Recipient of a MacArthur Foundation genius grant in 1994. He was also honored as a 2014 National Endowment for the Arts Jazz Master.
He mastered the E-flat, B-flat, and contrabass clarinets; the flute; and the sopranino, soprano, C-melody, F mezzo-soprano, E-flat alto, baritone, bass, and contrabass saxophones. He recorded more than 100 albums.
He fathered two children, one of whom, Tyondai Braxton, became a professional musician and played with math rock band Battles.
He was in the Circle quartet with Dave Holland.