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

Badness (Sintel): 0.731

Overview to extensions

The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds 4375/4374. Narayana (84 & 118) adds 65625/65536. Vishnean (16 & 50) adds 126/125. There is also an unnamed 50 & 84 temperament, which tempers out 225/224. These all use the same generators as classical vishnu.

Quarvish (68 & 270) adds 2401/2400, splitting the generator in four. Decavish adds 420175/419904, with a 1/10-octave period.

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 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

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

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

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 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

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 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

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 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

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 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