Limmic temperaments

The limma family tempers out the Pythagorean limma, 256/243. As a consequence, the 3/2 is always represented by 3\5, 720 cents. While quite sharp, this is close enough to a just fifth to serve as one, and some people are fond of it.

Blackwood

Subgroup: 2.3.5

Comma list: 256/243

Mapping: [⟨5 8 0], ⟨0 0 1]]

Mapping generators: ~9/8, ~5

POTE generator: ~5/4 = 399.594

Badness: 0.063760

Blacksmith

Subgroup: 2.3.5.7

Comma list: 28/27, 49/48

Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]

Mapping generators: ~7/6, ~5

Wedgie: ⟨⟨ 0 5 0 8 0 -14 ]]

POTE generator: ~5/4 = 392.767

Badness: 0.025640

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 49/48, 55/54

Mapping: [⟨5 8 0 14 29], ⟨0 0 1 0 -1]]

POTE generator: ~5/4 = 394.948

Vals: Template:Val list

Badness: 0.024641

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 49/48, 55/54

Mapping: [⟨5 8 0 14 29 7], ⟨0 0 1 0 -1 1]]

POTE generator: ~5/4 = 391.037

Vals: Template:Val list

Badness: 0.020498

Farrier

Subgroup: 2.3.5.7.11

Comma list: 28/27, 49/48, 77/75

Mapping: [⟨5 8 0 14 -6], ⟨0 0 1 0 2]]

POTE generator: ~5/4 = 398.070

Vals: Template:Val list

Badness: 0.029200

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 49/48, 66/65

Mapping: [⟨5 8 0 14 -6 7], ⟨0 0 1 0 2 1]]

POTE generator: ~5/4 = 396.812

Vals: Template:Val list

Badness: 0.022325

Ferrum

Subgroup: 2.3.5.7.11

Comma list: 28/27, 35/33, 49/48

Mapping: [⟨5 8 0 14 6], ⟨0 0 1 0 1]]

POTE generator: ~5/4 = 374.763

Vals: Template:Val list

Badness: 0.030883