Something I've been thinking a lot about recently is how some great players have their own voice in improvised music, but still have that connection to some sort of musical tradition while others don't. While listening to some of my favourite musicians (e.i Larry Grenadier, Ethan Iverson, Drew Gress and so on) a lot of them seem to have the jazz tradition in their playing whilst keeping their own voice. On the other hand a lot of the NY down town scene musicians seem to take musical traditions from other genres, such as Jamie Saft, Trevor Dunn and others who arguably take a lot of their sound from rock music before the millennium and bring that energy to their brand of jazz/improvised music.
From reading further into this, Craig Taborn (pianist) talks about how he feels improvising freely with William Parker and Gerald Cleaver and how rooted they are to the tradition of jazz and makes the music their playing some what deeper with out making direct references to any stylistic genre within jazz. On the other hand I watched an interview with Mary Halvorson who discusses not taking direct influence from music and making it your own. She talks about when she studied guitar with Joe Morris and how he'd never touch a guitar in those lessons, so that she would sound only like herself and couldn't take any of his vocabulary. Wayne Krantz also takes this idea, but to a more extreme example. He doesn't listen to any music at all so he can't take any influence from it, therefore anything that he plays is completely unique.
I've also wondered wether there was a similar argument in the 1940s when the bebop movement was starting or in the 1970s when a lot of the ECM guys were trying to break away from more old school jazz approach. If some one were to try and strengthen their connection to the jazz tradition (musically and spiritually), how would some one go about that, or is it a natural thing someone is born with? A lot of people see it's essential that you could hear your connection to the jazz tradition, but can one turn their back on everything and try and create something completely original? As conclusion to this, I think different things work for different musicians; after all you gotta be really good to make a mark in this music anyway!