1 The 12-note sketches are contained in six sketchbooks The first was purchased by the Pierpont Morgan Library, New York, in 1976, the remaining five by Paul Sacher in 1984 for the Paul Sacher Stiftung in Basle These five books, which are the second to sixth of Webern's sketchbooks, have been given the numbers I-V by the Sacher Stiftung and are referred to by these numbers belowGoogle Scholar

2 Boulez, Pierre, ‘Propositions’, Polyphonie, 2 (1948), 64–72 (p. 67); trans, as ‘Proposals’, Stocktakings from an Apprenticeship, trans Stephen Walsh (Oxford, 1991), 47–54 (p. 49)Google Scholar

3 Carl Dahinaus, trans Derrick Puffett and Alfred Clayton, ‘Problems of Rhythm in the New Music’, Schoenberg and the New Music (Cambridge, 1987), 45–61 (p 54) The difference between the two views expressed here is interesting as both were written from the Darmstadt perspectiveGoogle Scholar

4 Boulez's statement has been understood by Edward T Cone as an argument for considering Webern's metres as purely conventional and disregarding them in performance (see Cone, ‘Beyond Analysis’, Perspectives of New Music, 6 (1967–8), 33–51, repr in Perspectives on Contemporary Music Theory, ed. Benjamin Boretz and Cone (New York, 1972), 72–90, and more recently in Music A View from Delft, ed Robert P Morgan (Chicago, 1989), 55–75 (p. 64) But Boulez's insistence on relating all of Webem's ametrical techniques to the metre in which they are notated – as ‘cross rhythm, syncopation, accents on weak beats, counter-accents on strong beats’ and so on – seems to me to emphasize the fact that while these techniques are working against convention, they are doing it from within, and that their effects are thus to a degree dependent on the expectations associated with the convention (as opposed to the music of someone like, say, Messiaen, whose rhythms do truly avoid a regular metrical organization)Google Scholar

5 Musical Form and Musical Performance (New York, 1968), 82Google Scholar

6 Concerning the second movement of op 27 see Cone. ‘Beyond Analysis’, David Lewin. ‘A Metrical Problem in Webern's Op 27’, Journal of Music Theory, 6 (1962), 124–32, and again (but taking a different view). ‘A Metrical Problem in Webern's Op. 27’, Music Analysis, 12 (1993), 343–54, Peter Westergaard, ‘Webern and “Total Organization”. An Analysis of the Second Movement of the Piano Variations, Op 27’, Perspectives of New Music, 1 (1962–3), 107–20 Concerning the third movement, see Cone, ‘Analysis Today’, Musical Quarterly, 46(1960), 172–88, repr in Problems of Modern Music, ed Paul Henry Lang (New York, 1960), 34–50, and more recently in Music A View from Delft, 39–54, Westergaard, ‘Some Problems in Rhythmic Theory and Analysis’, Perspectives of New Music, 1 (1962–3), 180–91, James Rives Jones, ‘Some Aspects of Rhythm and Meter in Webern's Opus 27’, ibid., 7 (1968–9), 103–9Google Scholar

7 There are no extant sketches for the first song of op 17. and either the same is true of sketches for the String Trio, op 20, or these sketches are privately owned and inaccessibleGoogle Scholar

8 All the examples in this paper are my transcriptions of sketches contained in the sketchbooks owned by the Sacher Stiftung. I have omitted only Webern's row numbers, as they are not germane to this discussionGoogle Scholar

9 The pages of the sketchbooks are numbered consecutively, beginning with the first left-hand page, and it was Webern's habit to sketch on a right-hand page First and to move on to the facing left-hand page after. Thus the sketches on p 41, a left-hand page, directly proceed to those on p 44, the nght-hand page of the next openingGoogle Scholar

10 Note that the rhythm of the second sketch in 3/4 is the same as that later used to open the first movementGoogle Scholar

11 This movement was composed over a period of three and a half years during which the songs of opp 23 and 25 were also written The sketches for the first movement of op 24, which cover 29 sketchbook pages, are discussed at some length in my forthcoming article, ‘Webern's Nemesis Symmetrical Construction and the First Movement of the Concerto. Op 24‘Google Scholar

12 In reviewing Kathryn Bailey, The Twelve-Note Music of Anton Webern (Cambridge, 1991), in Music Analysis, 13 (1994), 300–5Google Scholar

13 Boynton, Neil, ‘The Combination of Variations and Adagio-Form in the Late Instrumental Works of Anton Webern’ (Ph D dissertation, University of Cambridge, 1993), 84–105, esp. pp 94–6Google Scholar

14 This is the case in theory, at least In fact there are more rests than this in the second violin and cello parts as a result of Ausfälle The rests in the second violin part articulate its line into the series [3–2]-[2–3]-[4]-[2–5]-[4], the cello's series is [3–2]-[2–3]-[4]-[4–3]-[4]Google Scholar

15 The second violin's A in the third bar (this note is played by the cello at the same time, though the cello note is not marked) and the two Ds that occur simultaneously in violin 2 and viola in the ninth bar have been marked, the two second violin notes have been removed in the following sketch (The round brackets enclosing the dyad G-A♭ in violin 1 in the eighth bar of Example 8 indicate that these notes are to be superseded by those written on the stave above.)Google Scholar

16 Thus the final sketches of the three sections are in 5/8, 3/4 and 2/4, compared with 2/4, 3/8 and 2/4 in the published scoreGoogle Scholar

17 Westergaard (‘Webern and “Total Organization”’, 113) wrote of this movement ‘The frequency (almost three quarters of the time) with which consecutive figures begin a dotted quarter apart constantly tempts the listener to hear the movement in terms of a 3/8 meter ’ Lewin wrote in 1962 (‘A Metrical Problem in Webern's Op 27’, Journal of Music Theory, 127) ‘while no musician I know who is familiar with the piece has any difficulty in hearing it in 2/4, I have observed that none (including trained musicians and students) who hears the piece performed before having seen the score hears it in 2/4, rather, it is universally heard in 3/8 (with a vague uneasiness) ’ And in 1993 (‘A Metrica] Problem in Webern's Op. 27’, Music Analysis, 343) he asked ‘Since one hears such a strong rhythmic pattern in groups of three quavers at the beginning of the movement, and since no other regular small groupings of quavers are anywhere nearly as audible, what is the sense of the written 2/4 time signature?’ On both occasions he rationalizes the written metre in a number of ways But one is tempted to ask whether the choice of metre was not made simply in order that each section – each of the ‘variations’ – would be 11 bars longGoogle Scholar

18 Musicology (London, 1985), 139Google Scholar

19 New York, 1961Google Scholar

20 Musicology, 139Google Scholar

21 In fact one of the first things one realizes when studying the Webern sketchbooks is that all the works composed there must have been written out at least once more before the fair copy To my knowledge, however, these manuscripts are not extantGoogle Scholar

22 Although both Schoenberg and Berg were heavily influenced by numerology and a few of Berg's metres at least were probably determined by numbers with extramusical associations there is no evidence of this sort of preoccupation on the part of Webern, whose undisputed fascination with numbers was of another sort altogether, and manifested itself in charts and calculations directly related to his musicGoogle Scholar

23 ‘Beyond Analysis‘Google Scholar

24 ‘Composition with Twelve Tones’, Style and Idea, ed. Leonard Stein, trans Leo Black (London, 1975), 225 For more on this, see Regina Busch's three-part article ‘On the Horizontal and Vertical Presentation of Musical Ideas And on Musical Space’, trans Michael Graubart, Tempo, 154 (1985), 2–10, 156 (1986), 7–15, and 157 (1986), 21–6Google Scholar