Conlon Nancarrow may be most famous for his player piano studies, all of which were performed at the Southbank Centre last weekend, but his instrumental music is worth a listen too. His Third String Quartet is perhaps his most important effort for 'actual' performers rather than machines, but on Sunday night the Arditti Quartet also made a decent case for the First Quartet. And they threw in a magnificent Ligeti performance for good measure as well.

Nancarrow had an obsession with canons and intricate tempo relations, and wrote player piano studies with parts in all manner of obscure ratios – there's one at (1/√π):√(2/3), for example. While there are certainly signs of more compositional restraint in his instrumental works, an aspect of this ludicrous precision is always present, even in the early String Quartet no. 1. A dense maze of harsh polyphony, this work was played impeccably by the Ardittis with some stunningly tight staccato playing and expertly-handled forays into harmonics. There are moments of beauty in the score, and moments of great harshness, but all were played with the same ease – and also with as much attention to detail as the score demands.

The String Quartet no. 3 is canonic, with parts written in different tempi at the ratio of 3:4:5:6 – so each player has similar material, but at drastically different speeds. It's not a work for those after easy listening, although – as with the First Quartet – there is a huge range of styles and sounds within the work. Perhaps inevitably, it was the passages in this piece which didn't sound like they were canonic which were the most enthralling; I was amazed at how such detailed and intricate textures as these could have been found through such technically rigorous writing. There are sections which sound like melody and accompaniment, and sections which sound like the instruments are engaged in dialogue – often, there is nothing to suggest that all four players are in fact playing the same line.

That a real sense of mutual engagement emerged from within this performance is a testament to the brilliant musicality of the Arditti Quartet – to interact with the other performers while at the same time having to ignore their tempi is no mean feat. This was a fascinating piece, played with baffling facility, and throughout I had that amazing sensation of 'I don't quite understand how this has happened', which underpins all the best 'difficult' music concerts.

Despite the complete virtuosity of this performance, though, Nancarrow was slightly upstaged this evening by a rendition of Ligeti's String Quartet no. 2 which fell between the two Nancarrow quartets. The work is stylistically diverse, and while it occasionally demonstrates a Nancarrow-esque interest in pattern and intricacy, there are other dimensions on offer as well. The first movement is a stunning study in texture, timbre and dynamics, while the third is mechanistic, with pizzicato rhythmic ticking and oddly impressionistic overtones. The Ardittis communicated this piece with an incredible intensity, relishing the frequent moments of harshness as much as the occasional bluesy harmonies; they are masters of contrast as well as precision, and this was a performance to remember.

An arrangement by Paul Usher of the Player Piano Study no. 33 was a fittingly difficult encore for the group. Given the complexity of the material, it shouldn't have been surprising to see group members conduct each other through sections of this piece, but after their earlier show, any signs of struggle came across as a little unusual. This piece was perhaps a touch more impressive than enjoyable, unlike the pianola studies themselves – which just goes to show the real skill which went in to Nancarrow's own quartet writing.

This was a great finale to the Southbank's Nancarrow celebration – even if Ligeti shone as brightly in it as the man himself. Live Nancarrow performances may be difficult to come by, but they're more than worth it when they happen.