Reviewing a performance by Mr. Barbieri in 1983, Jon Pareles of The New York Times wrote that he “makes some of the most raucous sounds ever to emerge from a tenor saxophone,” adding: “His horn screams, grunts, honks, bleats, groans. Even in ballads, he works up to a hefty, throbbing tone that sounds like it could burst at any moment.”

Early in his career Mr. Barbieri was a prominent member of the jazz avant-garde, making records with the trumpeter Don Cherry, the pianist and composer Carla Bley and others that challenged the music’s harmonic and rhythmic conventions. He later developed a more melodic approach that acknowledged his Latin American heritage, and that won him a large and loyal worldwide audience.

His first taste of international fame came when he was asked to write and perform the music for “Last Tango in Paris,” the director Bernardo Bertolucci’s sexually explicit 1972 film starring Marlon Brando and Maria Schneider. Mr. Barbieri’s theme won a Grammy Award for best instrumental composition.

“It was like a marriage between the film and the music,” Mr. Barbieri said of his soundtrack in a 1997 interview with The Associated Press. “Bernardo told me, ‘I don’t want the music to be too much Hollywood or too much European, which is more intellectual. I want a median.’”

He went on to write several more film scores.

Leandro Barbieri was born on Nov. 28, 1932, in Rosario, Argentina, and moved to Buenos Aires in 1947. He earned the nickname Gato (Spanish for cat) in the 1950s because of the way he scampered from one Buenos Aires nightclub to another with his saxophone to make it to his next gig.