I observed some characteristics of moving from one major chord to another.

M chord interval away n shared chord tones chord tone (from->to)
m2 up, M7 down 0  
M2 up, m7 down 0  
m3 up, M6 down 1 5->3
M3 up, m6 down 1 3->1
P4 up, P5 down 1 1->5
TT up, TT down 0 move m2,M2,m3 away
P5 up, P4 down 1 5->1
m6 up, M3 down 1 1->3
M6 up, m3 down 1 3->5
m7 up, M2 down 0  
M7 up, m2 down 0  

There are two “cells” of chords:

  • no common tones (+/-m2, +/-M2, TT)
    • each of these can be alternated with the 1 chord to walk up the inversions
    • creates synthetic scales
  • with common tones (+/-m2, +/-M2, TT)

Again, this is only considering the major chords.