In the late 1940s and early ’50s Mr. Brubeck also led a trio with Ron Crotty on bass and Cal Tjader on drums. It was around this time that he started to develop an audience. He was given an initial boost by the San Francisco disc jockey Jimmy Lyons, later the founder of the Monterey Jazz Festival, who plugged the band on KNBC radio and helped secure it a record deal with Coronet.

In 1951 the trio expanded to a quartet, with Mr. Desmond returning. (The permanent lineup change was perhaps inevitable, as Mr. Desmond was desperate to join his old friend’s increasingly popular band, but it may also have had to do with physical necessity: Mr. Brubeck had suffered a serious neck injury while swimming in Hawaii, limiting his dexterity, and he needed another soloist to help carry the music.)

Quickly the constitutionally different men — Mr. Brubeck open, ambitious and imposing; Mr. Desmond private, high-living and self-effacing — developed their lines of musical communication. By the time of an engagement in Boston in the fall of 1952 they had become one of jazz’s greatest combinations.

The next part of the equation was a record label, and for that Mr. Brubeck had found another booster: Fantasy Records, just started by the brothers Max and Sol Weiss, who owned a record-pressing plant and had little interest in jazz apart from wanting to make a profit from it.

They did, eventually, with Mr. Brubeck. But Iola Brubeck also played a role in the growth of his audience. Before Mr. Brubeck became a client of the prominent manager Joe Glaser, she handled her husband’s business affairs. In 1953 she wrote to more than a hundred universities, suggesting that the quartet would be willing to play for student associations. The college circuit became the group’s bread and butter, and by the end of the 1950s it had sold hundreds of thousands of copies of its albums “Jazz at Oberlin” and “Jazz Goes to College.”

In 1954 Mr. Brubeck became only the second jazz musician (after Louis Armstrong) to be featured on the cover of Time magazine. That year he signed with Columbia Records, promising to deliver two albums a year, and built a house in Oakland.