Keemic family

From Xenharmonic Wiki
Jump to: navigation, search

These are the planar temperaments tempering out the keema, 875/864.

Supermagic

Comma: 875/864

7 and 9 limit minimax

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

Eigenmonzos: 2, 4/3, 7/5

Lattice basis: 6/5 length=0.8879 3/2 length=1.3391

Angle(6/5, 3/2) = 77.834

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

Map: [<1 0 0 5|, <0 1 0 3|, <0 0 1 -3|]

Generators: 2, 3, 5

Edos: 7, 8, 15, 18, 19, 22, 26, 34, 37, 41, 56, 60

Projection pair: 7 864/125

Scales: supermagic15

11-limit

Commas: 100/99, 385/384

Map: [<1 0 0 5 2|, <0 1 0 3 -2|, <0 0 1 -3 2|]

EDOs: 7, 15, 19, 22, 37, 41, 63, 104, 145c, 201ce, 242ce, 264bce, 305bce

Badness: 0.000641

Supernatural

Commas: 225/224, 245/243

Map:[<1 0 2 -1 0|, <0 5 1 12 0|, <0 0 0 0 1|]

EDOs: 19, 22, 41, 82e, 101cd, 104, 123ce, 142cd, 224cde, 265cde

Badness: 0.000888