Mint 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 mint family of rank-3 temperaments tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.

Mint

Subgroup: 2.3.5.7

Comma list: 36/35

Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

• WE: ~2 = 1196.3575 ¢, ~3/2 = 696.5144 ¢, ~5/4 = 403.0537 ¢

error map: ⟨-3.643 -9.083 +9.455 +13.864]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 695.2474 ¢, ~5/4 = 401.1263 ¢

error map: ⟨0.000 -6.708 +14.813 +20.543]

Optimal ET sequence: 4, 5, 7, 8d, 9, 12, 41cd, 53cdd

Badness (Sintel): 0.281

Nickel

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44

Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 2 2], ⟨0 0 1 -1 1]]

Optimal tunings:

• WE: ~2 = 1198.7814 ¢, ~3/2 = 688.1375 ¢, ~5/4 = 391.4822 ¢

error map: ⟨-1.219 -15.036 +2.731 +13.530 +14.002]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 687.9993 ¢, ~5/4 = 391.2274 ¢

error map: ⟨0.000 -13.956 +4.914 +15.945 +15.908]

Optimal ET sequence: 7, 9, 12, 21, 28

Badness (Sintel): 0.557

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44

Mapping: [⟨1 0 0 2 -2 -1], ⟨0 1 0 2 2 3], ⟨0 0 1 -1 1 0]]

Optimal tunings:

• WE: ~2 = 1199.6174 ¢, ~3/2 = 684.7864 ¢, ~5/4 = 390.1319 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 684.7716 ¢, ~5/4 = 390.0622 ¢

Optimal ET sequence: 7, 9, 12f, 16, 21, 28, 37b

Badness (Sintel): 0.605