To precisely map out the influence of Steve Reich’s work, both in America and the rest of the world across the last half-century or so, would be a near-impossible task. And it’s certainly not for lack of case material – from ambient to math-rock to techno and many places in between, the genres and artists whose creative output has been shaped, either knowingly or unknowingly, by Reich are innumerable.

In fact, to call it merely influence would be to undersell his impact. It’s not hyperbole to say his compositions changed music in the latter half of the 20th century. Early tape loops like “It’s Gonna Rain” (1965) and “Come Out” (1966), in which Reich cut up and relentlessly replayed snippets of speech, increasingly out of phase with one another until you begin to hear sounds that aren’t there, were captivatingly neurotic and hallucinatory – and formed the basis of what we now know as minimalism, a hugely important force in popular American culture.

Tonight at the Barbican for a celebration of Reich's 80th birthday, we're joined by dazzling array of musicians who, with the man himself watching on, take us through some of the most experimental, successful and revolutionary pieces in the Reich oeuvre.

We begin with the most simply conceptual piece of the night, “Pendulum Music”, first conceived in essay form in the late Sixties and revised into the early Seventies. Seventeen microphones (it’s usually fewer – Reich commented in a post-concert Q&A that he’d never seen it performed with so many before) hang upside down, like sleeping bats, each above a speaker and accompanied by a person. They are then held up at a 45 degree angle, and simultaneously allowed to swing freely. As each microphone passes the monitor, a humming feedback is created, first only for a moment and then, as the arc and speed of the microphones’ swing ebbs away, the hums broaden and stretch out. The different frequencies coalesce, creating an obscure pattern of sound. As the performers sit cross-legged and the stage lights dim, the whole thing feels sombrely cultish.

Next is “Nagoya Guitars” (1996), a nimble interplay between two guitarists chasing each other’s melodies, with each melody chasing its own tail, before rapidly changing direction. It’s a pleasantly assured peformance, and cleanses the palette before the feast that is “Electric Counterpoint” (1987). One of Reich’s best-known compositions, it was written to be performed by a single guitarist accompanied by tape of the other parts. But to see it performed as it is tonight, fully realised with a rare ensemble of 11 guitars and two basses, feels like a privilege. It is deeply affecting, as it gracefully floats and swells. Fidgety, interlocking guitar melodies give way to chordal echoes and a feeling of fledgling euphoria. It is 15 minutes of bliss.

Bliss, which is succeeded by terror in the Grammy award-winning “Different Trains” (1988). Through personal recollection and audio recordings of others, Reich draws parallels between his train journeys as a child across America during the Second World War, and those bound for Nazi concentration camps in Europe at the same time. Trains are integral to the piece, both melodically and rhythmically. When recalling Reich’s own journeys, the sound of train whistles, mimicked by the masterful quartet of Britten Sinfonia musicians on stage, is exploratory and hopeful. In the second movement, the whistles are nightmarish, piercing through the other instrumentation. The fingerprints of “It’s Gonna Rain” and “Come Out” are to be found here, too, with the voices – of Reich’s old governess, a train porter, and Holocaust survivors – used as a melodic source, but also as a haunting account of the unearthly terror suffered. Fear, reverence, mourning, reflection – it’s all captured in “Different Trains”.

After a European premier of a new composition, “Pulses”, a lush ensemble piece, the night closes on the elaborately ambitious audio-visual piece “Three Tales” (2002), a collaboration between Reich and his wife, video artist Beryl Korot. Split into three parts, it ruminates on landmarks in technological progression, and the perils that accompany them: the Hindenburg disaster, nuclear testing and the cloning of Dolly the sheep. There’s certainly a lot going on – it’s the kind of piece that takes multiple viewings to fully absorb – but that’s not to say there isn’t a striking immediacy to it. During the nuclear section, numbers sinisterly count down on the screen behind the stage, operatically copied by a choir; during the Dolly movement, scientists’ forewarnings are chopped up and looped almost maniacally; and on the Hindenburg movement, a stuttering, unravelling drumbeat accompanies slow motion footage of the fiery disaster. It all’s very disquieting and thought-provoking.