It must be one of the loveliest things to do in the world: sit at a piano with a dear friend – one you’ve known for over 60 years – and play through a Schubert duet, a piece of music redolent with the warmth of shared intimacy. It felt for all the world like a fireside winter’s evening in a comfortable living room – the epitome of Gemütlichkeit – and as Martha Argerich and Daniel Barenboim progressed smoothly along Schubert’s Rondo in A, D951, you had to pinch yourself to remember that this was the Royal Albert Hall, with 5000 people watching and countless more listening on the radio. At a leisurely 12 minutes, it was a generous, broadcast-schedule-busting encore.

What surprised me even more was that in Argerich’s officially programmed piece, Liszt’s Piano Concerto no. 1 in E flat major, she achieved almost as much of a feeling of intimacy. This isn't a word you normally associate with a Liszt concerto, and I couldn’t help being struck by the polar opposition between Argerich and the last time I heard the same concerto at the Proms, by the ultimate showboater Lang Lang. Often, this felt like a chamber piece as she duetted with one or other of the instruments in the orchestra, meticulously achieving balance with each. Argerich’s has an unequalled ability to shape a phrase and control its timbre: a silvery cascade of notes would get just the faintest tinge of acceleration and deceleration to lend character, combined with a rise and fall of volume more controlled than a Kaufmann messa di voce. She would deliver pure reflective poetry, and then morph seamlessly into one of those Lisztian rolls of bass thunder, delivered with authority, without you being able to spot the join.

In the gamut of conducting styles from overall shaper to micro-manager, Barenboim is at the far end of the micro-manager side: beating strict time, exceptionally clear in his cues. It worked well in the Liszt: the West-Eastern Divan orchestra delivered a restrained performance with a lot of precision, a perfect foil for Argerich’s virtuosity.

The opening work, Jörg Widmann’s Con Brio, did not impress me. It seemed mainly an exercise in conjuring different sounds out of the orchestra, by whatever means – unvoiced breathing for the winds, wrong-end-of-stick rim shots for the timpani, and so on. It may interest the experts as an orchestral étude, but I got little from it.

No-one in the audience could have failed to appreciate the significance of the second half programme of a series of Wagner excerpts: here was an orchestra whose very existence is a statement of reconciliation between races, performing music by one of the most notorious racial supremacists, culminating in the overture to Hitler’s favourite opera Die Meistersinger von Nürnberg. It was a grand political statement, and every last audience member will have wanted the performances to be out of the top drawer. In the event, the performances were competent but, if measured against the best I’ve heard in an opera house, left plenty to be desired.

There were high points. The low woodwinds were superb throughout, especially in the opening overture to Tannhäuser, blending wonderfully with trombones and horns into a resonant soundscape. Cellos and basses provided a driving pulse. At no point could I fault Barenboim’s artistic choices as to tempi or how to conduct the music, but this isn’t an orchestra with the biggest sound: the full swell of the high register of the strings wasn’t achieved and occasional inaccuracies in timing took their toll.

The Götterdämmerung excerpts suffered from the relatively limited size of the orchestra. In any case, it’s not clear to me that even a perfect orchestra could have got the best out of this music when played as a “greatest hits” style of excerpts. In particular, Siegfried’s Funeral March is at its most magical because of the web of musical motifs and narrative that has preceded it: individually, it’s still a fine piece of music, but it’s so much more powerful in context, three hours into an opera where you have already nearly been drained emotionally.

But still, in spite of any cavils, seeing these musicians perform Wagner’s music with energy and commitment is a powerful emotional statement in itself. More generous encores, from Meistersinger and Lohengrin, left the audience thoroughly satisfied.