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

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

Mapping: [<1 0 2 -1|, <0 1 2 3|, <0 0 -3 -1|]

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

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:

[|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