Later he studied musicology and philosophy with Johannes Wolf and Friedrich Blumein at the University of Berlin (1929–31), as well as taking composition lessons (1927–32) with John Ireland.
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Among Schnabel's many piano pupils were Gavin Williamson, Victor Babin, Clifford Curzon, Rudolf Firkušný, Adrian Aeschbacher, Lili Kraus, Leon Fleisher, Stefan Bardas, Carlo Zecchi, Claude Frank, Leonard Shure, Alan Bush, Vitya Vronsky, Nancy Weir, Konrad Wolff, Jascha Spivakovsky, Eunice Norton, Henry Jolles, Maria Curcio, Noel Mewton-Wood and radio personality Karl Haas.
She also championed works by Ernest Bloch, Alan Bush, and Malcolm Arnold, and won praise from leading composers for the technical refinement and structural integrity of her interpretations.