Archytas family

Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from 12edo and also a feature of 22edo and 27edo.

Comma: 64/63

7-limit minimax

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

Eigenmonzos: 2, 6/5, 7/5

9-limit minimax

[|1 0 0 0>, |3/2 1/2 0 -1/4>, |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]

Eigenmonzos: 2, 6/5, 9/7

Lattice basis: 3/2 length 1.0508 5/4 length 2.3219

Angle(3/2, 5/4) = 90 degrees

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

Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]

Generators: 2, 3, 5

EDOs: 5, 7, 10, 12, 22, 27, 49

Scales:

• archytas12
• archytas12synch

Music:

Chris Vaisvil

• 12 archytas hobbits with ale

Joel Taylor

• Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3

Ares

Commas: 64/63, 100/99

Minimax tuning

[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, |3 -1 0 -1/2 1>]

Eigenmonzos: 2, 11/9, 9/7

Lattice basis: 3/2 0.9878 6/5 1.4312

Angle(3/2, 6/5) = 75.0475 degrees

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

Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]

Generators: 2, 3, 5

EDOs: 12, 15, 22, 27e, 34d, 49

Badness: 0.000469

Scales: ares12

Vulcan

Commas: 56/55, 64/63

Map: [<1 0 0 6 9|, <0 1 0 -2 -2|, <0 0 1 0 -1|]

Generators: 2, 3, 5

EDOs: 5, 10, 12, 15, 27e

Badness: 0.000577