There is an article by Marijke Rowland in the Modesto Bee which is a conversation with Branford Marsalis. Much of the dialog is devoted to the music of Heitor Villa-Lobos and the influence of Brasilian music on his classical compositions. Branford brings up an interesting point: we often think of Russian composers influenced by peasant music as classical. Bartók, Dvořák and Kodály were influenced by Eastern European traditional music, as Elgar and Vaughn-Williams were by English folk music. Heitor had grown up with Samba music which had a huge influence on his music
This article made me think about my own influences. I grew up playing trombone in a variety of big bands, playing everything from classical Benny Goodman and Glenn Miller to more recent composers like Chic Corea and Chuck Mangione. In concert band and orchestra we played other "classics" from Beethoven to Bernstein. We didn't play any of the more "radical" composers, like Schoenberg or Messian, but then again, I grew up in the mid-west and "radical" is not something that goes over well in that area.
My education here in Edinburgh did a wonderful job of exposing me to these more radical composers, as well as a number of even more obscure forms of music (Luc Ferrari is one that comes to mind). The result? I'm not sure yet. Rhythm is certainly a huge aspect of my music (as I posted here), but so is the repetitive nature of minimalism, although I don't think anything I write could really be classified as minimalist. Perhaps you could call it post-minimalist and perhaps there will be new "box" for it at some point in the future. For now, it's an amalgamation of several styles and yet firmly classical.