Keenanismic family

The keenanismic family of rank-4 temperaments tempers out the keenanisma, the 11-limit comma 385/384 = [-7 -1 1 1 1⟩ of 4.503 cents.

Keenanismic

Comma list: 385/384

Mapping: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]

Transpose: [2 3 5 7 385/35]

Minimax tuning:

[|1 0 0 0 0>, |0 1 0 0 0>, |7/3 1/3 2/3 -1/3 -1/3>, |7/3 1/3 -1/3 2/3 -1/3>, |7/3 1/3 -1/3 -1/3 2/3>]

Eigenmonzos: 2, 3, 7/5, 11/5

Badness: 15.159 × 10^-9

Martwin

Comma list: 385/384, 325/324

Mapping: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]

Transpose: [2 3 5 7 385/35 324/25]

Minimax tuning:

||1 0 0 0 0 0>, |0 1 0 0 0 0>, |2/3 4/3 1/3 0 0 -1/3>, |17/3 -5/3 1/3 0 -1 2/3>, |2/3 4/3 -2/3 0 1 -1/3>, |2/3 4/3 -2/3 0 0 2/3>]

Eigenmonzos: 2, 3, 11/5, 13/5

Badness: 2.206 × 10^-6

Ancient

Comma list: 385/384, 625/624

Mapping: [<1 0 0 0 7 -4|, <0 1 0 0 1 -1|, <0 0 1 0 -1 4|, <0 0 0 1 -1 0|]

Transpose: [2 3 5 7 385/35 625/48]

Badness: 2.573 × 10^-6