Clara, as so often in Schumann’s works, is palpably referenced in a musical cipher: ‘The oboe theme in the first movement with the notes C-H-A-A is clearly one of Schumann’s Clara motifs.’ Some of the concerto’s performing traditions, too, probably go back to Clara herself; nevertheless, Schiff questions some recurring tropes in its interpretations. ‘I cannot understand why, after the opening cascade, often the woodwind suddenly play at around half tempo. There is absolutely no indication of that in Schumann’s score. I do insist, whatever the opening tempo is in bar one, that it doesn’t change in bar four.

‘There are numerous tempo changes in the concerto, with many transitions and the improvisatory character that is omnipresent in Schumann’s music. He gives metronome markings to all the movements, and these are sometimes quite surprising. The first movement is minim=84: I think it’s incredibly fast. The second movement, which people call a slow movement, is not at all a slow movement.’ Headed ‘Intermezzo’, it goes ‘at a moderate pace’.

Yet even the composer sometimes needs questioning. ‘Strangely, in the middle of the first movement, for the A flat major episode, Schumann gives the metronome mark “dotted minim=72” – which is absolutely identical with the metronome mark of the last movement. But just try to play these two sections in the same time! It feels very strange indeed. There are plenty of examples in Schumann when I don’t think he could have meant something literally.’

As for the finale, catching the right atmosphere and rhythmic sense is just the first of its many challenges. ‘It starts triumphantly, but then you realise that this is a waltz. It has to dance. And it contains an infamous passage where there is a ‘hemiola’ – a constant, three-against-two pattern. Here, if a conductor tries to beat time, then you are in trouble – but not if you are just making music and listening to each other.

‘When we work on this passage, I say to orchestral musicians or students that we should try to ignore the bar lines, because the bar lines are the trouble! A bar line is not music. Bar lines are like walls of prison cells, and we must liberate ourselves from those walls. They are a necessity for notating music, but that is their only function. In this passage one must not indicate the downbeats, but rather conceal them.’

How does all this work without a conductor? ‘Well,’ Schiff says, with a smile, ‘you need a perfect orchestra. By which I mean an orchestra which is not really an orchestra – like my Cappella Andrea Barca, the Chamber Orchestra of Europe, or the OAE. They make music with a chamber music attitude, with give and take, listening to each other.’

The OAE’s 19^th-century instruments, he says, create crucial transparency in the orchestral textures: ‘There is a certain lightness; this is not a heavyweight concerto.’ He is playing a Blüthner piano from the 1850s, ‘slightly later than the concerto, but not dramatically so. It comes from southern Germany, near Freiburg. It’s a lovely piano and I think it’s very good for these pieces.

‘Early pianos are never bass-heavy because of their parallel-strung strings, and the bass strings are much thinner than on a modern concert grand. Each register of the keyboard is different: not evenly spread, but with distinct sonic character and a beautiful cantabile tone. Obviously it doesn’t have the volume of today’s concert grands, but some years ago I played the Schumann Concerto on a Streicher piano from a Dutch collection in the Royal Festival Hall, where sometimes one can have difficulties projecting across an orchestra even with a very powerful modern piano. But on this period instrument, it was no problem whatsoever.’

Schiff and the OAE have programmed the concerto with works that complement it, the first being the Konzertstück for Piano and Orchestra, Op. 92 – enjoying a much-deserved moment in the sun. ‘It is a very poetic piece with fantastic writing, especially for the winds and the prominent solo horn,’ Schiff says. ‘Horn players love it!’ Why is this rare gem so neglected? ‘In a usual concert format, a piece about a quarter of an hour long can be awkward to programme. Usually you don’t just play a 15-minute piece; you have to play another one or two. Still, that shouldn’t be an obstacle…’

The concerto’s first movement, he points out, originally stood alone and could have been similar. ‘It’s a perfect movement. Then he added the other two – and the way he goes from the Intermezzo into the finale with that transitional passage, the model may have been the Mendelssohn Violin Concerto, which is also beautifully through-composed.’

And Mendelssohn completes the programme: extracts from his incidental music to A Midsummer Night’s Dream form an encore of sorts to the unforgettable series of Mendelssohn concertos and symphonies that Schiff and the OAE performed a year ago.

‘I wanted to revisit Mendelssohn and there is nothing I love from him more than this music,’ Schiff says. ‘It is really out of this world. Some people have maintained that Mendelssohn is a wonderful composer, but didn’t bring anything new into music. I think this is a false accusation. Think of this feather-light Scherzo; and think of his understanding of Shakespeare at such a young age. The Overture is a composition of someone scarcely more than a child, but when you hear those opening four chords, it’s just magical. Something special happens to the listener.’

Mendelssohn and Schumann seem a perfect pairing. You could almost imagine that tonight the Davidsbündler are returning to relish another performance, side by side in harmony.