Tetrahedrons of temperaments

Seven-limit linear temperaments can be arranged into tetrahedrons of
relationships; I use the example of the
meantone-pajara-tripletone-magic-semisiths-superpythagorean
tetrahedron below. We can use either the four equal temperaments--12,
19, 22, and 27; or the four commas--64/63, 126/125, 225/224,
245/243--as verticies. The six temperaments are the six edges. Given
any edge, it will connect to four other edges with a common vertex
(implying a common comma.) One other edge will be skew to the given
edge; this gives a complementary temperament. The two temperaments
together exactly specify 7-limit JI. So, for instance, knowing octave
and fifth in meantone and also in superpythagorean means we know the
precise 7-limit interval in question.

Meantone
[12, 19] [126/125, 225/224] [1, 4, 10, 4, 13, 12]

Pajara
[12, 22] [64/63, 225/224] [2, -4, -4, -11, -12, 2]

Tripletone
[12, 27] [64/63, 126/125] [3, 0, -6, -7, -18, -14]

Magic
[19, 22] [225/224, 245/243] [5, 1, 12, -10, 5, 25]

Semisixths
[19, 27] [126/125, 245/243] [7, 9, 13, -2, 1, 5]

Superpythagorean
[22, 27] [64/63, 245/243] [1, 9, -2, 12, -6, -30]