Didymus rank three family

These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Euterpe

Commas: 81/80, 99/98

Minimax tuning

[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, |0 0 0 1 0>, |-1 0 -1/2 2 0>]

Eigenmonzos: 2, 5, 7

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

EDOs: 5, 12, 26, 31, 88

Badness: 0.000536

Calliope

Commas: 81/80, 45/44

Minimax tuning

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

Eigenmonzos: 2, 7/3, 11

Map: [<1 0 -4 0 -6|, <0 1 4 0 6|, <0 0 0 1 0|]

EDOs: 7, 12, 19, 26, 45

Badness: 0.000530

Erato

Commas: 81/80, 126/125

Map: [<1 0 -4 -13 0|, <0 1 4 10 0], <0 0 0 0 1|]

EDOs: 12, 19, 31, 81

Badness: 0.000558

Clio

Commas: 81/80, 176/175

Minimax tuning ||1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, |0 0 0 1 0>, |-4 0 2 1 0>]

Eigenmonzos: 2, 5, 7

Map: [<1 0 -4 0 -12|, <0 1 4 0 8|, <0 0 0 1 1|]

EDOs: 7, 12, 24, 31, 105, 129

Badness: 0.000738

Polyhymnia

Commas: 81/80, 385/384

Thalia

Commas: 81/80, 55/54

Melpomene

Commas: 81/80, 56/55

Urania

Commas: 81/80, 121/120

Lattice basis: 11/9 length 0.2536 8/7 length 2.807

Angle(11/9, 8/7) = 90 degrees

Map to lattice: [<0 2 8 0 5|, <0 0 0 -1 0|]

Map: [<1 1 0 0 2|, <0 2 8 0 5|, <0 0 0 1 0|]

EDOs: 7, 14c, 24, 31, 100de, 131bde, 162bde

Badness: 0.000842

Spectrum: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5

Scale: urania24

Terpsichore

Commas: 81/80, 540/539

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

EDOs: 19, 31, 81, 112b

Badness: 0.000850

Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11