Hemimage family

The hemimage family of temperaments are rank-3 temperaments tempering out 10976/10935.

Hemimage

Subgroup: 2.3.5.7

Comma list: 10976/10935

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

Mapping generators: ~2, ~3, ~27/14

Minimax tuning:

• 7-odd-limit

[[1 0 0 0⟩, [5/8 1/8 -1/8 3/8⟩, [5/8 -7/8 7/8 3/8⟩, [0 0 0 1⟩]

Eigenmonzos: 2, 8/7, 6/5

• 9-odd-limit

[[1 0 0 0⟩, [5/9 2/9 -1/9 1/3⟩, [10/9 -14/9 7/9 2/3⟩, [0 0 0 1⟩]

Eigenmonzos: 2, 10/9, 8/7

Badness: 0.199 × 10^-3

Projection pair: 5 10976/2187 to 2.3.7

Uni

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891

Mapping: [⟨1 0 2 -1 6], ⟨0 1 2 3 -1], ⟨0 0 -3 -1 -1]]

Minimax tuning:

• 11-odd-limit

[[1 0 0 0 0⟩, [16/11 6/11 1/11 0 -3/11⟩, [0 0 1 0 0⟩, [19/11 14/11 6/11 0 -7/11⟩, [32/11 -10/11 2/11 0 5/11⟩]

Eigenmonzos: 2, 11/9, 5/4

Badness: 0.702 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 540/539

Mapping: [⟨1 0 2 -1 6 11], ⟨0 1 2 3 -1 -4], ⟨0 0 -3 -1 -1 -1]]

Vals: Template:Val list

Badness: 1.06 × 10^-3

Tin

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 729/728

Mapping: [⟨1 0 2 -1 6 -2], ⟨0 1 2 3 -1 3], ⟨0 0 -3 -1 -1 1]]

Vals: Template:Val list

Badness: 1.07 × 10^-3

Turan

Subgroup: 2.3.5.7.11

Comma list: 441/440, 10976/10935

Mapping: [⟨1 0 2 -1 -7], ⟨0 1 2 3 6], ⟨0 0 -3 -1 1]]

Minimax tuning:

• 11-odd-limit

[[1 0 0 0 0⟩, [19/12 -2/3 1/12 0 1/4⟩, [19/6 -10/3 7/6 0 1/2⟩, [37/12 -8/3 7/12 0 3/4⟩, [19/6 -10/3 1/6 0 3/2⟩]

Eigenmonzos: 2, 10/9, 11/9

Badness: 0.936 × 10^-3