London, along with a large portion of the world, spent most of summer 2012 in awe of an elite group of athletes, cheering on their every move as they undertook a series of arcane but technically demanding tasks in public. Watching someone throw a big pointy stick or run a long way may not be activities that many people enjoy on a day-to-day basis, but that’s irrelevant: if the tasks are performed with enough virtuosity, as they were by last year’s Olympians, then they are compelling to watch on their own terms; the event becomes in part a celebration of these brilliant professionals’ skill.

Experiencing the almost impossibly difficult music of Pierre Boulez live is in many ways a similar experience: it is thrilling to watch a performer tested to the very limit of their ability. But here, music has an added bonus over sport: the sounds produced during this virtuosic display are beautiful too. And Tamara Stefanovich did a spellbinding job of Boulez’s infamously tough Second Piano Sonata on Sunday afternoon at Southbank Centre, starting it almost before she was fully seated at the piano, dispatching every technical impossibility with breezy calm, turning the pages of that behemoth of a score with a nonchalant flick. It would have been excellent entertainment even if the sounds produced didn’t have that incredible lucidity and elegance that Boulez grants them.

That’s not to downplay the piece’s violence: it was meant as a kind of death-blow to the traditional sonata, which adopted its outlines (four movements including a slow one and a scherzo) only to destroy them through brute force. But it proceeds with such incredible confidence that there’s also a logic to the whole thing, and despite its bucketfuls of notes, the score is rarely dense. Stefanovich found its voice with apparent ease. Boulez once told her, she related to Tom Service in an interview, that playing the fourth movement was like putting one’s hand in a beehive. She emerged unstung.

The Boulez Second Sonata was the second half of a well programmed recital which had begun with piano pieces by Ligeti, Stockhausen and Messiaen, forming the second of three concerts in The Rest is Noise’s “Post-War World” weekend. The weekend examined classical music in the aftermath of the Second World War, though in fact the concerts took a slightly narrower focus than that, spotlighting Karlheinz Stockhausen most of all (his music featured in all three) and essentially zeroing in on the so-called “Darmstadt School”, named for the summer school which was then the focus of various important strides in composition, mainly concerning serialism. This is precisely the repertory which seems to remain at the heart of contemporary classical music’s image problem, and so while it was good that The Rest is Noise covered it at all, it would have been even better if it had received more than three concerts.

But the first half of Stefanovich’s recital amply proved the capacity of this music to defy our expectations: Stockhausen’s Klavierstück IX, after all, ends with a birdsong-like passage which made me wonder whether Stefanovich had artfully moved straight into the Messiaen which followed (Le courlis cendré, from the Catalogue d’oiseaux, a huge book of piano pieces incorporating transcriptions of real birdsong). Stefanovich played both these pieces with a deft touch, but it was the opening number – Ligeti’s Musica ricercata – which was most memorably performed. This charming composition has eleven movements, the first of which contains just two different notes. Ligeti increases the number of notes used in each movement, culminating in a marvellously intense final fugue which involves a complete descending chromatic scale. Along the way, we hear everything from waltzes to gentle folk melodies. It’s a piece of grace and wit, and Stefanovich was its equal: her take was soft and melodic, rather than neo-modernistic, as demanded by most of the music to come.

The reception with which she was greeted after the Boulez proved just how exciting it is to watch music like this brought to life. But sadly, Stefanovich’s performance was witnessed by rather fewer people than last summer’s Olympics: empty seats have been hard to come by so far at The Rest is Noise, but this Queen Elizabeth Hall turnout was a disappointing response to some of the most taxing music programmed so far. Still, those of us who were there had much to cheer about.