Born: December 11, 1908; Died: November 5, 2012.

Elliott Carter, who has died aged 103, was America's finest, most enduring modern composer, whose works were an enthralling, if at times perplexing, challenge to all who listened to them or performed them.

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His endearingly Puckish personality, which was one of his sometimes irascible charms, helped him escape the disparagement which might more often have come his way if his music had been generally perceived as forbiddingly difficult, with nothing other than its complexity to commend it.

Carter was an iconoclast of an admirable sort. His prentice years were spent in the shadow of Aaron Copland, likewise a pupil of Nadia Boulanger in Paris, but he soon turned aside from an influence so immediately acceptable. Charles Ives (without the tunes) was more his sort of American composer, and Ives is what Carter's music sometimes sounds like. He was a composer who never compromised, and whose output, during his second half-century, possessed all his integrity.

Edinburgh was lucky to hear two of his major works in the 1970s, when his music was not yet established in Britain. First, from Solti and the Chicago Symphony Orchestra, came his Variations for Orchestra. Then, four years later, Boulez and the New York Philharmonic brought the Concerto for Orchestra, the sort of gigantic group composition, with every player a soloist, in which Carter excelled.

Though a critic of the period mistook the second piece for a repeat of the first one, his gaffe was less serious than it seemed. The works were so clearly the product of the same meticulously individual mind that the four-year gap transformed them into a compelling entity. At least the critic loved both performances, and said so.

But these two milestones were not his only works to win a Scottish airing. In 2003, the Pacifica Quartet arrived armed to the teeth with Carter's five string quartets, which they played in a single, to some ears inscrutable, concert. The Edinburgh Quartet, some years before, had already had a go at one of the early quartets and, after days of rehearsal, decided never to try another, although the players accepted the music was not a dialogue between four people but an assertion from four strong individuals.

The performance, as I remember it, was plucky but doomed – though at least something of its multiple personality was caught. The Pacifica Quartet, however, had all five works in their bones, and even in the unfriendly acoustics of the Festival Hub they made the music into vivid chapters of Carter's ongoing musical life.

If, in Peter Williams's words, the definition of a composer is someone who is still composing, Carter, a born-and-bred New Yorker, represented them to perfection.

As he grew older – and we are talking of when he was in his 90s rather than his 70s – he produced music increasingly alert and, if you allowed it to be, captivating.

His centenary years were filled with new works and spry public appearances – he was never "the grand old man" of American music. Each performance was an event to look forward to, something more and more of us found to be an irresistible prospect.

Elliott Carter is predeceased by his wife Helen Frost-Jones, a sculptor and art critic.

They are survived by their son David, and a grandson.