In Invisible Man, music is a recurring motif. Jazz and the blues, more specifically, relate to the writing style and mood of the novel respectively. Himself a jazz musician, Ellison has said:
The blues is an impulse to keep the painful details and episodes of a brutal experience alive in one's aching consciousness to finger its jagged grain, and to transcend it, not by the consolation of philosophy but by squeezing from it a near-tragic, near-comic lyricism.
The novel begins with lyrics from Jazz great Louis Armstrong's song which says, "What did I do to be so black and blue?" In chapter 1, a jazz clarinet plays for the cupie doll white woman in the ring. In chapter 2, it's "London Bridge Blues." In chapter 4, there's "Live a Humble." In chapter 6, there's a blues guitar and piano harmonizing. And so on...
So the blues and jazz are intwined because they are the two greatest African-American art forms. The blues is an emblem of suffering and jazz is a creative impulse; together, they achieve a duality of the Black experience.
Stylistically, the novel is written with a jazz feel of stream-of-consciousness, part of the "Keep that ... boy running" mantra that is echoed in the first chapter. Ellison's pace feels furious, then languid, then furious again. It's all part of an improvisational and existential look at race and identity. Characters, motifs, and themes appear, disappear, and then reappear in the novel like a riff in a sax or piano solo.