Arnold Schoenberg (1874-1951) is often portrayed as a composer who began as a heart-on-sleeve late Romantic only to evolve during the First World War into an austere, mathematically-obsessed deviser of musical puzzles. Yet to claim that in his music he replaced tonality with its absolute opposite, atonality, as the twelve-tone method swept away all trace of traditional harmonic and thematic processes, is as misleading as to argue that romantic warmth...