Hemifamity family

7-odd-limit: 3 and 7 1/7c sharp, 5 just

[|1 0 0 0>, |10/7 1/7 1/7 -1/7>, |0 0 1 0>, |10/7 -6/7 1/7 6/7>]

Eigenmonzos: 2, 5/4, 7/6

9-odd-limit: 3 1/8c sharp, 5 just, 7 1/4c sharp

[|1 0 0 0>, |5/4 1/4 1/8 -1/8>, |0 0 1 0>, |5/2 -3/2 1/4 3/4>]

Eigenmonzos: 2, 5/4, 9/7

Badness: 0.153 × 10^-3

Projection pairs: 7 5120/729

Music

By Gene Ward Smith

Choraled play

By Chris Vaisvil

Hemifamity27

Pele

Subgroup: 2.3.5.7.11

Comma list: 441/440, 896/891

Mapping: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]

11-odd-limit

[|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>, |17/5 -2 6/5 0 -1/5>, |16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]

Eigenmonzos: 2, 10/9, 11/9

Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]

Lattice basis:

3/2 length = 0.3812, 56/55 length = 1.5893

Angle(3/2, 56/55) = 90.4578 degrees

Badness: 0.000648

Projection pairs: 7 5120/729 11 655360/59049

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 364/363

Mapping: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|]

Minimax tuning:

13-odd-limit

Eigenmonzos: 2, 10/9, 13/10

15-odd-limit

Eigenmonzos: 2, 15/13, 6/5

Badness: 0.703 × 10^-3

Laka

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5120/5103

Mapping: [<1 0 0 10 -18|, <0 1 0 -6 15|, <0 0 1 1 -1|]

Minimax tuning

[|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, |0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, |2 0 3/7 -5/7 5/7>]

Eigenmonzos: 2, 5/4, 14/11

Projection pairs: 5120/729 11 14348907/1310720

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 847/845

Minimax tuning:

13- and 15-odd-limit

[|1 0 0 0 0 0>, |13/8 -1/2 1/8 0 0 1/8>, |13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>, |25/8 -9/2 5/8 0 0 13/8>, |13/4 -3 1/4 0 0 5/4>]

Eigenmonzos: 2, 11/8, 14/13

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 352/351, 540/539, 847/845, 442/441

Mapping: [<1 0 0 10 -18 -13 32|, <0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]

Minimax tuning:

17-odd-limit

[|1 0 0 0 0 0 0>, |13/12 0 0 1/12 1/6 -1/12 0>, |-7/4 0 0 5/4 3/2 -5/4 0>, |7/4 0 0 3/4 1/2 -3/4 0>, |0 0 0 0 1 0 0>, |7/4 0 0 -1/4 1/2 1/4 0>, |35/12 0 0 23/12 5/6 -23/12 0>]

Eigenmonzos: 2, 11/8, 14/13

Akea

Subgroup: 2.3.5.7.11

Comma list: 385/384, 2200/2187

Mapping: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]

Mapping generators: ~2, ~3, ~5

11-odd-limit

[|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>, |26/9 0 13/18 -7/18 -1/3>, |26/9 0 -5/18 11/18 -1/3>, |26/9 0 -5/18 -7/18 2/3>]

Eigenmonzos: ~2, ~14/11, ~7/5

Badness: 0.998 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 385/384

Mapping: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]

Minimax tuning:

13- and 15-odd-limit

[|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, |26/9 0 13/18 -7/18 -1/3 0>, |26/9 0 -5/18 11/18 -1/3 0>, |26/9 0 -5/18 -7/18 2/3 0>, |26/9 0 -7/9 1/9 2/3 0>]

Eigenmonzos: 2, 14/11, 7/5

Lattice basis:

3/2 length = 0.5354, 27/20 length = 1.0463

Angle (3/2, 27/20) = 80.5628 degrees

Map to lattice: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|]

Badness: 0.822 × 10^-3

Scales: akea46_13

Kapo

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5120/5103

Mapping: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]

Mapping generators: ~2, ~3, ~128/99

11-odd-limit:

[|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>, |14/5 6/5 0 7/15 -16/15>, |16/5 -6/5 0 13/15 -4/15>, |16/5 -6/5 0 -2/15 11/15>]

Eigenmonzos: 2, 11/9, 9/7

Badness: 0.994 × 10^-3

Lono

Subgroup: 2.3.5.7.11

Comma list: 176/175, 5120/5103

Mapping: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|]

Badness: 1.18 × 10^-3

Namaka

Subgroup: 2.3.5.7.11

Comma list: 3388/3375, 5120/5103

Mapping: [<1 0 0 10 -6|, <0 2 0 -12 9|, <0 0 1 1 1|]

Badness: 1.74 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 676/675, 847/845

Mapping: [<1 0 0 10 -6 -1|, <0 2 0 -12 9 3|, <0 0 1 1 1 1|]