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When last the Kennedy Center saw Anthony Braxton, he was premiering a new (and still unrecorded) piece in March of 1992. Long enough ago, in fact, that much of the publicity material surrounding this season’s Braxton concert hypes it as his KenCen debut. But if that’s not correct, it might as well be. The torch has been passed since that last visit; in 1992 the Center hadn’t even appointed its first artistic advisor for jazz, then-septuagenarian Dr. Billy Taylor. The new advisor, 37-year-old Jason Moran, is determined to create new audiences for the music—and new possibilities for it at one of the country’s most hallowed jazz institutions.

Heretofore the jazz program has been good, but safe, and Braxton is a definitive break from that. The Chicago native is a walking embodiment of the avant-garde: Braxton is a precise and highly theoretical composer, so abstruse that even his song titles often look like exercises from a geometry textbook. He’s also a saxophonist, to put it loosely; most frequently he plays alto sax, but in any given performance he’s likely to haul out baritone and soprano saxes, plus varieties you never even knew existed, like the bass and contrabass or the sopranino and mezzosoprano saxes. Even before he got tenure at Wesleyan University, you’d have pegged Braxton as an academic.

But he doesn’t always sound that way. Braxton’s music is heady stuff, but it often swings hard and uses the raw phrasing of the blues. It’s rich with melody, too: unconventional, beholden to its own logic, but melodic nonetheless. Braxton’s also working with a quartet of exciting young innovators—reedist Ingrid Laubrock, guitarist Mary Halvorson, and horn player Taylor Ho Bynum—and Moran himself will guest on piano. $38.