"Lonely Woman" by Ornette Coleman
The archetypal jazz track has a "head", a melody over well-defined chord changes, at the beginning and end. In between, the chord changes are repeated over and over while the musicians improvise. This track is similar. There is a melody, but its structure is not as clear and rigid as a typically Tin Pan Alley jazz standard. Similarly, the chord changes are not clearly defined, but rather implied by the melody itself. When the melody ends, Coleman improvises briefly over accompaniment that again arises organically from the melody, before the original melody returns. (In the standard jazz parlance, he only takes one chorus.) But the "head" choruses feel so improvisatory that the line between melody and improvisation, between head and chorus, is really blurred.
Listening to this track still makes me feel slightly overwhelmed and confused -- the way it felt to listen to jazz when I was first learning about it.