Daniel Barenboim was onto something earlier this Proms season when he spoke of the “communion” between the Royal Albert Hall audience and the performers: there is a sense of deep, serious, joyous concentration at the Proms that more than compensates for the disappointing acoustic. I think it may have something to do with the hall’s structure: whether you’re promming in the Arena and jostling for position, or seated somewhere around the huge, sweeping circle that surrounds it, you will be completely and utterly aware of your fellow audience members at all times – probably facing them directly, in fact. And somehow, this awareness focuses the collective concentration tightly onto the music. It’s a reminder, which only comes once a year but thankfully lasts all summer, that the real test of live music isn’t how good it sounds – it’s how well it’s listened to. At a late-night Prom like this one, with just two pianos, two pianists and some Schubert in front of an audience of thousands, the listening is almost impossibly intense.

So is the piano music of Schubert, with its twists, turns, surprises, mood swings. But that's not the side of him that Imogen Cooper, rightly considered a leading Schubert interpreter, brings out most of all: Schubert was also a Classical composer, and there is a subtle thread of orderly, maybe even Mozartian logic that runs through even his most capricious changes of mood or texture or key. Cooper’s Schubert flows; it travels somewhere. Even in a movement as changeable as the finale of the C minor Piano Sonata, D.958, Cooper makes it sound easy, natural, despite the persistently shocking switches of tonality it contains. Do we lose a little of Schubert’s wackiness in this refined approach? Perhaps we do, but it’s worth it for the sheer beauty of what results.

Surprisingly, this sonata – like the Grand Duo, D.812, which followed it – had never previously been heard at the Proms. Like the other two piano sonatas dating from 1828, Schubert’s final year, it’s a substantial piece, although it seems to grow in stature over its 30-odd-minute spell, as it drifts further away from the overbearing influence of Beethoven which haunts the stern, C minor opening. Though Cooper plays with brilliance in sections such as this, it’s the gentler moments which stick in the memory: her serene, melodic slow movement; her deft placement of that otherworldly D flat major chord after the first movement has moved to E flat major. Darker parts are dealt with honestly, never shied away from – but the overall impression is one of grace.

For the Grand Duo, Cooper was joined by another prominent Schubertian, Paul Lewis, seated unusually at a different piano altogether to play the lower part in this four-hands composition. Despite the performers’ physical distance from each other, there was no lack of intimacy, with their every move communicated effectively through both eye contact and their obvious shared vision for how the piece should be played. Their respective registers (Cooper high, Lewis low) may have subtly emphasised the slight differences between these two pianists’ playing styles – Cooper’s approach is a little cleaner, more sparkling; Lewis’ has a fuzzier, softer edge – but there was no doubting their unity of interpretation. Co-ordination was immaculate throughout; civilized, egalitarian: again, the lighter side of Schubert seemed triumphant here. C major was a key in which Schubert loved to be daring, and though the Grand Duo is on the whole more epic than experimental, there is room within it to find a little more edge than Cooper and Lewis did here.

But this Classical, refined Schubert was no disappointment: what a beautiful celebration of this eternally fascinating composer – and indeed of the Royal Albert Hall, a place in which an almost ridiculous number of people can come together to witness the most private of musical acts. Wigmore Hall may have the better acoustic, but this is the better venue. Roll on the Proms 2014.