Rank four temperaments

441/440

Commas 441/440, 364/363

13-limit minimax

[|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]

Eigenmonzos: 2, 11/10, 8/7, 16/13

15-limit minimax

[|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, |5/4 -3/4 5/4 -1/4 -1/4 1/4>, |17/8 -11/8 5/8 -1/8 3/8 1/8>, |5/2 -3/2 1/2 -1/2 1/2 1/2>, |17/8 -11/8 5/8 -9/8 3/8 9/8>]

Eigenmonzos: 2, 14/13, 6/5, 11/9

Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657

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

<0 0 1 0 -1 -2|, <0 0 1 1 1 1|]

Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|,

<0 0 1 0 -1 -2|, <0 0 0 1 2 3|]

Generators: 2, 3, 5

Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393

385/384

Commas 385/384, 325/324

13 and 15 limit minimax

[<1 0 0 0 0 0|, <0 1 0 0 0 0|,

<2/3 4/3 1/3 0 0 -1/3|,

<19/6 -1/6 -1/6 1/2 -1/2 1/6|,

<19/6 -1/6 -1/6 -1/2 1/2 1/6|,

<2/3 4/3 -2/3 0 0 2/3|]

Eigenmonzos: 2, 14/11, 13/10, 4/3

Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247

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|]

Generators: 2, 3, 5, 7

Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253

9801/9800

Commas 2080/2079, 1716/1715

13 and 15 limit minimax

[|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]

Eigenmonzos: 2, 6/5, 16/13, 9/7

Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299

Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|,

<0 0 1 0 1 0|, <0 0 0 1 1 2|]

Generators: 99/70, 3, 5, 7

Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892