Porwell family

The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.

Hewuermity

Comma: 6144/6125

7 and 9 limit minimax

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

Eigenmonzos: 4/3, 7/5

Map: [<1 0 1 4|, <0 1 1 -1|, <0 0 -2 3|]

Generators: 2, 3, 35/32

Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 229, 251, 282, 381

Badness: 0.000142

Projection pairs: 3 6125/2048 to 2.5.7

Zeus

Commas: 121/120, 176/175

Minimax tuning

[|1 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0>, |22/9 2/9 1/3 -4/9 0>, |22/9 2/9 -2/3 5/9 0>, |10/3 2/3 0 -1/3 0>]

Eigenmonzos: 2, 9/7, 7/5

Lattice basis: 11/10, 11/8

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

Angle(11/10, 11/8) = 87.464 degrees

Map: [<1 0 1 4 2|, <0 1 1 -1 1|, <0 0 -2 3 1|]

Generators: 2, 3, 11/10

EDOs: 6, 7, 9, 15, 22, 31, 46, 53, 68, 77, 99, 130e, 229e

Badness: 0.000400

Projection pairs: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5

Zeus11[22] hobbit transversal

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,

11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,

11/6, 15/8, 64/33, 2

Zeus11[24] hobbit transversal

33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,

11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,

11/6, 15/8, 64/33, 2

Euler(1155) genus in zeus temperament

Tinia

Commas: 66/65, 121/120, 176/175

Map: [<1 0 1 4 2 2|, <0 1 1 -1 1 1|, <0 0 -2 3 -1 -1|]

EDOs: 7, 9, 15, 24, 31, 77f, 108ef

Badness: 0.000808

Tridecimal Zeus

Commas: 121/120, 176/175, 351/350

13-limit minimax

[|1 0 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0 0>, |22/9 2/9 1/3 -4/9 0 0>, |22/9 2/9 -2/3 5/9 0 0>, |10/3 2/3 0 -1/3 0 0>, |14/3 -8/3 1 1/3 0 0>]

Eigenmonzos: 2, 9/7, 7/5

15-limit minimax

[|1 0 0 0 0 0>, |0 1 0 0 0 0>, |11/5 1/5 2/5 -2/5 0 0>,|11/5 1/5 -3/5 3/5 0 0>, |13/5 3/5 1/5 -1/5 0 0>, |38/5 -12/5 1/5 -1/5 0 0>]

Eigenmonzos: 2, 4/3, 7/5

Lattice basis: 11/10 length 0.7898 11/8 length 1.002

Angle(11/10, 11/8) = 106.7439 degrees

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

Map: [<1 0 1 4 2 7|, <0 1 1 -1 1 -2|, <0 0 -2 3 -1 -1|]

Generators: 2, 3, 11/10

Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130e

Badness: 0.000934

Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5

Zeus13[22] hobbit transversal

260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2

Jupiter

Commas: 540/539, 5632/5625

Map: [<1 0 1 4 -5|, <0 1 1 -1 6|, <0 0 2 -3 8|]

EDOs: 9, 22, 31, 53, 99e, 108, 121, 130, 152, 282, 434de, 465d, 617de, 747def, 899def

Badness: 0.000562