16-tet and melodic inversion

Inverting a melody often seems to have the effect of changing major to
minor, and vice versa. For instance, the 18th variation of Rachmaninov's
"Rhapsody on a Theme of Paganini" transposes A minor to D-flat major. The
intervals remain the same size, but they are rearranged from top to bottom.
A 16-tet scale can be arranged to play diatonic melodies with minor thirds
in place of major ones and vice versa. Now imagine combining these two
effects. You could have an inversion of a melody that has the same
alternation of major and minor as the original version, but in a different
tuning. This would be an interesting phenomenon to explore in a composition
that alternates between two or more different tunings (16 - 19 - 23 - 26?).

Has anyone used this effect in their music? Would it even work? It looks
fine on paper, and I did a couple of tests in Cakewalk with simple
melodies. I suppose I'll have to tune an inverted 16-tet scale on my DX7II
to find out if it works with more elaborate music.