Mr. Babbitt, an advocate and innovator of Arnold Schoenberg’s rigid 12-tone method, created music that was often described as cerebral and academic. His compositions—ordered right down to elements such as timbre and duration—were challenging to both the player and listener.

He later became known for his trail-blazing electronic music, when he was hired by RCA as consultant composer to work with their RCA Mark II Synthesizer at the Columbia-Princeton Electronic Music Center. He claimed to revel in the degree of precision he could achieve in his music, freed from the shackles of unreliable musicians.

Despite the austerity of his most famous work, Mr. Babbitt cultivated at an early age an appreciation and an encyclopedic knowledge of theater music, and enjoyed going to musicals. He at one time composed a full show, Fantastic Voyage, though it was never produced.

Mr. Babbitt's greatest contribution to the theatre, however, is probably his role as an early influence on the work of Stephen Sondheim.

Sondheim became the avant-garde composer's pupil shortly after the young man attended Williams College. "I just wanted to study composition, theory, and harmony without the attendant musicology that comes in graduate school," Sondheim told biographer Meryle Secrest. "But I knew I wanted to write for the theatre, so I wanted someone who did not disdain theatre music. Milton, who was a frustrated show composer, was a perfect combination." Mr. Babbitt remembered that Sondheim didn't seem "interested in becoming what one would call a serious composer, but he wanted to know a great deal more about serious music because he thought it would be suggestive and useful."

Sondheim later said that one of the key lessons he took away from Mr. Babbitt was how to structure a piece of music so that it would make a coherent whole, whether it went on for three minutes or half an hour.

Mr. Babbitt is survived by a daughter, Betty Anne Duggan, and two grandchildren, Julie and Adam.