Keenanismic temperaments

This is a collection of rank-3 temperaments tempering out the keenanisma, 385/384. For the rank-4 keenanismic temperament, see Keenanismic family.

Headquarters

Headquarters tempers out 1500625/1492992 = [-11 -6 4 4⟩ in the 7-limit, and the keenanisma, 385/384, the kalisma, 9801/9800, as well as the Alpharabian comma, 131769/131072 = [-17 2 0 0 4⟩, in the 11-limit. It features the split of the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most interesting to those who would like to make extensive use of quartertones. It can be viewed as one which is joined by the three quartertone-size equal temperaments: 22, 24, and 26. It shares the optimal patent val, 284, with keenanismic.

7-limit

Subgroup: 2.3.5.7

Comma list: 1500625/1492992

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

Mapping generators: ~1225/864, ~35/24, ~5

Wedgie: ⟨⟨⟨ 4 -4 -6 11 ]]]

POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326

Badness: 0.7042 × 10^-3

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 9801/9800

Mapping: [⟨2 1 0 7 8], ⟨0 2 0 3 -1], ⟨0 0 1 -1 0]]

Wedgie: ⟨⟨⟨ 4 -4 0 -6 2 -2 11 17 -17 -31 ]]]

POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315

Badness: 0.5292 × 10^-3