Pierre Boulez, born a century ago, was a giant in many fields: composer, conductor, impresario, polemicist, and innovator. But, as a lifetime of guerilla interviews attests, he was also one of music’s trenchant and caustic voices. Opera fans made him ‘want to vomit’; the best thing to do with the opera houses was to blow them up; the Mona Lisa should not simply be defaced but destroyed; Shostakovich was merely the ‘third pressing’ of Mahler, and so on. My favourite is about American minimalist composer John Adams, whose opera The Death of Klinghoffer Boulez set briskly aside as ‘bad film music’. ‘I cannot say I will spit on his music’, Boulez offered generously, ‘but I cannot say I admire it either.’ One is put in mind of a scene from Mad Men, where Don Draper is confronted by an embittered lackey: ‘I don’t think about you at all’, Draper says.

In his centenary year it’s nice to be reminded of what a strong flavour Boulez was, especially in a world, today, where musicians mostly give their interviews in soft-focus. Yet listening to his music at anniversary concerts over the last few months has reminded me that all this chest-beating is only one part of the story. There is explosive violence in his work, yes, reflecting an insurgent sensibility, but also an intense sensuality and mystery, both seductive and forbidding.

The title of a recent book by Caroline Potter, Organized Delirium (Boydell & Brewer) on his life and legacy, sums up Boulez’s steely focus and the fantastical atmosphere of his music. It could be a description of the contradictory states it demands from listeners: feline attentiveness, but also somnambulant immersion, allowing oneself to be carried along by its textural and harmonic rapids without attempting to grasp its unfathomable complexity – a dream whose latent content remains ungraspable.

The BBC dedicated a Total Immersion day to Boulez at London’s Barbican at the end of March, featuring chamber concerts, talks, a documentary screening, and an all-Boulez programme from the BBC Symphony Orchestra and Singers, conducted by Martyn Brabbins. Boulez made a huge impact during his time as Chief Conductor of the BBC Symphony, inducting its musicians into the ways of the avant-garde, making them fearsome advocates of new music. He was relentlessly demanding, thanks to a terrifyingly acute ear, which could pick out wobbly intonation even among the densest 20th-century scores.

All of their ingenuity and experience was required for ferociously difficult works such as Cummings ist der Dichter (1970), where a lack of subtitles or programme text made an already challenging work fall a little flat. So, too, was I left a bit flummoxed by two early electronic works that opened the programme – exemplary instances of Musique concrète well-matched to the Barbican’s hulking brutalism, but whose gurgles and crackles felt ultimately like museum pieces.

The afternoon saw pianist Tamara Stefanovich perform one of Boulez’s most challenging and confrontational pieces: the Second Piano Sonata (1947-48), which she recently recorded to acclaim; she stepped in for a student of the Guildhall School of Music and Drama who was indisposed, demonstrating nerves of steel.

The commonplace title of this early work is part of the iconoclasm. Boulez felt, as with all established forms, that it had exhausted itself, so like the shell of a house gutted by fire, could be pulled down beam-by-beam and built up again from scratch. We hear this violence, as well as an experimental quest for something new, across its 30-minute span. There are the vestiges of the old – a four-movement shape, with a slow second movement and scherzo-like third – but the musical development comes so fast and thick that it is hard for the ear to catch it, as Stefanovich’s arms flew up and down the keyboard.

It’s thrillingly and exhaustingly virtuosic, though a piece I still find unyielding. What surprises, as so often in Boulez, are the moments of sheer beauty that emerge unexpectedly. The finale, alternating percussive, angular music with more lyrical trains of thought, doesn’t end with a blaze of keyboard-thumping daring, but music of strange, meandering stillness, gently lilting, perfumed arabesques that float up to the gentlest high B-flat.

Stefanovich returned for the evening concert with Douze Notations, the piano miniatures Boulez composed in 1945 while a student. They were born of stringent creative limitations – a 12-note sequence (which can manifest as harmony or melody, reversed or inverted) for 12 bars of music, generating 12 pieces in turn. Their brevity allows one to appreciate Boulez’s gestural brilliance, and to hear with fresh ears simple musical intervals (a fifth, a seventh, a semitone). This organisation produces a play of rigour and caprice that recalls, of all things, Baroque music, with toccata-like passagework from the style brisé of brilliant French keyboardists such as Rameau or Couperin. (The first opera Boulez ever conducted, in 1964, was Rameau’s Hippolyte et Aricie, for which he expressed grudging admiration.)

The afternoon recital concluded with Dialogue de l’ombre double for clarinet and tape, in which Guildhall student Beñat Erro Díez shadow-boxed with a recorded musical doppelganger for 20 minutes. It was given the simplest theatrical treatment, plunging the soloist into darkness between his contributions. The clarinet, somehow the most shamanic of the woodwind family, is given to strange little flickers and curlicues, its melismatic figures suddenly flaring up and then dying out. Works of this kind for live instrument and magnetic tape were state-of-the-art in the 1960s and 1970s – see Stockhausen’s pioneering Gesang der Jünglinge or Reich’s ‘phase’ pieces for piano or violin. An unwavering belief in their necessity led Boulez to oversee the construction of IRCAM, his musical research centre beneath the Place Georges-Pompidou in Paris. Vast banks of computers were given over to the creation of works of strange, alien beauty.

But what Erro Díez revealed in his dazzling performance was not glimpses of the future but a distant past. Boulez grew up in Montbrison, near Lyon, a district of France home to many of the astonishing cave paintings that represent humanity’s first artistic gestures. The ritualistic character of the piece, with its echoes and chiaroscuro, suggests the flames flickering on the cave walls as some offering made or spirit invoked. Boulez may have made all sorts of claims about turning away from recent musical history, but the real roots of his art had never seemed more apparent.

It’s not so surprising to find something so atavistic in Boulez’s work. He toyed for a while, as a young man, with becoming an ethnomusicologist. French modernism had long drawn on music from Japan, Indonesia, and South Asia in various ways since Javanese gamelan came to the Paris Expositions Universelles in the late 19th century and inspired Debussy, with all sorts of Orientalist complexities entailed. Boulez followed suit. For a while he played the ondes Martenot – the electronic B-movie wobbler beloved of Olivier Messiaen – for a theatre company which then toured to South America in 1950s.

This trip found explicit expression in Pli selon pli, the remarkable settings of Mallarmé for soprano orchestra that capped off the Total Immersion day and stands, at over an hour, as Boulez’s magnum opus. Boulez was impressed in Peru by the music of Candomblé, the syncretic meeting of West African, Brazilian and Roman Catholic traditions, based mainly on percussion with a strong attraction to the sounds of harp and piccolo. Consequently, the piece features three and four of each.

Crafted in five parts and taking decades to write, Boulez sets three sonnets by Mallarmé as well as some scattered lines. It begins with a bang, and unfolds with a kind of violent sensuality. The movement at the centre of this vast structure – Improvisation II sur Mallarmé – a setting of ‘Une dentelle s’abolit’ (lace abolishes itself) – uses just ten instruments: vibraphone, celesta, harp, piano, tubular bells, and reams of untuned percussion, creating a strange, still twilight of dead sounds – the ‘creux néant musicien’ (hollow void musician) of the poem. There are moments of remarkable tone painting, as if from Ravel: a gently rolling cymbal, suggesting fog, in the first movement.

The final movement pulls the entire ensemble back into its inexorable momentum, an increasingly fraught and complex crescendo, lasting nearly half an hour. As the title ‘Tombeau’ suggests, it is headed towards only one thing. The piece concludes with an exceptional piece of orchestral drama – a gasped ‘Mort!’ from which funereal trombones surge forth, before the violent, dry snap of the piece’s beginning brings it to a sudden close. Such an arresting move is unsurprising given Boulez spent many of his formative years as a theatre musician; one remarkable story reports him and his ondes Martenot lowered from the ceiling of the Folies Bergère on glittering platform. What a pity he never did write that opera of En attendant Godot.

Anna Dennis, soprano soloist that evening, is in many respects the ideal performer of this music, and accomplished an heroic feat. She has a pure and imposingly hieratic sound, which imbued her presence with the otherworldly detachment of a mystic or medium, at home in this hallucinatory pattern of images. From this straight sound, her vibrato would warm and bloom to reveal a rich sensuality or violent delirium, tracing the fluctuating and unpredictable moods of Mallarmé’s poems with remarkable precision.

I was back at the Barbican, at the end of May, for a performance by Ensemble intercontemporain of Sur Incises for three harps, three pianos, and percussion. The Ensemble was founded by Boulez in 1976 and dedicated solely to the creation of new music; like the London Sinfonietta, founded before even them in 1968, they were (and remain) the sleek shock troops of experimental music.

‘Incises’ means ‘interpolations’ but also suggests a kind of cut or incision. Together these capture the essence of Boulez’s 38-minute piece, whose games of imitation require surgical precision: hardly a problem for Ensemble intercontemporain, as seasoned exponents of this music, and guided with effortless clarity by Nicolò Umberto Foron. The precision required is not dissimilar to watching an expert Formula One pit crew, who act separately but in rapid concert as the car comes racing into a stop.

The work is a study in different qualities of attack and decay. A harp is a string instrument, like a piano, which can be struck or plucked, though it is more brittle and transient; vibraphones and marimbas share their keyboard set-up, and are both similarly and differently hammered, producing in turn different kinds of resonances. On top of this there are the complex overtones produced by crotales and tubular bells, as well the duller attack of the steel drums. The audience must fine-tune their ears to hear rippling patterns of repetitions with acute differences, in music that is caught between frenetic activity and a kind of unearthly stasis. The final 90 seconds of the work is Boulez at his finest: pianos jangling and quivering in protest, before a miraculous unison chord featuring crotale, tubular bell, and glockenspiel, followed by a final low murmur.

Foron, a former assistant at Ensemble intercontemporain and now assistant conductor at the LSO, is only 27. The other performance of Sur Incises I saw recently was at the Royal Academy of Music, where students were guided through it by Susanna Mälkki. It was thought years ago that only a handful of professional musicians in the world would be able to play this music, let alone conservatoire students. A new generation of musicians is making Boulez their own; in time they will be the ones who decide whether he deserves future anniversary treatment. As I write, a supergroup of the sparkiest artists of their generation, assembled by mercurial guitarist Sean Shibe, are touring Boulez’s dizzying song cycle after René Char Le marteau sans maître to the Boulez Saal, Elbphilharmonie, Aldeburgh Festival, and BBC Proms. What they have to say about this music will tell us a lot about its next century.