Schonberg, Harold C., The Great Pianists (New York: Simon & Schuster, 1987, 1963).
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She says she was told by Roch Serra (who was told by the Liszt scholar Professor Milstein, who was told by Vera Timanova, who was told by Sophie Menter herself), that Liszt was indeed the composer of the piece, but he did not want Tchaikovsky to be aware of this.