Tasked with inventing the world’s most intimidating musician, a novelist could do worse than to create Anthony Braxton. If the name alone—building rhythmically toward that spiky, algebraic x—fails to daunt, consider this sentence from his voluminous writings: “Composition No. 105B is a material and principle generating structural world that establishes a multiple construction structural identity in its principal material identity (sense) as well as a medium tempo constructed sensibility in its extended sense.”

Note that rather than name his compositions, Braxton numbers them; he also “titles” them with schematic doodles that look like Feynman diagrams rendered by Keith Haring. One of the rare MacArthur “geniuses” for whom scare quotes are widely thought unnecessary, he has his own foundation—the Tri-Centric, a name ripe for conspiracy spinning by hats both tinfoil and red—devoted to the propagation of his work, which ranges from solo improvisations to opera cycles, and has, for half a century, been a crucial strain of yeast in the ferment of the avant-garde.

You might not guess, on this evidence, that Braxton’s music has personality to burn: laughter, passion, intrigue. And while his sound world is often closer to Berio, Stockhausen, Cage, and Ives than to what most of us think of as jazz, the Chicago-born saxophonist plays jazz standards as fluently and feelingly as nearly anyone alive.

Braxton “titles” his compositions with doodles that look like Feynman diagrams rendered by Keith Haring.

How many listeners came to Bird by way of Charlie Parker with Strings, to later Coltrane by way of “My Favorite Things,” to Cecil Taylor by way of his early versions of Ellington and Cole Porter? Meeting a challenging musician through the medium of standards is like viewing a strange new landscape through the windows of a tour bus, the contours of the song (chord changes, melody, patchily remembered words) providing a comforting prop. Conversely, it can be like seeing a familiar landscape through a dragonfly’s eyes. And few eyes are more kaleidoscopic than Braxton’s. On his many recordings of standards (mostly live and with a quartet), his sax often envelops the melody like a swarm of bees, each waggle-dancing its own revelatory tale. In perhaps the most accessible of the many events celebrating Braxton’s 75th birthday, he will lead a quartet that includes the formidable British pianist Alexander Hawkins. —Evan Eisenberg