Mirkwai family
The mirkwai family of planar temperaments tempers out the mirkwai comma, 16875/16807.
Mirkwai
Comma list: 16875/16807 (mirkwai)
Mapping: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]
Mapping generators: ~2, ~3, ~7/5
- [|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>]
- Eigenmonzos: 2, 8/7, 6/5
- [|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>]
- Eigenmonzos: 2, 10/9, 8/7
Badness: 0.342 × 10-3
Projection pairs: 5 84375/16807 7 16875/2401 to 2.3.7/5
Indra
Comma list: 540/539, 1375/1372
Mapping: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]
Mapping generators: ~2, ~3, ~7/5
- [|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>, |6 6 -1 0 -3>, |20 18 -6 0 -9>]
- Eigenmonzos: 2, 11/9, 5/4
Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]
Lattice basis:
- 15/14 length = 0.6184, 55/36 length = 0.7585
- Angle (15/14, 55/36) = 68.1048 deg
Badness: 0.266 × 10-3
Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
Scales: indra31
Shibi
Comma list: 540/539, 729/728, 1375/1372
Mapping: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]
EDOs: 41, 72, 111, 183, 224, 703
Badness: 0.721 × 10-3
Yajna
Comma list: 540/539, 625/624, 1375/1372
Mapping: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]
Mapping generators: ~2, ~3, ~7/5
Minimax tuning:
- 13-odd-limit
- [|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>, |8/5 2/5 -3/5 0 0 2/5>, |44/25 26/25 -24/25 0 0 11/25>, |62/25 48/25 -27/25 0 0 3/25>, |8/5 2/5 -8/5 0 0 7/5>]
- Eigenmonzos: 2, 10/9, 13/10
- 15-odd-limit minimax
- [|1 0 0 0 0 0>, |0 1 0 0 0 0>, |5/4 1/2 0 -5/16 0 5/16>, |1 1 0 -1/4 0 1/4>, |5/4 3/2 0 3/16 0 -3/16>, |1 1 0 -5/4 0 5/4>]
- Eigenmonzos: 2, 14/13, 4/3
Vals: Template:Val list
Badness: 0.700 × 10-3
Vibhu
Comma list: 351/350, 540/539, 1375/1372
Mapping: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]
Vals: Template:Val list
Badness: 0.826 × 10-3
Vish
Comma list: 325/324, 364/363, 540/539
Mapping: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]
Vals: Template:Val list
Badness: 0.930 × 10-3