Composer Elliott Carter in 1960. (Associated Press / December 10, 2003)

Elliott Carter, the great American composer who was born in the horse-and-buggy era but whose music persistently looked ahead by reflecting and unabashedly celebrating the intricacies of modern life, died Monday of natural causes at his home in New York, according to his close friend and assistant, clarinetist Virgil Blackwell. He was 103.

Not only did Carter long outlive all of the significant composers of his generation, he astonished the musical world by remaining inventive and prolific up to the end. On Oct. 25, Los Angeles Philharmonic musical director Gustavo Dudamel conducted the world premiere of Carter's most recent piece, "Dialogues II," at La Scala in Milan.

"This is music that comes from a very deep soul," Dudamel said Monday night. "While we mourn his loss, what he achieved as a composer, as an artist and as a creator will be eternal. I am very honored to have been a part of this."

Carter was never a favorite with general audiences because of the complexity of his works, but he ultimately wore down his detractors and was in such demand that two months before his 97th birthday in 2005, he had competing premieres given by the Boston Symphony and the Chicago Symphony on the same night. His 100th birthday was celebrated at Carnegie Hall with more premieres, and every subsequent birthday brought new works.

The third of "the three Cs" of American music, Carter, like his contemporaries Aaron Copland and John Cage, did much to define the American sound in the 20th century. Restless, inquiring and perpetually up to date, his music tended to be ever-changeable, and his most important contribution was rhythmic invention. He resisted a constricting regular pulse, seeking instead a more organic way of thinking about time.

In his Second String Quartet, for instance, each instrument has a distinct personality with its own musical intervals, melodic materials and its own rhythmic gait. Like characters in a play, the two violins, viola and cello are constantly coming and going, entering into competition or conflict, falling in and out of love. Eventually, they learn to get along.

Carter's sense of rhythm and meter had its mathematical component as well. He experimented with the effects of playing different melodies at different speeds at the same time. But this technique, rather than making everything sound at cross purposes, rewarded anyone willing to concentrate hard enough with the experience of relativity without the bother of space flight.

For Carter, this was the poetry of science, and for all his technical innovations, poetry and often pretty difficult poetry, was usually his inspiration. He was fluent in several languages, and in old age, when he tired after a morning of composing, his idea of taking it easy was to read Goethe in German, Proust in French or Dante in Italian.

Not surprisingly, then, Carter never composed for the casual listener. His most complicated scores, where everything is in perplexing flux, can at first seem to approach a state of chaos. But after repeated hearings, a listener eventually sorts out the various intertwining lines and meters, and the fragmentary gibberish reveals its fascinating inner workings and purpose.

Such music creates extraordinary difficulties for the performer. But although Carter suffered more than his share of inadequate performances, he was championed by many of the finest musicians of his day. The Juilliard String Quartet made a specialty of his five string quartets, a cycle now considered in a class with those by Béla Bartók and Arnold Schoenberg.

Among conductors, Carter received ferocious support from Pierre Boulez at the New York Philharmonic in the 1970s and later from Daniel Barenboim at the Chicago Symphony and James Levine at the Boston Symphony. He received greater acceptance in Europe, where state-supported orchestras typically have more rehearsal time and where audiences associate difficulty with substance.

Elliott Cook Carter was born in New York City on Dec. 11, 1908. His father, a lace importer who traveled regularly to France, often took him on trips abroad and taught him French at a young age. But his early musical education was limited to standard piano lessons.

Classical repertory, he said, didn't interest him as a teenager, but the rise of Modernism in the '20s did. He was fired up by what he encountered in Paris — as a teenager he bought one of the first copies of James Joyce's novel "Ulysses," which was banned in the United States. All the latest art in the New York of the time appealed to him, whether the visual experiments of the Surrealists and Dadaists or music by Stravinsky, Schoenberg, Ravel, Scriabin and Varèse.

At 16, he was introduced to composer Charles Ives, who encouraged the teenager to pursue a career in music and wrote him a recommendation to Harvard, noting that "his reliability, industry, and sense of honor are what they should be — also, his sense of humor — which you do not ask me about."

At Harvard, Carter majored in English literature, classical Greek and philosophy as well as music. He attended all the important premieres in Boston and New York. In 1931, he found himself seated next to George Gershwin when Leopold Stokowski conducted the first American performance of Alban Berg's "Wozzeck" in Philadelphia.

After earning a master's in music in 1932, Carter still felt his technique inadequate. Following in the footsteps of Copland and other young Americans, he spent three years in Paris studying with famed pedagogue Nadia Boulanger, who put him through his paces in counterpoint. This, Carter later claimed, was what made it possible for him to indulge in his fancy for producing musical lines of radically different character.

But he was not satisfied with any of his early musical experiments and destroyed them all. Upon returning to New York in 1935, he became the music director of Ballet Caravan, the forerunner of New York City Ballet, and began writing in a populist style. The climate of the times — the Depression and the run-up to World War II — as well as the practical necessities of dance music, Carter felt, demanded something audience-friendly.

During the war, Carter, whose allergies prevented him from enlisting, worked for the Office of War Information and wrote an upbeat, Coplandesque "Holiday" Overture and First Symphony. But even in these, he peppered his populism with dissonance, thorny counterpoint and dense instrumental textures.

After the war, Carter wrote two large-scale sonatas, one for piano and one for cello and piano, in which he developed a technique that came to be known as metric modulation. Through mathematical rhythmic relationships that created imperceptibly changing meters, his music shifted from one pulse to the next the way automatic transmissions seamlessly shifted gears. A listener could tell that something had changed, but not right away and not exactly how.

As part of a journey of self-discovery, Carter spent the fall of 1950 to the spring of 1951 in the lower Sonoran Desert in Arizona, where he became fascinated by the weather and exotic wildlife. There, for the first time, he wrote a work intended to satisfy only himself. In a study of Carter's music, the composer David Schiff said the daunting 40-minute First String Quartet "is probably the first musical composition to rival the formal daring of Eliot, Joyce, Proust or Eisenstein."