Vishnuzmic family
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]]
Wedgie: ⟨⟨ 14 6 74 -23 78 155 ]]
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]]
Wedgie: ⟨⟨ 14 6 -10 -23 -55 -40 ]]
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]]
Wedgie: ⟨⟨ 14 6 -44 -23 -109 -119 ]]
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]]
Wedgie: ⟨⟨ 56 24 26 -92 -116 -7 ]]
- 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
Wedgie: ⟨⟨ 70 30 100 -115 -38 148 ]]
- 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