Keenanismic family

From Xenharmonic Wiki
Jump to: navigation, search

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

Keenanismic

Comma: 385/384

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

Map: [<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]

EDOs: 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212 and 284

10^9*Badness: 15.159

Martwin

Commas: 385/384, 325/324

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

Map: [<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]

EDOs: 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212 and 299

10^6*Badness: 2.206

Ancient

Commas: 385/384, 625/624

Map: [<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]

EDOs: 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190

10^6*Badness: 2.573