Naked City

This is a band led by avant-garde composer and saxophonist John Zorn who's done lots of interesting work mixing composition with improvisation in a way that works surprisingly well.

This particular project's debut album (released in 1989) is testing the limits of the traditional "rock band". 

Zorn's ridiculously tight band make many sudden turns, showing a childlike interest in almost all genres and inspired by the way music for cartoons have a structure that is not defined in the same way as most music, but still makes sense.