The 20th century's accumulation of musical history was arguably the single biggest hurdle for its composers to negotiate. If you think it was hard for Brahms to write string quartets and symphonies in the 1860s and 70s, then imagine what it was like for composers in the second half of the 20th century, with the freight of all of those late Romantic, modernist, and avant garde traditions on their shoulders to add to everything else in the historical pantheon.

If you're Stravinsky, you escape these historicist pressures by – well, by being Stravinsky and viewing the past, the present, and the future through the prism of your own creative genius; if you're Pierre Boulez or Karlheinz Stockhausen, you have the self-assurance and arrogance of youth to believe what you're doing is the only possible option for new music, the ne plus ultra to which the trajectory of music history has been leading. Or, like John Cage or Steve Reich, you simply acknowledge the past in order to forget it, to start again in an ever-present now.

But what do you do if you're a composer of supreme historical awareness, who understands only too well the achievements of your predecessors, from Monteverdi to Schoenberg, if you're somebody for whom the act of writing a single note or chord is already at best a conversation and more often than not a confrontation with the musical past – and one, inevitably, that you're not going to win every time you compose a new piece? Alexander Goehr is, I think, exactly that sort of composer: a musician for whom there is no such thing as an innocent note, someone for whom nearly every work is the hard-won prize of a historicist battle, and in which each gesture, each phrase, is loaded with musical and cultural meaning. That's what gives his music its craggy, conflicted, and essentially pessimistic character. Goehr's is a voice that matters because, on his own terms, his music reveals one of the signal sounds of the 20th and 21st centuries in the heightened consciousness of its negotiation with history, and also because of the effect that his personality and his leadership had on British music in the postwar period.

That's because without Goehr, musical modernism would have taken even longer to arrive in Britain than it did. Goehr's family moved to Britain from Berlin shortly after his birth in 1932, and in the 1950s, Goehr became the eldest and most musically experienced member of the so-called Manchester school, along with Peter Maxwell Davies and Harrison Birtwistle – it was Goehr who founded the New Music Manchester group. Goehr's father Walter had been a pupil of Schoenberg's, and a conductor who brought both the extremes of music history – the Second Viennese school, the British premiere of Olivier Messiaen's Turangalîla Symphony, and Monteverdi's Vespers – to life for British audiences, and so Alexander was the conduit between the recent music of continental modernism and his fellow students in Manchester. Goehr continued his European education in the formative time he spent during 1955 and 1956 in one of the solar plexuses of postwar 20th century music: Olivier Messiaen's class at the Paris Conservatoire. His account of that time, of Messiaen's teaching, and of the reactions and rebellions of his fellow students Karlheinz Stockhausen and Pierre Boulez, is one of the most riveting accounts of postwar music.

Goehr couldn't follow Stockhausen or Boulez into the brave new world of the avant garde; his open letter to Boulez (published in Finding the Key, a collection of his writings) is a powerful creative credo, refuting the scorched-earth policy to the past that the young turks of Darmstadt indulged in. As he writes, the music sanctioned by Boulez's ideological approach to serialism would mean "a conscious elimination of sensuous, dramatic or expressive elements, indeed of everything that in the popular view constitutes music".

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He has not been afraid to put his money where his mouth is, either; in 1961, after the fiasco of the premiere of his cantata Sutter's Gold in Leeds, Goehr's feeling was that his choral parts may simply have been too difficult: how can you imagine the possibility of the autonomous work of modernist music, he writes, "when people who sing for pleasure [like the amateur choir who performed Sutter's Gold] are deprived of true satisfaction in the performance of new work?" Goehr's alternative path, as composer, teacher and proselytiser, was a commitment to contemporary music's power to communicate the social and cultural conflicts of the 20th century by remaining true to a Schoenberg-like belief in the continuity of musical traditions.

Which all rather raises the question: what does Goehr's music sound like? Even as he articulates the necessity for modern music to be sensuous or pleasurable, his music only rarely gives you that simple satisfaction. Which is precisely its strength. Instead, Goehr's works – like the dark drama of the misleadingly titled Little Symphony, the bleaker-still strains of the Symphony in One Movement, the heightened emotional drama of the Piano Concerto, or the concentrated drama of Behold the Sun for soprano and ensemble – are invitations to get stuck into the labyrinths of contemporary music's tussle with the musical past, to feel the mud on music's historical shoulders (to paraphrase Edoardo Sanguineti, one of Luciano Berio's favourite writers, another composer who refused to reject the past). Or listen to his involvingly knotty Third String Quartet: music like that quartet, or Goehr's other chamber works, makes me think of him as a kind of 21st century Brahms, as a composer as released as he is trapped by tradition. The intensity of the quartet's drama is catalysed by that essential dichotomy. But there are simpler pleasures to be had from Goehr's music: his reconstructions around Monteverdi's mostly lost opera Arianna, or the joyful neo-classicism of Marching to Carcassonne for piano and ensemble, one of his most unbuttoned and sheerly joyful and tuneful pieces.

Two other works show the depth of Goehr's engagement with musical traditions and how he attempts to transcend them. He has composed a series of piano pieces designed as a contribution to piano-playing pedagogy, studies in contemporary counterpoint called Symmetry Disorders Reach. In its conscious debt to Bach, this results in some of Goehr's most direct music. As does, for me, his opera Promised End, that fragmentary retelling of King Lear, that story of "old men who get it wrong when they have power and influence – and then get into a mess", as he described it to me. Goehr's music is defiantly uneasy listening. But its expressive unease sounds out a relationship with the musical past that is one of fundamental legacies of 20th and 21st century music.

Five key links

String Quartet No 3

Little Symphony

Arianna

Marching to Carcassonne

Promised End