Roach, a virtuoso who could interpret throbbing tempos with nuance and raw power, was among a handful of musicians who ushered in wholesale changes in jazz, the New York Times reported.
Roach paid as much attention to a song's melody as he did to keeping its beat, pushing his role beyond just keeping time. He also led a group that was among the first in jazz to perform pieces in times other than the standard 4/4 count. And he used music as political commentary, beginning in the volatile 1960s.
He one of the first jazz musicians to teach full time at the collegiate level when he was hired at the University of Massachusetts. In 1988, he became the first jazz musician to receive a genius grant from the MacArthur Foundation.
Roach has appeared in concert with a rapper, and composed music for an off-Broadway production of three Sam Shepard plays, for which he won an Obie Award.
Roach is survived by three daughters and two sons.