An influential composer, theorist and teacher who wrote music that was intensely rational and for many listeners impenetrably abstruse. Milton Byron Babbitt was born in Philadelphia on May 10, 1916, and grew up in Jackson, Miss. He began studying the violin when he was 4 but soon switched to clarinet and saxophone. Early in his life he was attracted to jazz and theater music. But Mr. Babbitt set his course toward serious avant-garde composition in 1932, when he played through the scores of some Schoenberg piano music that an uncle had brought home from Europe. At the time, Mr. Babbitt was a 16-year-old philosophy student at the University of Pennsylvania. The next year he became a composition student of Marion Bauer and Philip James at New York University, and in 1935 he began studying privately with Roger Sessions. During World War II, Mr. Babbitt taught mathematics at Princeton and undertook secret research in Washington. In the 1950s Mr. Babbitt was hired as a consultant by RCA, which was developing the most sophisticated electronic-music instrument of the time, the Mark II synthesizer. The Mark II became the centerpiece of the new Columbia-Princeton Electronic Music Center in 1959. Mr. Babbitt was one of the center's first directors, along with Sessions, Vladimir Ussachevsky and Otto Luening. Mr. Babbitt's wife, Sylvia, died in 2005. He is survived by a daughter, Betty Anne Duggan, and two grandchildren, Julie and Adam.