Hemimage family

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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:

[[1 0 0 0, [5/8 1/8 -1/8 3/8, [5/8 -7/8 7/8 3/8, [0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.5/3.7
[[1 0 0 0, [5/9 2/9 -1/9 1/3, [10/9 -14/9 7/9 2/3, [0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.7.9/5

Optimal ET sequence17c, 19, 39d, 41, 58, 77, 80, 99, 217, 239, 338, 357, 456, 695

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:

[[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]
eigenmonzo (unchanged-interval) basis: 2.5.11/9

Optimal ET sequence17c, 19, 22, 39d, 41, 58, 80, 99e, 121, 179e, 220e, 300bdee, 399bcdeee

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]]

Optimal ET sequence17c, 22, 36f, 39d, 41, 58, 80, 99ef, 121, 179ef, 300bdeef

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]]

Optimal ET sequence17c, 19, 22f, 36, 39df, 41, 58, 99ef, 157eff

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]
eigenmonzo (unchanged-interval) basis: 2.9/5.11/9

Optimal ET sequence17c, 19, 36, 39d, 41, 58, 99e, 118, 159, 217, 335

Badness: 0.936 × 10-3