Vishnuzmic family
- 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 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 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 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 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]]
- 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
- 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