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The occasion for this article is the recent appearance of revised editions of two important works on serialism—Josef Rufer's Composition with Twelve Tones, first published in English in 1954 (now Composition with Twelve Notes, Barrie and Rockliff, 35/–), and George Perle's Serial Composition and Atonality (subtitled ‘An Introduction to the Music of Schoenberg, Berg and Webern'), which originally appeared in 1962 (Faber, 55/–). In addition I shall be referring to two recent events in London which proved to be stimulating contributions to the discussion of serialism: the seminars given by Milton Babbitt during the third SPNM Composers' Weekend, and a talk entitled ‘Schoenberg and the future’ given by Pierre Boulez as part of the South Bank Summer Music festival.
page 4 note 1 These and other important properties of the twelve-tone system are discussed by Milton Babbitt in his article ‘Twelve-Tone Invariants as Compositional Determinants’ ( Problems of Modern Music, ed. ling, Paul Henry, New York 1960, p. 108)Google Scholar.
page 5 note 1 Hindemith, Paul, Craft of Musical Composition, Bk.I., translated by Mendel, Arthur (revised edition, London 1945) pp. 217–219 Google Scholar.
page 5 note 2 See especially Lewin, David, ‘ Moses and Aaron—Some General Remarks, and Analytic Notes for Act 1, Scene 1’ (Perspectives of New Music, Vol.6 No. 1, p. 1)Google Scholar.
page 5 note 3 A revised and corrected edition of Structural Functions of Harmony has just been published by Ernest Benn' price 50/–(Ed.)
page 6 note 1 e.g. the analysis of Op. 19 No. 2 by Travis, Roy, ‘Directed Motion in Schoenberg and Webern’ (Perspectives of New Music, Vol. 4 No. 1, p. 75)Google Scholar, and the analysis of Op.16 No.1 by Payne, Anthony in Schoenberg (Oxford Studies of Composers No. 5), London 1967, pp. 21–26 Google Scholar.
page 6 note 2 e.g. Forte, Allen, ‘Context and Continuity in an Atonal Work, A Set-Theoretic Approach” (Perspectives of New Music, Vol. 1 No.2, p. 72)CrossRefGoogle Scholar.
page 7 note 1 See for example Kassler, Michael, ‘Toward a Theory that is the Twelve-Note-Class System’ (Perspectives of New Music, Vol.5 No.2, p.1)CrossRefGoogle Scholar, and O'Connell, Walter, ‘Tone Spaces’ (Die Reihe, English edition, Vol.8, p.34)Google Scholar.
page 7 note 2 See for example Wood's, Hugh review in the Musical Times, 09 1968 Google Scholar, and my reply to it in the Musical Times, November 1968; also Walker's, Alan two articles entitled ‘Words and Music’ in Composer, Nos. 13 and 14Google Scholar (both about Perspectives of New Music, much of which is written using the same terminology as Perle's book), and the subsequent discussion in Composer, No.15.