A packed-out Royal Festival Hall saw the London Sinfonietta lead us through a programme of music by the grand old man of American minimalism, Steve Reich. Clapping Music started us off. It’s a piece underpinned by a simple musical mechanism – the play of a simple rhythmic pattern against itself – yet fiercely virtuosic and flamboyant in its execution. I don’t think I’ve seen a performance of Clapping Music that doesn’t begin with performers ostentatiously rolling up their sleeves; the piece has comic bathos – two performers occupying a grand stage doing nothing more (nor less) than clapping – as well as a barnstorming daring. It’s a high-wire act that requires fearsome concentration and is utterly thrilling to watch, not least because a single foot (hand?) wrong spells disaster. (You can even try your hands at performing it yourself by downloading the London Sinfonietta’s Clapping Music app. What could be more exciting for a couple this Valentine’s Day?)

Sinfonietta principal percussionist David Hockings was joined by his colleague Timothy Palmer in a bravura display. For a piece of such apparent simplicity there is an awful lot to think about: the kind of timbre the ideal clap should produce, and the dynamics and shaping of the rhythmic pattern. They summoned, with nerves of steel, the dynamic flamenco music that initially inspired Reich, who, as we learned in a video projection at the start, had tired of lugging round weighty percussion instruments on tour.

Runner for Large Ensemble (2016) received its first UK performance, cast in five movements and lasting a quarter of an hour. It is scored for a contingent of clarinets, flutes and oboes with pianos and various percussion, but gets its distinctive sound from a tenebrous core of violas, cellos and bass. What connects the movements is continuity of pace, but with each subsection playing with different note durations, creating that dilatory feel so characteristic of Reich’s music.

The darker hues enriching the piece, which places the ensemble’s violas at its centre, evokes the melancholic, restive counterpoint of Bach’s Brandenburg Concerto no. 6, with its similar tenor and alto core. This effect was heightened by the strings’ restrained deployment of vibrato. Reich’s melodic cells were florid and embroidered, underlined by piquant harmonies and woodwind bite evoking Stravinsky’s astringent neo-Baroque Dumbarton Oaks.

Reich’s programme note remarked that the piece’s rapid opening meant it had to pace itself to ensure the musicians made it through, and the middle movements were certainly less animated, even to the extent that the work’s initial stylishness lost its crispness; more of a jog than a gallop, at times. But the ending delivered: the rich middle-register textures gave way to harmonics in the strings and undulating upper winds and pianos, bathing the hall in cold and bright musical light, channelling the hovering textures of Sibelius’ orchestral works. Andrew Gourlay conducted with unpretentious precision, eschewing a baton clarifying Reich’s textures with vigour.

Music for 18 Musicians (1976) is such an established masterpiece that you can buy a T-shirt featuring a diagram of it. There is something extravagant and indulgent about performances of it, with the battery of mallet percussion and four pianos, whose background glow enfolds and enraptures. It’s a work whose musicality spins out of a tension between the capricious and the mechanical. Underlying pulses and patterns from pianos and percussion are set against clarinets, strings and female voices. The latter group play two ‘breaths’, repeating a group of notes or melodic shape for as long as is comfortable. The best performances of this work are intensely spatial and theatrical, with the swelling and shifting centres of textural and timbral gravity hovering visibly across the stage. It has moments of distinctive visual intensity: three players clustered in concentration around a marimba, and musicians bustling around Reich’s great palpitating machine, maintaining its strange mechanisms. My companion described it as “bureaucracy as choreography”, which I think captures the work’s blending of caprice and process. The movement was directed by experienced Reich vocalist Michaela Haslam, a quarter of Synergy Vocals.

The work’s supposed simplicity belies considerable musical challenges, not least of ensemble, where large tectonic shifts between sections are coordinated by ringing octaves in the metallophone, and modulations between the 11 chords through which each section must cycle ushered in by the bass clarinet of Timothy Lines. The group of clarinets, strings, and vocalists must judge perfectly shaped crescendos and diminuendos across their sustained interjections, and blending sonorities and registers without showing the seams. This execution requires not just technical control but imagination and texture; the London Sinfonietta were unerringly competent, with individual colours brightening and darkening smooth and sustained ensemble work. Synergy Vocals got a bit lost in the landscape, but were still creamy and suave. Nearly an hour passed in a blink, followed by a warm and deserved ovation.