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), an unnoticeable comma of about 3.34 cents in size.

Vishnu

The generator for the vishnu temperament is a classical chromatic semitone, seven of which make a perfect fourth, and 5/4 is found as a half-octave period minus three generators. Its ploidacot is diploid epsilon-heptacot. It is a member of the diaschismic–gothmic equivalence continuum with n = 7/2; thus it is most naturally used as a 34-form.

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. Vishy (16 & 18) adds 50/49. There is also an unnamed 50 & 84 temperament, which tempers out 225/224. These all use the same generators as classical vishnu.

Trivish (84 & 186) adds 250047/250000, splitting the semi-octave period in three. Quarvish (68 & 270) adds 2401/2400, splitting the generator in four. Decavish (50 & 220) adds 420175/419904, splitting the semi-octave period in five.

Septimal vishnu

Septimal vishnu may be described as the 118 & 152 temperament, tempering out 4375/4374, the ragisma, and 29360128/29296875, the quasiorwellisma, aside from the vishnu comma. 270edo is an excellent tuning for this temperament, with generator 16\270 (71.1 cents), but it can be tuned to 422edo, 692edo, or 962edo. It extends naturally to the 11-limit by identifying a stack of four 5/4's as 11/9, tempering out 5632/5625.

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

Named by Xenllium in 2021, narayana tempers out 65625/65536, the horwell comma, as well as 321489/320000, the varunisma, and may be described as the 84 & 118 temperament.

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

Named by Petr Pařízek in 2011, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the starling comma. It is also supported unideally by the 84d (= 34 + 50) val, as the 7 is flat but the 11 is sharp such that they have opposing tendencies.

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

Vishy

Named by Godtone in 2026 after its inaccurate but simple interpretation of its half-octave period as 7/5~10/7, vishy tempers out 50/49 and represents the absolute simplest way to reach prime 7 by interpreting three ~25/24 generators as a significantly flat ~8/7. Its mapping might be deemed favorable because of all primes being reached in a negative number of generators, with the most complex, 11, being reached in -9 (as in vishnean). In fact, this temperament's mapping is identical to that of vishnean up to a simpler, higher-damage mapping of 7 in the same direction as all the other primes. It is also supported by 50edo via the 50d val, recommendable for its lower damage on prime 7, being close to an optimal tuning of it. It is also recommendable in 84edo via the 84dd val, where 7 is ~1.7 ¢ sharper but everything else is significantly more accurate.

Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of 34edo, 50edo and 84edo (with 2.3.5.11 subgroup fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation.

Subgroup: 2.3.5.7

Comma list: 50/49, 110592/109375

Mapping: [⟨2 4 5 6], ⟨0 -7 -3 -3]]

Optimal tunings:

• WE: ~7/5 = 598.870 ¢, ~25/24 = 70.644 ¢

error map: ⟨-2.260 -0.982 -3.895 +12.463]

• CWE: ~7/5 = 600.000 ¢, ~25/24 = 71.911 ¢

error map: ⟨0.000 +0.969 +0.654 +18.141]

• CEE: ~7/5 = 600.000 ¢, ~25/24 = 71.954 ¢

error map: ⟨0.000 -5.631 -2.175 +15.313]

Optimal ET sequence: 16, 18, 34d

Badness (Sintel): 3.96

11-limit

Other than 176/175, 11-limit vishy also tempers out 625/616 and 1331/1323.

Subgroup: 2.3.5.7.11

Comma list: 50/49, 176/175, 864/847

Mapping: [⟨2 4 5 6 8], ⟨0 -7 -3 -3 -9]]

Optimal tunings:

• WE: ~7/5 = 598.823 ¢, ~25/24 = 70.710 ¢
• CWE: ~7/5 = 600.000 ¢, ~25/24 = 71.104 ¢
• CEE: ~7/5 = 600.000 ¢, ~25/24 = 72.021 ¢

Optimal ET sequence: 16, 18e, 34d

Badness (Sintel): 2.03

Trivish

Trivish tempers out 250047/250000, the landscape comma, with a 1/6-octave period. It may be described as the 84 & 186 temperament. It is more significant in the 11-limit, where it tempers out the kalisma and the olympia. In the 13-limit, the generator can be taken as a ~14/13. 270edo is an obvious tuning for it, but it can be tuned to 354edo, 624edo or 894edo. It was named by Flora Canou in 2026 for the fact that it splits the period of vishnu in three.

Subgroup: 2.3.5.7

Comma list: 250047/250000, 134217728/133984375

Mapping: [⟨6 5 12 22], ⟨0 7 3 -8]]

mapping generators: ~18375/16384, ~2205/2048

Optimal tunings:

• WE: ~18375/16384 = 199.9885 ¢, ~2205/2048 = 128.8583 ¢

error map: ⟨-0.069 -0.005 +0.123 +0.054]

• CWE: ~18375/16384 = 200.0000 ¢, ~2205/2048 = 128.8643 ¢

error map: ⟨0.000 +0.095 +0.279 +0.256]

Optimal ET sequence: 84, 186, 270, 624, 894, 1164

Badness (Sintel): 1.51

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977, 151263/151250

Mapping: [⟨6 5 12 22 33], ⟨0 7 3 -8 -19]]

Optimal tunings:

• WE: ~55/49 = 199.9885 ¢, ~320/297 = 128.8582 ¢
• CWE: ~55/49 = 200.0000 ¢, ~320/297 = 128.8661 ¢

Optimal ET sequence: 84, 186, 270, 624, 894, 1164

Badness (Sintel): 0.807

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375

Mapping: [⟨6 5 12 22 33 28], ⟨0 7 3 -8 -19 -9]]

Optimal tunings:

• WE: ~55/49 = 199.9922 ¢, ~14/13 = 128.8565 ¢
• CWE: ~55/49 = 200.0000 ¢, ~14/13 = 128.8621 ¢

Optimal ET sequence: 84, 186, 270, 624, 894, 2058f

Badness (Sintel): 0.791

2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.19

Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249

Mapping: [⟨6 5 12 22 33 28 30], ⟨0 7 3 -8 -19 -9 -7]]

Optimal tunings:

• WE: ~55/49 = 199.9909 ¢, ~14/13 = 128.8564 ¢
• CWE: ~55/49 = 200.0000 ¢, ~14/13 = 128.8630 ¢

Optimal ET sequence: 84, 186, 270, 624, 894

Badness (Sintel): 0.591

Quarvish

Quarvish tempers out 2401/2400, the breedsma, and may be described as the 68 & 270 temperament.

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 & 220 temperament. It was named by Xenllium in 2021 for the fact that its period is 1/10 octave.

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