Lately I've been experimenting a lot with inverting melodies, and I have a question. Let's say I have a simple melody in a A minor And I invert that melody note for note holding the A as the edge of the melody, in other words the flipping point, the note that doesn't change... Does that mean that the tonic of the inversion of the melody in A minor is the major sub-dominant? I've noticed that if I have an A minor triad, and I invert it using the A as the center, the chord becomes a D major... I imagine this is always then in terms of all tonal melodies, correct?

If your flipping point is A in an A minor melody, the tonic will remain A, but approached from the opposite direction (may not sound the same). Inversions can be effective in small doses, but they do not need to be intervalic inversions (like a twelve-tone row, for instance). Tonal inversions are just as effective (i.e. - stay in key but invert by scale degree). Also, try inverting from different scale degrees. Your tonality will depend on how you harmonize your inversions (i.e. - don't invert everything!) Hope this helps!

Glenn Stallcop