Whose music does Conway claim to play on the piano? What does his answer baffle those around him? (prologue)

From the text:

He played well, of course, some Brahms and Scarlatti, and a lot of Chopin. Once or twice I glanced at Conway and judged that he was enjoying it all, which appeared very natural, in view of his own musical past....In the meantime a rather odd thing was beginning to happen. Conway had sat down at the keyboard and was playing some rapid, lively piece that I didn't recognize, but which drew Sieveking back in great excitement to ask what it was. Conway, after a long and rather strange silence, could only reply that he didn't know.