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Published online by Cambridge University Press: 15 December 2021
Hans Abrahamsen has reused the same rhythm across four pieces spanning 33 years: in his Ten Studies, for solo piano, and Six Pieces, for horn trio (both from 1984), in Schnee (2008) and in Three Pieces for Orchestra (2017). Because self-borrowing is crucial to Abrahamsen's compositional practice, this rhythm provides a case study in his compositional priorities, particularly in the role canonic techniques play in his music. Although the rhythm's formal properties lend it a marked asymmetry at the foreground, it is presented in Schnee as part of a canon with highly symmetric pitch materials. But despite this apparent conflict between symmetries and asymmetries, Abrahamsen's music freely combines different approaches to the rhythm, as long as it is linked to a high-register shimmer, suggesting that Abrahamsen's noted uses of canons are largely for textural ends.
An updated version of this article was published in January 2022, all of the corrections were minor typographical changes.
1 William Robin, ‘Hans Abrahamsen: Fame and Snow Falling on a Composer’, The New York Times, 21 December 2017, sec. Arts, www.nytimes.com/2016/03/13/arts/music/hans-abrahamsen-fame-and-snow-falling-on-a-composer.html (accessed 30 September 2018). Further ruminations on this quotation can be found in Howell, Tim and Powell, Richard, ‘Telling the Time: Communication and Temporality in Nordic New Music’, in The Nature of Nordic Music, ed. Howell, Tim (Abingdon and New York: Routledge, 2020), pp. 209 and 217Google Scholar, and in March, Daniel, ‘Processes, Paradoxes and Illusions: Compositional Strategies in the Music of Hans Abrahamsen’, Journal of the Royal Musical Association, 146, no. 1 (2021), pp. 51–56CrossRefGoogle Scholar.
2 Strictly speaking, the Ten Studies were completed in 1998, but the first seven movements – including the one featuring this rhythm – were composed in 1983–84.
3 Kramer, Jonathan D., The Time of Music: New Meanings, New Temporalities, New Listening Strategies (New York: Schirmer Books, 1988), pp. 55–57Google Scholar.
4 Strictly speaking, in 1984 there were only seven studies; the last three were written in 1998. However, ‘For the Children’ is one of the original seven.
5 There is a small but significant difference at the very end of the movement: the last note of Figure 1 is omitted so that the piece can end on a dyad, and that dyad is preceded by a brief caesura to enhance its finality.
6 The notation of this figure is identical to that of Figure 1, albeit without arrows; note that the movement is re-barred, and that some notes in the first half are played by a different hand. There are several alterations in rhythm in beyond omissions in the first half: a few notes are still missing in the first bar after the midpoint, and as in Ten Studies the last note is gone, with the preceding dyad delayed by a (now written-out) caesura.
7 Bálint András Varga, The Courage of Composers and the Tyranny of Taste: Reflections on New Music (Woodbridge: Boydell & Brewer, 2017), p. 15.
8 www.wisemusicclassical.com/catalogue/works/?composer=%22Hans+Abrahamsen%22&yearComposed=%5B1988%2C1998%5D (accessed 22 January 2021).
9 At least according to Abrahamsen's own telling in the liner notes to Hans Abrahamsen and Ensemble Recherche, Schnee. 2009, Winter & Winter, 910 159–2.
10 Much of this article's analysis of these canons is adapted from my own MA thesis: Noah Kahrs, ‘Process versus Projection in Abrahamsen's Schnee’ (MA thesis, Eastman School of Music, 2019), pp. 12–22, http://hdl.handle.net/1802/34938 (accessed 8 August 2021).
11 The inversions take place in diatonic (white-note) pitch space, with notated D4 and A5 as fixed pitches. The left hand of Piano 1 in Canon 5a contains what I believe is a typo; my figure shows the seventh note as a C for conformity with the process, with the actual notated B in parentheses.
12 Richard Powell and Tim Howell interpret this exchange of rhythms as a form of inversion on its own, particularly because it is so aurally salient: Richard Powell, ‘Articulating Time: Listening to Musical Forms in the Twenty-First Century’ (PhD dissertation, University of York, 2016), pp. 153–55, http://etheses.whiterose.ac.uk/17150/ (accessed 17 February 2018); Howell and Powell, ‘Telling the Time’, p. 206.
13 Liner notes to Abrahamsen and Ensemble Recherche, Schnee. The same process also applies to Canon 1b.
14 In each hand, notes in a given segment are linked under a dashed slur; segments of the same length are all under the same solid slur. Bar lines here are synonymous with solid slurs and do not correspond to notated bar lines in the score.
15 In particular, for all segment lengths from 7 to 1, all possible contiguous segments are presented, moving from the end of the theme to the beginning. It is not difficult to more formally encode this process computationally: a one-line rendition in Python is [k+1 for i in range(7) for j in reversed(range(i+1)) for k in range(j, j+7–i)].
16 In both canons, winds double Piano 1 and strings double Piano 2.
17 Liner notes to Abrahamsen and Ensemble Recherche, Schnee.
18 From the publisher's website: www.wisemusicclassical.com/work/34990/Schnee--Hans-Abrahamsen/ (accessed 15 June 2020).
19 As with the inversion between the canons, this inversion operates in diatonic pitch space, about a notated D4–A5 axis. As a consequence of the underlying processual RI symmetry, each canon's piano parts invert to one another in their first and last seven notes.
20 Indeed, psychological studies have shown that pitch and timbre are so much more prominent as auditory features that they can even cause our perception of space to be incorrect; see Diana Deutsch, ‘Grouping Mechanisms in Music’, in The Psychology of Music, ed. Diana Deutsch (San Diego: Academic Press, 2013), pp. 212–24.
21 Liner notes to Abrahamsen and Ensemble Recherche, Schnee.
22 Sara Bakker, ‘Ending Ligeti's Piano Etudes’, in Form and Process in Music, 1300–2014: An Analytic Sampler, ed. Jack Boss, Heather Holmquest, Russell Knight, Inés Thiebaut and Brent Yorgason (Newcastle-upon-Tyne: Cambridge Scholars, 2016), pp. 114–18.
23 See Act 1 Scene 4, beginning at p. 90 of the score to The Snow Queen.
24 Robert Hasegawa, ‘Creating with Constraints’, in The Oxford Handbook of the Creative Process in Music, ed. Nicolas Donin (New York: Oxford University Press, 2020), https://doi.org/10.1093/oxfordhb/9780190636197.013.17.
25 Ligeti is quoted as describing his own structures as inaudible in Jonathan Bernard, ‘Inaudible Structures, Audible Music: Ligeti's Problem, and His Solution’, Music Analysis, 6, no. 3 (1987), p. 209. For more on the role of serialism in Ligeti's instrumental micropolyphony, see Bernard, pp. 207–10; Benjamin R. Levy, Metamorphosis in Music: The Compositions of György Ligeti in the 1950s and 1960s (New York: Oxford University Press, 2017), pp. 85–102. For the role of serialism in the Requiem, see Levy, pp. 169–78; Jennifer Iverson, ‘Ligeti's Dodecaphonic Requiem’, Tempo, 68, no. 270 (2014), pp. 31–47.