bwulf said:
Most Western harmony, for the last 400-500 years, has to do with the half step movement of 3rds and 7ths. For example, in the key of C, the 7th(F) of the V(G7) moves a half step down to the 3rd(E) of the tonic(C). It's that old tension and release thing.
This is true, and it's where the tonal justifications for some really cool changes come from. Not all changes are strictly V I relationships, but there is often some sort of tonic relation ship in there. Like mediants for example. If you move by a third, the five of three is the 5^ (^ meaning scale degree) of I, so there's a sort of V/I in a mediant relationship.
Alot of Jazz changes come from Impressionist music. Art Tatum is a good example of a jazzer who dug imprerssionists and helped to shift the direction of jazz.
if you study Debussy's "sunken cathedral" most of the mediant relationships involve a V/I in the bass, with the completion of the voicings fo the chords in the right hand being of a chromatic mediant relationship.
Somthing used even in bach's time is indirect resolution, or "deceptive cadence" which usually means going to vi. However, you can use a combination of a minor ii V i with a chromatic mediant relation ship to go to a half diminished vi (six on the major instead of natural minor six). Alot of times you'll hear jazz tunes end with a ii V7 I7, ii V7 I7, ii V7 IV13, or somthing like that as well, which is basically the same thing. Extended tertain harmony allows you to voice two chords simultaneously, while adding a whole new world of color.
Study chord relationships, and this will allow you to improvise on a set of changes given to you, not just within the changes, but to reharmonize as you go.
As a bassist you can end a cheesy soudning ii V I sound cooler by going to IV in the bass, while the rest of the band, unawares will go to I7, combining to make a IV13 in incomplete voicing, which is very cool. I figured this out on accident during a jam. It's a pretty standard reharm ending thing too, so try and find new ones for sure!
I'm still getting used to this right now, so those two are the only examples I can think of off the top of my head (and the only two I've had work on a gig, and both were on accident, but I was listening so I kept it, and then did the theory AFTER... okay well I did a little theory right on the spot, but I didn't figure out why it worked, just what the change i'd created was by playing what I had against the change given.)
The other thing is tritone substitutions. These are way cool, and while they sound more "out" than the extended tertain stuff (to me anyways), I think they are way easier to think about because you can isolatie them from the other changes and just play without having to thinking vertically. Tritone subs are really cool. They tend to be tritone subs for V7, built on b2, but coltrane did alot of stuff with them, changing the standard
I, iv, ii, V7, I into I biii, biv, bII7, I, as well as tons of other stuff that I have no idea about yet. They work really well for circle of fifth progressions, which is why you so often see those descending changes, like in the C section of Autumn Leaves... that tree that goes down by step is a iii7, V7/ii (or VI), ii7, V7 with tritone subs on every other chord.
Tritone subs are all based around the 7th and 3rd, which in a Dominant chord are a tritone apart, and which are the two common tones between tritone substitution and chord for which the substitution is being used. You still have the " ti do" relationship in the V/I, but the ti is really the 7th of the tritone sub, and the 3rd of the sub is the 7th of the V which goes down by step. Clear as mud? Sit down and play a V7 and then a V7 a tritone away, and see which notes you keep in common, and how voiceleading works for both of them and you'll get the idea.
So yeah, the reason any of this theory is around is just ways to justify and rationalize the use of sounds that players and composers have used. What it really all boils down to is music as heard, so LISTEN LISTEN LISTEN.