Double Diatonic Diads

Triads and higher are going to be more difficult than I previously
thought. So as a diversion, here is the unique energy states (interval
vectors) of two stacked necklaces of diatonic diads (white keys only!)
There are 40. The first column is the vector (0,1,2,3,4,5,6 values)
and the second column how many times they appear in my analysis of
117 combinations of diads where I have reduced for mirror image
combinations only...

0,0,0,0,1,2,1 2
0,0,0,0,2,2,0 1
0,0,0,1,0,3,0 2
0,0,0,1,1,1,1 1
0,0,0,2,0,2,0 2
0,0,1,0,1,2,0 4
0,0,1,0,2,0,1 1
0,0,1,1,0,1,1 3
0,0,1,1,1,1,0 7
0,0,1,2,1,0,0 2
0,0,2,0,0,2,0 2
0,0,2,0,2,0,0 1
0,0,2,1,0,1,0 5
0,0,2,2,0,0,0 1
0,0,3,0,0,0,1 1
0,1,0,1,0,2,0 3
0,1,0,1,1,0,1 1
0,1,0,2,0,1,0 2
0,1,1,0,0,1,1 1
0,1,1,0,1,1,0 4
0,1,1,1,0,0,1 1
0,1,1,1,1,0,0 2
0,1,2,0,0,1,0 3
0,2,0,0,0,2,0 1
0,2,0,0,1,0,1 1
1,0,0,1,1,1,0 9
1,0,0,2,0,0,1 2
1,0,1,0,0,2,0 7
1,0,1,0,1,0,1 3
1,0,1,1,0,1,0 11
1,0,2,0,1,0,0 4
1,1,0,0,0,1,1 3
1,1,0,0,1,1,0 5
1,1,0,1,0,1,0 1
1,1,1,1,0,0,0 6
2,0,0,0,0,2,0 3
2,0,0,0,2,0,0 2
2,0,0,2,0,0,0 3
2,0,2,0,0,0,0 3
2,2,0,0,0,0,0 1