But Mr. Babbitt expanded on Mr. Schoenberg’s approach. In Mr. Schoenberg’s system, a composer begins by arranging the 12 notes of the Western scale in a particular order called a tone row, or series, on which the work is based. Mr. Babbitt was the first to use this serial ordering not only with pitches but also with dynamics, timbre, duration, registration and other elements. His methods became the basis of the “total serialism” championed in the 1950s by Pierre Boulez, Luigi Nono and other European composers.

Mr. Babbitt began exploring this path in Three Compositions for Piano (1947) and Composition for Four Instruments (1948), and adhered to it through his entire career. He composed prolifically for chamber ensembles and instrumental soloists and created a substantial and varied catalog of vocal works. He also composed a compact but vital group of orchestral pieces and an enduring series of works for synthesizer, often in combination with voices or acoustic instruments.

Mr. Babbitt liked to give his pieces colorful titles, often with puns (“The Joy of More Sextets,” for example), and said that in selecting titles he tried to avoid both the stale and the obscure. Yet when Mr. Babbitt explained his compositional approach in essays, lectures and program notes, they could be as difficult to understand as his music. In one program note, he spoke of “models of similar, interval-preserving, registrally uninterpreted pitch-class and metrically durationally uninterpreted time-point aggregate arrays.”

He often said in interviews that every note in a contemporary composition should be so thoroughly justified that the alteration of a tone color or a dynamic would ruin the work’s structure. And although colleagues who worked in atonal music objected when their music was described as cerebral or academic, Mr. Babbitt embraced both terms and came to be regarded as the standard-bearer of the ultrarational extreme in American composition.

That reputation was based in part on an article published by High Fidelity magazine in February 1958 under the title “Who Cares if You Listen?” The headline was often cited as evidence of contemporary composers’ disregard for the public’s sensibilities, and Mr. Babbitt objected that it had been added by an editor, without his permission. But whatever his objections, the article did argue that contemporary composition was a business for specialists, on both the composing and listening end of the transaction, and that the general public’s objections were irrelevant.