As a non-composer, I always find it a little disconcerting when composers completely disagree with me about new music. And when I talk to two composers separately, and they offer matching opinions opposed to my own – as happened last night at the Wigmore Hall – I definitely end up feeling slightly wrong-footed. But on reflection, the experience has only served to remind me why I like new music in the first place: there’s no consensus about it; opinions are being forged now; we can all play a role in deciding what it means and how successful it is. How much more exciting than hearing music that everyone agrees is great.

This particular concert featured the Arditti Quartet, and was originally meant to include the JACK Quartet as well but Hurricane Sandy prevented them from reaching the country. While I had been looking forward to hearing the hotly-tipped JACKs, you can hardly complain about spending an evening in the company of the Arditti Quartet, who were on as spectacular form as ever. And the substitute programme they presented hardly felt thrown together, still containing two of the four originally-billed UK premières, from Hans Abrahamsen and Rebecca Saunders, and adding recent quartets by James Clarke and Wolfgang Rihm. All made for a compelling recital of highly personal – which is to say, subjective – new music.

The first two items made an intriguing pair: James Clarke has had some association with the British compositional movement called “New Complexity”, while Hans Abrahamsen has likewise been involved with “New Simplicity”. Stylistic differences were hence to be expected, although the most noticeable one was simply the two pieces’ loudness – Clarke’s was harsh and abrasive, full of abrupt shrieks, and Abrahamsen’s was a whisper throughout, which was frequently played in hushed harmonics.

I was impressed by the dynamic force of Clarke’s piece, whose sudden sharp crescendos and angry sonic blocks often fitted into a surprisingly easygoing waltz-time, but the more direct style of Abrahamsen’s quartet was also more affecting. Harmonically gentle throughout, the most memorable of the four movements were the first and third, where players added themselves one by one to a strange, ecstatic wandering around a modal scale. The first movement built up from first violin to cello, using extreme high pitches, and the third went the other way, from cello to first violin. Not, well, “complex”, but it won my attention, perhaps especially because of the Ardittis’ infinitely detailed performance.

Rebecca Saunders’ Fletch was something of a return to the soundworld of Clarke’s quartet, but a little more exploratory in nature. It investigated a field of musical ideas around one initial element – in the composer’s words, “an up-bow sul pont double-harmonic trill, often with a fast glissando, crescendo-ing rapidly out of nothing to fortissimo”. I don’t find such descriptions very appetizing, and the piece, energetic though it was, played out in similarly rather technical terms, a step beyond what I could hear. Even though – like the Clarke piece – there was a real visceral thrill to it, it felt a little like a party I wasn’t invited to, despite its completely exemplary performance from the players.

The whole of the second half was devoted to Wolfgang Rihm’s String Quartet no. 13 (2011), and it was a piece which merited this close attention. Very fast almost throughout, it’s a busy, angular composition, expressionistic in quite a mainstream Germanic sort of way. For brief moments, it sounded a little like it was from 1920s Vienna (the programme notes’ mention of Alban Berg was spot on), but it flitted about stylistically more than this suggests. Individual musical details – a harsh repeated pizzicato note on cello, for instance – were occasionally repeated obsessively, and a quizzical, self-questioning air hung over it all. In terms of its shape and structure, I am none the wiser after a single hearing, and I suspect this was the most personal work on this intensely personal programme. Rihm ends the quartet with a series of panicked and violent shrieks of chords punctuating silence, and I remembered for the first time that evening that it was Halloween. The piece is a creation of brilliance, but again, I found it difficult to sympathise with.

This all sounds a bit mixed, but it was a thrilling experience all the same. The Arditti Quartet are particularly adept at communicating difficult music clearly, and here they told four stories to us in the most brilliant way possible. Whatever I thought of the stories, hearing them like this was a treat – albeit a tricky one at times.