I judge a lot of music by asking: “Would I like to have written it?” And with my favorite Carter pieces, I certainly would. I love the Double Concerto for Harpsichord and Piano with Two Chamber Orchestras. There’s nothing like it in music: the concept, the way it makes time and rhythm move, the instrumentation – that bloody harpsichord! Whether it’s playable or not, I’m not sure, because it’s so difficult. Along with Pierre Boulez’s Le Marteau Sans Maître, the Double Concerto is one of the unique signposts of the 20th century.

For me, Carter is a symbol of what it means to be a committed artist. He made no compromises, no concessions to public taste. Although he took on the accoutrements of European new music and of serialism, his was a true American voice, much like that of his contemporaries John Cage and Morton Feldman. They were each uniquely American, rather like the abstract expressionist painters.

I last saw him at the Aldeburgh festival in 2009, when we both had new works being premiered. I remember we went to a restaurant with a lot of people, and everyone had to leave for a concert. He said, “Can’t we just stay here?” which I thought was rather sweet. I said I would stay with him, but then, like a couple of reluctant schoolboys, we had to go to this concert. Neither of us had a piece in it, and I’d gladly have sat with him. I’m sorry about that moment.