Vishnu family: Difference between revisions
m Units, misc. cleanup, - redundant category |
Switch to Sintel's badness, WE & CWE tunings |
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| Line 11: | Line 11: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{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]] ( | [[Badness]] (Sintel): 0.731 | ||
== Septimal vishnu == | == Septimal vishnu == | ||
| Line 26: | Line 28: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{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]] ( | [[Badness]] (Sintel): 1.06 | ||
=== 11-limit === | === 11-limit === | ||
| Line 41: | Line 45: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{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 | {{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }} | ||
Badness ( | Badness (Sintel): 0.469 | ||
==== Ananta ==== | ==== Ananta ==== | ||
| Line 56: | Line 60: | ||
Optimal tuning: | Optimal tuning: | ||
* | * WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{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 ( | Badness (Sintel): 0.978 | ||
==== Acyuta ==== | ==== Acyuta ==== | ||
| Line 71: | Line 75: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{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 ( | Badness (Sintel): 0.653 | ||
== Vishnean == | == Vishnean == | ||
| Line 86: | Line 90: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{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]] ( | [[Badness]] (Sintel): 4.08 | ||
=== 11-limit === | === 11-limit === | ||
| Line 101: | Line 107: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{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 ( | Badness (Sintel): 2.38 | ||
=== 13-limit === | === 13-limit === | ||
| Line 116: | Line 122: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{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 ( | Badness (Sintel): 1.68 | ||
== Narayana == | == Narayana == | ||
| Line 131: | Line 137: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{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]] ( | [[Badness]] (Sintel): 2.39 | ||
=== 11-limit === | === 11-limit === | ||
| Line 146: | Line 154: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{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 ( | 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: | ||
* [[ | * [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{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]] ( | [[Badness]] (Sintel): 1.14 | ||
=== 11-limit === | === 11-limit === | ||
| Line 176: | Line 187: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{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 ( | Badness (Sintel): 0.657 | ||
== Decavish == | == Decavish == | ||
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: | ||
* [[ | * [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{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]] ( | [[Badness]] (Sintel): 2.90 | ||
=== 11-limit === | === 11-limit === | ||
| Line 209: | Line 222: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{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 ( | Badness (Sintel): 1.22 | ||
=== 13-limit === | === 13-limit === | ||
| Line 224: | Line 237: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{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 ( | 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
- 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 sequence: 16, 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]]
- 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 sequence: 34d, 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]]
- 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 sequence: 16, 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]]
- 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 sequence: 34, 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
- 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 sequence: 68, 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
- 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 sequence: 50, …, 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