (~36/35 = 48.8500 ¢)
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8506 ¢ (~36/35 = 48.8506 ¢)

Optimal ET sequence: 50, …, 220, 270, 590, 860, 1130

Badness (Sintel): 0.905