Muhal Richard Abrams has been performing and recording under his own name for nearly 50 years…yet if you own all 27 of his albums, and have seen him as many times in concert, you still have no more idea what he’s going to do at the Kennedy Center than someone who’s never heard of him. A Chicago native, the pianist and composer was the founding president of that city’s Association for the Advancement of Creative Musicians, making him one of the most important living members of jazz’s avant-garde. He’s made his share of noisy free jazz, alien soundscapes, and to-the-point-of-dementia abstractions. But just as often, he’s done lyrical piano solos; hard-swinging big band showcases; down-and-dirty small ensembles; profound, kaleidoscopic evocations of the blues and 1920s jazz; contemporary classical treatises; and introspective pastel pieces of no known form or category. As jazz critic Gary Giddins wrote, “As soon as you think you know his music, he switches stations.” Which raises vital, important questions: Does an improvising musician ever want his music to be knowable? Can an artist with such expansive range still develop a personal style? At the same time, Abrams does assemble through-lines in his music: It’s all inventive, uncompromising, and almost ruthlessly compelling. Oct. 10 at Kennedy Center Terrace Theatre. $32.