Born and educated in Argentina but long resident in Germany, the composer Mauricio Kagel was for more than half a century one of the most inventive and wide-ranging figures in contemporary music. One of the most influential, too. His work defies easy characterisation. He adhered to no recognisable idiom or style, and he was at pains throughout his career to establish no school. “I’m very hard to imitate,” he said. Yet there can be few involved with the late 20th-century musical avant-garde who have not been in some way touched and inspired by his tireless exploration of music’s purpose and possibilities in the world.

Mauricio Kagel was born in Buenos Aires in 1931, to a polyglot Jewish family who had arrived in South America from Eastern Europe in the late 1920s. Growing up in a city of immigrants, he relished the cosmopolitan character of Argentina’s capital, just as he would relish later the sense of being something of an outsider wherever he was at home.

Kagel has described the Buenos Aires of his youth as a city in which “the intellectual climate was unbelievably dense, just as complex as it was contradictory — a really fantastic city, bubbling over with culture”. He made the most of the riches on offer. Preferring to read philosophy and literature at university rather than attend a conservatory, he studied music intensively with private teachers, taking lessons in theory, piano, organ, cello, singing and conducting. As a composer he was self-taught, his work influenced as much by his literary and philosophical studies as by any musical exemplars. Jorge Luis Borges was one of his teachers, and many of the blind author’s preoccupations — with fantasy, absurdity and paradox; with knowledge, identity and time; with mysterious labyrinthine principles of order and organisation — may be detected in compositions from all stages of Kagel’s career.

Film was another early interest which was to endure. In 1950 Kagel was one of the co-founders of the Cinémathèque Argentine. Cinematic editing techniques — cutting, framing, fading, shifting focus — are evident in much of his subsequent musical composition, while the making of experimental films was to be an important strand in his work for many years, culminating in Ludwig van (1970), a multilayered musical and cinematic meditation on Beethoven’s life, music and reputation. The mixing of media, the blurring of artistic boundaries, were to be constants of Kagel’s work.

In 1955 he was appointed conductor at the Buenos Aires opera house, the Teatro Colón. Active in new music circles since his late teens, however, he already knew that he would have to move on. A catalyst had been his acquaintance with Pierre Boulez, who had visited Argentina in 1954 with the theatre company of Jean-Louis Barrault. Boulez told him: “You have to leave: for Europe.” Boulez also told him about the electronic music studio at West German Radio in Cologne, laboratory of the postwar European avant-garde. It was to Cologne that Kagel chose to go when he secured a German government exchange scholarship in 1957, and it was there that he lived for the rest of his life.

A year after his arrival in Germany he began a long association with the Darmstadt international summer school for new music, then — and for several years afterwards — the very centre of contemporary composition, attended by most of the leading figures of the day. Kagel’s works of this period are marked by the strict serialism then associated with Darmstadt, and by an interest both in electronic music and in aleatory techniques. But his determinedly idiosyncratic approach was evident quite early on.

Very much aware both of his Jewish background and of Germany’s recent history, Kagel could see — as its critics could not — that the rigour and austerity of the music of “Darmstadt” composers such as Boulez, Stockhausen and Nono was at least in part a response to the degradation and misappropriation of art and culture under the Third Reich. He could sympathise with that. At the same time, however, he was suspicious of musical fashion, hostile to all claims to cultural authority or leadership, resolutely unwilling to join any movement or school. The best of his own compositions from the late 1950s, while clearly of their time, already mix voices, instrumentalists, tape recordings, electronics and diverse compositional and performance techniques with a characteristic robustness and vigour that seem now like a mocking reproach to the aridity and dogmatism of some of his contemporaries’ then fashionable work.

The postwar serialist consensus was in any case already unravelling. In the decades that followed, Kagel’s own interests turned increasingly to the theatre. Or rather to the theatrical, in all its forms. Music as performance, as drama, became his abiding concern.

It found expression not in conventional works of music theatre but in experimental radio plays, in films, and in multimedia works for stage or concert hall in which the gestural dimension of music came to the fore. Instrumentalists moved around, spoke, interacted, dressed up, improvised, made mistakes. A bizarre theatrical battery of instruments was deployed — garden hoses, sirens, metal pipes, walking sticks, industrial machines, domestic appliances from coffee grinders to flushing lavatories: all feature in Kagel’s scores. A pioneering genre of “instrumental theatre” came into being, widely influential, uniquely Kagel’s own.

Kagel’s work of the 1960s and 1970s has something in common with the near-contemporary Theatre of the Absurd, with the experiments of John Cage, and with Happenings and the performance-based art of the Fluxus movement. There is the same peculiar invention, the same sort of humour — ironic, satirical, sometimes bleak.

At its worst, such work can now seem dated, its jokes laboured, its whimsies arch. The best of Kagel is much better than that. His later work is more often, more obviously, “pure music” and relates more clearly to the work of other composers and other times. But such concerns, and such discipline were always there, throughout his career. He may have rejected the consolations of tradition and delighted in the rude disruption of conventional form, but he remained a profoundly musical composer and a cultivated man. “There are only three or four interesting themes,” he once said. “Love, death, faith, nature. Literature, theatre and opera have lived off those forever.” Almost all his compositions — from the noisiest, zaniest extravaganza to the austere and often beautiful solo piano works — show the same deep awareness of musical history, the same considered engagement with music’s many meanings and its place in human life.

Kagel is survived by his wife, Ursula, and two daughters.

Mauricio Kagel, composer, was born on December 24, 1931. He died on September 18, 2008, aged 76