fmw, I did not get the impression of "rules" in jazz improv during my studies. Yes, a master can simply use the 3 notes of root+3rd+5th in a 12 bar blues and make it sound amazing. Give him the 7th, hold on to your hat, give him all 12 notes... I never got that deep into jazz studies, but that's just my impression.
mudrummer, I guess you must be just starting out? I think one of the first things to do is memorize every chord and all of the inversions, to the point where I can ask "D flat half-dim 7th 2nd inversion", and you immediately can blurt the answer out. Write them all down, study, have a friend quiz. That's just to start off. What a lot of jazz masters do help their students with is finding "voicings" that work with any improv or tune, and it gets far beyond simple lego-block chord building. That's been my impression.
A perhaps "easier" way to expand your jazz lexicon is to learn the "symmetrical scales". The chromatic being just one (or infinite) depending on how you look at it. The whole-tone is binary I suppose, only two of em. The minor third scales, there are only 3 of them ("inversions" included in each scale). The major third scale there are 4.... etc etc. Right there, that's not a ton of scales to learn. You can impose them numerous chords or scales. Of course the chromatic fits anywhere, the whole tone will fit into augmented chords (and so will the major 3rd scale), the minor third scale fits into diminished triads or fully diminished 7ths, etc etc. An idea to explore. Because even if they do not fit perfectly, what's wrong with a little spice after all?
Regarding the musicology bit, I agree the major is more commonly found in ethnomusics. In western music, I find that musicology majors are pretty much bent towards academics, whether as teachers or not. I remember when researching schools way back when, the two toughest ethnomusic programs in the states were UC Berkeley and Wesleyan in CT. My impression was that the first was mostly white folks who wrote books, and the latter had native masters from India, Africa, Japan, China, Indonesia... Anyways, the acceptance rates were less than 6% IIRC at both.
Lastly, its true that the first half of any western harmony text is based on the works of Bach because he's the only one ever to be blessed with The Golden Ears, the best ever. But, I wouldn't go so far to say he invented music theory. He in fact took what he liked from his predecessors, and completely absorbed the qualities in his own music. Well, that's my take! Thanks for the thread.
