Many temperaments, one scale type

When the number of notes to the scale is small, the number of temperaments associated to it can really pile up. Below I list a matrix M for the period-generator mapping for some 7-limit temperaments, followed by another generator mapping to the keys of a hex button lattice keyboard. The rows for these are can be obtained by matrix multiplication by [4 1]M and [3 1]M, corresponding to the 1/4-1/3 7-note MOS region. Next I list 7-limit JI intervals which when tempered give the tunings for the button generators. Note that despite all of the varied 4 and 3 button mappings, none correspond to the patent val mapping. As usual, you may want to set fixed width fonts.

keemun
[1 0 1 2]
[0 6 5 3]

[4 6 9 11]
[3 6 8 9]

[7/6, 36/35]

parakleismic
[1 5 6 12]
[0 -13 -14 -35]

[4 7 10 13]
[3 2 4 1]

[81/70, 28/27]

myna
[1 -1 0 1]
[0 10 9 7]

[4 6 9 11]
[3 7 9 10]

[7/6, 36/35]

superkleismic
[1 4 5 2]
[0 -9 -10 3]

[4 7 10 11]
[3 3 5 9]

[8/7, 21/20]

mohajira
[1 1 0 6]
[0 2 8 -11]

[4 6 8 13]
[3 5 8 7]

[35/32, 9/8]

hemififths
[1 1 -5 -1]
[0 2 25 13]

[4 6 5 9]
[3 5 10 10]

[49/45, 9/8]

beatles
[1 1 5 4]
[0 2 -9 -4]

[4 6 11 12]
[3 5 6 8]

[15/14, 8/7]

muggles
[1 0 2 5]
[0 5 1 -7]

[4 5 9 13]
[3 5 7 8]

[21/20, 6/5]

magic
[1 0 2 -1]
[0 5 1 12]

[4 5 9 8]
[3 5 7 9]

[25/24, 6/5]