In late 1959 he joined a big band being formed by Quincy Jones, who not that many years earlier, as a youngster, had taken a few trumpet lessons from him. The original plan was for the band to appear in a stage musical called “Free and Easy,” with music by Harold Arlen. But the show folded during a tryout in Paris, and Mr. Terry accepted an offer to join NBC-TV’s in-house corps of musicians.

The first black musician to land such a job at NBC, he soon became familiar to late-night viewers as a member of the band on “The Tonight Show,” led for most of his time there by Doc Severinsen. He also led a popular quintet with the valve trombonist Bob Brookmeyer and worked as a sideman with the saxophonist Gerry Mulligan and others.

When Johnny Carson began his popular “Stump the Band” feature on “The Tonight Show,” in which members of the studio audience tried to come up with song titles that no one in the band recognized, Mr. Terry would often claim to know the song in question and then bluff his way through a bluesy half-sung, half-mumbled number of his own spontaneous invention.

He recorded one such joking vocal in 1964, as part of an album he cut with the pianist Oscar Peterson’s trio. As he recalled it, the song, released as “Mumbles,” was recorded only because the session had gone so smoothly that the musicians had extra studio time on their hands. Much to his surprise he found himself with a hit.

When “The Tonight Show” moved to the West Coast in 1972, Mr. Terry stayed in New York. Jazz was at something of a low ebb commercially, but he managed to stay busy both in and out of the studios and even found work for a 17-piece band he had formed in 1967. Between 1978 and 1981 he took the band to Asia, Africa, South America and Europe under the auspices of the State Department. Most of his concert and nightclub work, though, was as the leader of a quartet or quintet.

Mr. Terry also became active in jazz education, appearing at high school and college clinics, writing jazz instruction books and running a summer jazz camp. He was an adviser to the International Association of Jazz Educators and chairman of the academic council of the Thelonious Monk Institute of Jazz. For many years he was also an adjunct professor at William Paterson University in Wayne, N.J., to which he donated his archive of instruments, sheet music, correspondence and memorabilia in 2004.