What are the principles of improvisation in jazz? I'm looking for it all, from King Oliver's original jazz to Charlie Parker figures that follow the chord changes to Monk to Bill Laswell to Bill Frisell. Too broad? Don't take the easy route and downvote, comment so I can split the question up well.
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Here are a few generalizations:
Traditional Jazz education: follow the chord tones and tensions.
Jerry Bergonzi method: Beginnings of improvisation are mostly in major or minor tetra chords.
Bebop: follow the chord tones but precede them with chromatics or double chromatic approaches, being sure to put the chromatics on a weak beat such as an upbeat.
Avant garde: play whatever you want.