There are some pretty good reasons to consider jazz both traditional and folk music, though there are some good reasons to not consider it as either, as well. A moot point, as we say. Jazz is really a process, and that process is at the root of most American popular music. It has been said that Bebop was one of the primary influences on Bluegrass(particularly by Earl Scruggs). Certainly there in Rock, and all the other forms of country, as well. Blues pretty much goes without saying.

I'll just duck, now:-)