Elliott Carter: Innovative composer hailed as one of the greatest of the 20th century

Carter in 1960, by which time he had embarked on a series of increasingly elaborate projects (AP)

Elliott Carter, who has died in New York at almost 104, could justly be described as the last of classical music's modern masters. Certainly he was the last whose musical ideals were formed by the radical modernism of the first three decades of the 20th century, and contact with some of its most innovatory figures. The earliest of these was that awesome American original Charles Ives, to whom Carter was introduced while still at school and who encouraged his early efforts. Another, encountered on Carter's youthful forays into the Bohemian world of Greenwich Village was the dynamic futurist Edgard Varèse. Meanwhile, he caught up with recent works of Scriabin, Stravinsky, Schoenberg and Berg, in what was an exceptionally adventurous phase of New York's cultural life in the 1920s.

These interests were not encouraged by his parents, who expected him to succeed to the family lace-importing business. When he revealed his ambition to become a serious professional composer, his father withdrew all but minimal support and refused ever to attend performances of his music. Possibly Carter's youthful enthusiasm for the most aggressively modernist trends reflected his necessary rebellion. Yet, by his own testimony, he had at first little idea how to compose such music himself. Nor did he discover how from the conservative music department at Harvard, where he switched instead to English Literature – though he did profit from the chance to study briefly with Gustav Holst, who appeared as visiting professor in 1932.

It was three years of rigorous study in Paris with the formidable Nadia Boulanger that finally equipped him with a professional technique. For all her insights, however, Boulanger was unsympathetic to the "ultra-modern" tendencies that had early exited him. And the US to which he returned in 1935 was too decimated by the Depression to care about radical experimentation; what was required was a more populist, morale-raising music as exemplified by Aaron Copland.

Carter admired Copland, and, as a Democrat, assented to the New Deal programme. But although the works he composed in the late 1930s and early '40s, including his Symphony No 1 (1942), were pleasing, they lacked Copland's "gift to be simple" while, arguably, inhibiting the emergence of his own gift to be complex until his late thirties.

Active as a pianist, oboist and conductor during his student years, he did not pursue these skills on account of "poor performing nerves". Instead, he turned to reviewing for the journal Modern Music and became, for a time, musical director of Ballet Caravan, which his Harvard friend Lincoln Kirstein had set up to tour American dance. It was for this company that Carter composed his earliest substantial orchestral score, the ballet Pocahontas (1939). Though it had the bad luck to be premiered on the same bill as Copland's instant hit Billy the Kid, Carter evidently regarded it as a breakthrough, destroying much of his previous output.

In 1939 he also married the sculptor Helen Frost-Jones and their son was born in 1943. During the war Carter taught music as a link subject between classics and maths at a liberal arts college, and ended up serving in the Office of War Information in Washington, where he found himself ever more desperately orchestrating national anthems as more countries came over to the Allies. Although, in their unobtrusively generous way, he and his wife later seemed to be in possession of considerable means, Carter continued for decades to serve the new music community as committee man, concert organiser and teacher of generations of student composers at such institutions as Columbia University and the Juilliard School.

But it was also around the end of the war that he began to find his true way, having decided that, Copland aside, the populist programme had failed to engage the masses. Beginning with his magisterial Piano Sonata (1946) he progressively cast aside such traditional forms and techniques in a radical effort to redefine every aspect of composition from the most basic elements of rhythm and pitch to the "time-sweep" of entire musical forms. Yet where much younger contemporaries such as Boulez appeared to regard technical innovation as a kind of aesthetic research, Carter never considered it as an end in itself but rather as a means to heightened expressivity. Nor was he hesitant in offering poetic or visual metaphors to help listeners get to grips with his music.

His primary approach was to derive the substance of his works from the specific sounds and playing techniques of the ensembles he was composing for – likening his scores to "auditory scenarios for the players to act out with their instruments". So the Sonata for Cello and Piano (1948) develops a tough dialectic out of the very incompatibility of the two instruments. And in the vast String Quartet No 1 (1950-51) – during the writing of which, Carter retreated to the Arizona desert in order to give his most daring ideas their head – the four players simultaneously pursue seemingly independent lines. Carter feared the resulting complexities might prove unperformable. To his surprise, the work was not only played with increasing virtuosity, but became the foundation of his international reputation.

Thus reassured, he embarked upon a series of increasingly elaborate projects. In the Variations for Orchestra (1955), he built a grandiose structure upon not one, but three themes; while in the fiercely concentrated String Quartet No 2 (1959), which won Carter the first of his two Pulitzer prizes, the players are "cast" like four perpetually arguing characters. The coruscating Double Concerto (1961) for harpsichord and piano emulates Lucretius in evolving a coherent world out of random sound-atoms, then dissolving it back into chaos again. The Piano Concerto (1965), composed on a Ford Foundation Residence in Berlin, finds its soloist increasingly oppressed by menacing walls of orchestral sound; while in the String Quartet No 3 (1971) the players are divided into two duos each simultaneously pursuing a quite different sequence of movements.

Yet the apogee of this heroic middle period was the Concerto for Orchestra (1969) inspired by a vision of America swept by great winds of change, which appeared shortly after Carter's 60th birthday. Here, the division of the orchestra into four mixed ensembles, each with its own material, interacting in constantly fluctuating speeds, creates an astonishing sensation of form like an on-going vortex.

The notion of different musics going on at once, had been pioneered in the 1900s by Ives, as Carter knew better than anyone. But where Ives seemed content to simulate the sonic chaos of real life, Carter always strove to produce an effect of multiplicity which further hearing would reveal as ordered and coherent: "a focused freedom," as he put it. Finding techniques to achieve this cost him immense effort and thousands of pages of sketches in his middle years, when he once remarked: "Each new work is a crisis in my life".

Had it been foretold to Carter at 60 that two-thirds of his output was still to come, he would have laughed it off. Yet over the 1970s and '80s, it gradually became apparent he was handling his hard-earned musical language with an increasing facility. Already the American Bicentennial commission, A Symphony of Three Orchestras (1976) – his aural panorama of New York – took him six months where it might have cost him two years a decade before. After avoiding vocal writing for some 27 years as unsuited to his angular style, he now found ways to set Elizabeth Bishop in his cycle Mirror on Which to Dwell (1986) – the first of a striking series of settings of poets to whom he felt close, including John Ashbery, Robert Lowell, John Hollander, William Carlos Williams, Wallace Stevens, Ezra Pound, Marianne Moore, ee cummings and TS Eliot.

From the early 1980s he also began to fill the gaps between larger projects with a steam of miniatures – solos, duos, trios – as if to write something characteristic for more or less every instrument in current use. Not that the larger projects stopped coming: two further string quartets, concertos for oboe, violin, clarinet, cello and flute and, at the age of 88, the completion of a 45-minute orchestral triptych entitled Symphonia (1993-97) which might have been thought summatory, had he not gone on to compose his first acknowledged opera What Next? (1998) at the age of 90.

Thereafter, the continuing flow of works may have been less crowded of texture, more lapidary of structure, but showed no sign whatever of any slackening in organisational grip or liveliness of ideas. After celebrating his 100th birthday in Carnegie Hall in December 2008 with a piano concerto entitled Interventions, he continued to compose up to a few weeks ago, producing some 20 further scores.

Those meeting Carter for the first time and imagining, from his more pugnacious pieces, some rough-hewn American giant, were often surprised to encounter a small, neat, genial man of civilized manner and vast cultural interests; a linguist who not only spoke French, Italian and German but had kept up his classical Greek and Latin; a vivid and wry witness of all those decades of artistic, intellectual and political upheaval he had experienced at first hand on both sides of the Atlantic. For the rest, it was as though he had delegated all his more combative characteristics to his truly remarkable wife, Helen, from whom he was inseparable: a lady of ancient New England descent with a lethal eye for pretentiousness and a devastating wit in disposing of it, yet full of shy kindness to those she trusted.

A talented sculptor – her fine head of Marcel Duchamp is in the Wadsworth Atheneum – she had decided to sideline her career in order to promote his. After dispatching him each morning to his workroom at 8.30 sharp, she would lift the phone and give battle on his behalf with the music directors and recording executives of the world. Towards the end, as she became frailer in health, if emphatically not in spirit, the situation was touchingly reversed. Carter claimed that he had lived a selfish life and now it was his turn to look after Helen. In the event, their determination to continue living as before in their modest Greenwich Village apartment was sustained, quite as much, by the care of a devoted circle of younger friends, several of them outstanding musicians.

Carter's compositional strategy had long been to address his music, in the first place, to its performers, believing that if he could give them something challenging to play, they, in turn, would convey this convincingly to audiences. Since the difficulties of his scores meant that only the most brilliant performers could get near them, this paid off. In later decades, his music was idiomatically interpreted by artists of the calibre of Boulez, Barenboim, James Levine, Oliver Knussen, Charles Rosen, Heinz Holliger and the Arditti Quartet, to name but a few.

There was a time, perhaps, in his mid-career when his most formidable scores were more respected than loved by the musical public. Yet, as he continued to step forward year after year to acknowledge the reception of his later pieces, respect turned to affection – never more so than on the last of his innumerable visits to Britain for the 2009 Aldeburgh Festival. And while many of his innovations were taken up by younger composers, the energy of his invention, often tumultuous in his middle period, increasingly mercurial later, remained unique. Back in 1983, after a particularly frenetic Carter premiere, one of our best younger composers reclaimed in disbelief, "But when is he going to start writing music like an old man?" In a sense, he never did.

Elliott Cook Carter, Jr, composer, writer and teacher: born New York 11 December 1908; married 1939 Helen Frost-Jones (died 17 May 2003; one son); died New York 5 November 2012.