‘One of the richest lives ever lived in American arts’ (p. 6) write Bill Alves and Brett Campbell of the life of Lou Harrison. They mention this almost in passing, but by the end of their immense and impressive biography of the American composer, instrument builder, performer and teacher (1917–2003) one is inclined to agree. Harrison's life and work is a brightly coloured thread running through the tapestry of twentieth-century American music, a list of his friends and collaborators a who's who of the country's most important artistic figures. I can't speak for his reception in the United States, but certainly in the UK it is a career whose significance has been under-appreciated: Harrison's music doesn't fit easily with the principal narrative constructs of American music – experimentalism and minimalism, uptown and downtown, academicism and populism. Yet it is also a career that touched nearly every one of those bases, participated in many of the founding conversations of American contemporary music, and nurtured at least one generation of highly original musicians.

Aged just 18 Harrison began taking classes with Henry Cowell – his enthusiasm for Cowell's music enough to compensate for not being able to afford the tuition fee (Cowell enlisted him as an assistant). Good fortune also attended his application to join Schoenberg's classes in Los Angeles a few years later: the Austrian composer was renowned for the stern discipline he expected from his students, and Harrison was nervous about what he would make of his youthful scores. After flipping through a few of them, Schoenberg simply said ‘You can join the class’, and returned to his own work. Later, in one of those classes, he would proclaim a piece of Harrison's – much to the younger man's embarrassment – as ‘Music I understand. Why do [the rest of you] not bring me such music?’

Between these encounters, Harrison discussed his music with Aaron Copland and befriended John Cage. Also in his circle as a young man were Virgil Thomson, Elliott Carter, Carl Ruggles and more. At 19 he started a correspondence with Charles Ives that led eventually to Harrison giving the first performance of Ives's Third Symphony, and to that work receiving the 1946 Pulitzer Prize for music. He also came within a whisker of editing the complete Ives edition. In a meeting at the elderly Ives's house the following year, Ives even announced to the openly gay Harrison, ‘When I was growing up, just to be a musician or to think of yourself as a musician automatically meant that you were a sissy. But all that seems to have changed now’, a declaration Harrison took to mean that Ives believed the derogatory ‘sissy’ label was no longer something to be ashamed of.

Contacts like these continued throughout Harrison's life, among the most important of them Terry Riley, the choreographer Mark Morris and the conductor Dennis Russell Davies. Yet for all these encounters’ fascination, and the opportunities they offer to see the lives of well-known figures from a new perspective (Cage's in particular), there are probably three main turning points in Harrison's life, at least in Alves and Campbell's telling of it.

Rock bottom is reached in 1947, not long after that meeting with Ives, when Harrison suffered a nervous breakdown just before his 30th birthday (he had already attempted suicide in 1943; only the long time it took to fill his flat with gas had saved him). Unhappy in the competitive, noisy, hothouse environment of New York he was having few pieces performed and watching his life unravel. His finances – always difficult anyway – became more troubled when the journal Modern Music, for which Harrison wrote reviews, folded. Ill-health and disorganisation meant he had to give up his position directing Cowell's New Music Edition (on whose board he sat with Cage, Carter and the composer Kurt List). He was drinking heavily and sleeping poorly. And in May his relationship with Edward McGowan, one of his few remaining points of stability, came to a sudden end. Found wandering Fifth Avenue in a daze by his friend John Heliker, Harrison was whisked to a psychiatric hospital by Cage, who continued to care for him during his illness.

Harrison took several years to fully recover, and anger and depression seem never to have been far away for the rest of his life. In 1953 he returned to California, at first to live with his parents at the age of 36. The move back to the Pacific coast – away from New York's noisy hypermodernity – helped restore him to health, but it was not until he crossed that ocean for the first time, in 1961, that he found his true calling. The visit came at the instigation of another central figure in American musical culture, the (then covert) Cold Warrior Nicolas Nabokov, who invited Harrison to the East–West Encounter – a CIA-funded instrument of ‘soft power’ that involved a two-week international conference in Tokyo, plus money to study in Southeast Asia. After hearing traditional Korean music for the first time at the conference, Harrison chose to spend his time in Seoul, and instruments such as the piri flute and gayageum psaltery would influence and appear in his music for many years to come. More significantly still, Harrison – an admirer of Asian music and culture from a very young age (his childhood home had been full of Asian artefacts) – had confirmed the blend of East and West that would define his music from now on, and for which he is best remembered. Twenty years later, Harrison would discover Indonesian – and especially Javanese – gamelan music and find it the final, supreme medium for his art.

The third turning point is his meeting Bill Colvig in 1967, the man who become his partner in love and music until Colvig's death in 2000. This moment arrives with Harrison aged 50 and bearing the many scars of a troubled life. ‘Across the room … Harrison spied amid a group of his acquaintances a man about his age with a pioneer's beard and an outdoorsman's build. “Oh”, he sighed, “isn't he beautiful?”’ (p. 284). The relief in that sigh is shared by subject and reader alike, and reverberates to the book's end. This is fine storytelling. (Another piece of luck: the ruggedly handsome Colvig had also been spotted by Ned Rorem that evening, but he ended up going home with Harrison.)

Colvig provided the emotional stability and practical support that Harrison clearly needed, building and organising their home, establishing a workshop and helping make many of Harrison's instruments (including the famous American gamelan, a Partch-inspired Westernisation of its Indonesian counterpart), and acting as a sponge for the composer's unpredictable temper. It was also a relationship of great tenderness: one of the supreme love affairs of twentieth-century music.

Almost every moment in Alves and Campbell's story is used to frame a particular piece of Harrison's. These are discussed sensitively and in some detail, but not too technically. (Musical terms are always explained on their first occurrence, and there is also an extensive glossary.) The pattern becomes a little repetitive after a while – a story from his life, details of what piece he was writing at the time, a short assessment of that work – but it is a device the authors use effectively to build a double portrait of Harrison through his life and his music.

Alves and Campbell have prepared an exhaustive biography of a beloved composer. Across almost 600 pages – including a complete catalogue of compositions that builds substantially upon, but also supplements that included in Leta Miller and Fredric Lieberman's Lou Harrison: Composing a Life (University of Illinois Press, 2006) – they detail, year-by-year, every moment in Harrison's life. It is, perhaps, a shade too exhaustive. At one moment, when Harrison has been invited to the 72-year-old Ives's house for lunch, I found myself disappointed not to learn what the two men and Ives's wife Harmony had eaten. Likewise, every little turn in Harrison's life starts to become endowed with a significance they can't all possibly bear. For all this, I did miss hearing more from Harrison's students – John Luther Adams, Barbara Benary, Peter Garland and others. What is the extent of his legacy as a teacher? What were his lessons like?

But it is a good story. Alves and Campbell tell it as a journey from darkness to light, a three-striped arc: from atonality to modality, from modern West to ancient East, and from mental breakdown to contentment. This is understandable, and it makes for a warm-hearted, page-turning read. That wealth of detail is accompanied by some wonderful images and stories – Cowell, Cage, Harrison and Thomson in Harrison's apartment playing a musical version of Exquisite Corpse; Harrison's first rehearsal of Ives's Third Symphony with the New York Little Symphony (faced with complaints that Ives's four-against-three polyrhythms were impossible to play, the rhythmically gifted Harrison countered, ‘Would you prefer that I conduct four in the right hand and three in the left, or vice versa?’ (p. 125)). Yet Harrison's life might also be read as a parable of the difference between excellence and true greatness. For all that he was embedded in the networks and friendships of twentieth-century American life, Harrison has not received – and may never receive – the same acclaim as his more obviously radical (and, it must be said, self-promoting) contemporaries. One of the book's most poignant moments comes in 1950:

Cage, Feldman and Wolff shot the breeze at Greenwich Village's Cedar Tavern with de Kooning, Kline, Pollock, Rothko and friends. Harrison, ‘still uncomfortable in social situations’, and drawn to studies of medieval modes and strict counterpoint that were far removed from the avant garde's radical spontaneity, ‘frequently cloistered himself in his messy apartment, meeting only occasionally with a few remaining friends – [Remy] Charlip, [Ben] Weber, Cowell – and his students’. Later, Alves and Campbell write, Harrison would bristle ‘at the success of Cage and other composers whose new aesthetic he could not bear’ (p. 294).

Harrison's story is also one of social awkwardness, outsidership, anger and frustration. It is strewn – and to his biographers’ credit they don't shy away from this – with damaged friendships, broken hearts and bad behaviour. As well as a tale of an American artist and the American arts, it is also one of sexuality, identity and difference in the twentieth century.

Too large to fit in my bag, I carried this book in my hands for several days while at the Huddersfield Contemporary Music Festival in November, plonking it on available surfaces and preparing my review in between concerts. Everyone who saw it was intrigued and they all had the same response, even those who had received their musical education in the United States: ‘Wow. There's a composer I know almost nothing about, but wish that I knew more of’. It is to be hoped that this generous, sympathetic and exquisitely researched book will answer that need, and give Harrison's music the profile that his life earned for it.