There would be so much to talk about, but I'll just pick on a little
subject, because its related to recent discussions:
When analysing melodic minor harmony, and the interchangeability of its
modes, and taking advantage of the fact that we have two dominant chord in
the melodic minor, a tritone apart, Levine outlines the strongest dominant
resolutions (paired because these dominant chords are the tritone sub of
each other):
1) 7alt descend a perfect 5th = 7(#11) decend a half step
2) 7alt descend a major 3rd = 7(#11) up a whole step
3) 7alt up a half step = 7(#11) descend a perfect 4th
The first resolution is the usual urge of the dominant V 7th chord to go
down a 5th, or conversely its subV7 to go down a half step.
The second I don't see it explained by Levine,(maybe I overlooked), but in
the light of plagal cadences discussions (another thing to thank Reed for),
this can only be explained by the IVm6 -> I move, here using the backdoor
dominant (using Bert Ligon's term) bVII7(9) instead. The major 3rd descent
of 7alt is then the result of tritone sub.
The third resolution I'm not really sure, but seems the 7alt up a half-step
is the source, because VII is largely used as a diatonic sub to V, retaining
the dominant function, thus resolving nicely to I.
Anyone care to coment on this?
Pedro