Layering rhythms on top of rhythms, he paid as much attention to a song’s melody as to its beat. He developed, as the jazz critic Burt Korall put it, “a highly responsive, contrapuntal style,” engaging his fellow musicians in an open-ended conversation while maintaining a rock-solid pulse. His approach “initially mystified and thoroughly challenged other drummers,” Mr. Korall wrote, but quickly earned the respect of his peers and established a new standard for the instrument.

Mr. Roach was an innovator in other ways. In the late 1950s, he led a group that was among the first in jazz to regularly perform pieces in waltz time and other unusual meters in addition to the conventional 4/4. In the early 1960s, he was among the first to use jazz to address racial and political issues, with works like the album-length “We Insist! Freedom Now Suite.”

In 1972, he became one of the first jazz musicians to teach full time at the college level when he was hired as a professor at the University of Massachusetts at Amherst. And in 1988, he became the first jazz musician to receive a so-called genius grant from the MacArthur Foundation.

Maxwell Roach was born on Jan. 10, 1924, in the small town of New Land, N.C., and grew up in the Bedford-Stuyvesant section of Brooklyn. He began studying piano at a neighborhood Baptist church when he was 8 and took up the drums a few years later.

Even before he graduated from Boys High School in 1942, savvy New York jazz musicians knew his name. As a teenager he worked briefly with Duke Ellington’s orchestra at the Paramount Theater and with Charlie Parker at Monroe’s Uptown House in Harlem, where he took part in jam sessions that helped lay the groundwork for bebop.

Image Max Roach at the Bell Atlantic Jazz Festival at Columbia University in 2000. Credit... Ozier Muhammed/The New York Times

By the middle 1940’s, he had become a ubiquitous presence on the New York jazz scene, working in the 52nd Street nightclubs with Parker, the trumpeter Dizzy Gillespie and other leading modernists. Within a few years he had become equally ubiquitous on record, participating in such seminal recordings as Miles Davis’s “Birth of the Cool” sessions in 1949 and 1950.