Horwell family

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The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.

Horwell

Comma: 65625/65536

7-limit minimax

[|1 0 0 0>, |16/7 6/7 -5/7 -1/7>, |16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>]

Eigenmonzos: 2, 7/6, 6/5

9-limit minimax

[|1 0 0 0>, |16/13 12/13 -5/13 -1/13>, |32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>]

Eigenmonzos: 2, 9/7, 7/5

Lattice basis: 5/4 length=0.6213 16/15 length=1.3863

Angle(5/4, 16/15) = 64.6379

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

Map: [<1 0 0 16|, <0 1 0 -1|, <0 0 1 -5|]

Generators: 2, 3, 5

Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995

Badness: 0.000173

Projection pair: 7 65536/9375

Horwellic

Commas: 3025/3024, 65625/65536

Map: [<1 0 0 16 10|, <0 1 0 -1 1|, <0 0 2 -10 -7|]

EDOs: 31, 87, 118, 193, 224, 311, 342

Badness: 0.000505

Zelda

Commas: 385/384, 3388/3375

Map: [<1 0 0 16 -9|, <0 1 0 -1 2|, <0 0 1 -5 4|]

EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee

Badness: 0.000642