Transformations

The relationship between Abrahamsen’s 1978 composition Winternacht and M. C. Escher’s 1955 lithograph Three Worlds has been examined in detail by Kevin Ernste: the second movement of Winternacht brings together images of three different musics (by Schubert, Beethoven and Chopin) alongside characteristically systematic pitch structures.Footnote ¹³ Abrahamsen has made explicit the influence of Escher’s graphic art on the transformational techniques found in his more recent output, with the latter’s interest in paradoxes and impossible worlds also finding echoes in some of its broader concerns. As an example, consider woodcuts such as Day and Night (1938) or the two works entitled Sky and Water (also 1938). In Day and Night, two intersecting flocks of geese fly across a mirrored landscape: black geese fly right to left into the daytime, their form gradually created out of the checkerboard fields of the ground below and at the point of crossover also becoming the background against which the white geese – flying in the opposite direction – are seen. In both Sky and Water I and II the transformation takes place vertically: white fish on a black background at the bottom of the picture gradually lose definition, becoming initially the tessellating pattern, and then the ground against which black birds are gradually revealed in increasing detail towards the top, and vice versa.

The musical equivalent becomes one of the primary structuring techniques for the canons in Schnee. Abrahamsen explains the conception:

Canon 1a presents this idea the most clearly. This movement involves two very closely related melodic strands played by the piano, along with what initially seems to be an accompaniment of repeated, very high string harmonics from the violin, viola and cello. The melodies, each given a precisely calculated, gradually accelerating rhythm, are shown in Example 1a. They are first played consecutively, before the music pauses briefly and then repeats – each presentation of the two melodies is restated directly. On the next iteration, the second melody overlaps with the first by two bars, creating a more complex resultant melodic stream. This process continues through subsequent passes, with the second melody moving two bars earlier each time; by the fourth run-through it starts one bar before the first, and by the sixth the two melodies have slid past each other completely. As Abrahamsen puts it: ‘So the initial phrase becomes the closing phrase, and vice versa – rather like the world of Escher’s pictures, where a white foreground on a black background on one side of the picture becomes a black foreground on a white background on the other.’Footnote ¹⁵ The resulting pitch order is shown in Example 1b; although both melodies contain the same number of pitches, the initial decisions about the rhythmic profile of each line creates small variations in the symmetry of the overlapping process as it unfolds. The musical result is also less straightforwardly linear than Abrahamsen suggests: the form becomes a kind of arch shape, with the central statements presenting the material in a more compact, denser form; this is mirrored by the string figuration which similarly thickens before returning to the opening, repeated-quaver idea.

Example 1

Abrahamsen, Schnee, Canon 1a: (a) piano melodies, bars 1–10; (b) crossover process. Schnee, music by Hans Abrahamsen, © Copyright 2008 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

The process is of course complicated by the high level of similarity between the melodies involved. Unlike Escher’s Sky and Water woodcuts, which involve distinct objects (that are nonetheless able to tessellate), here there are two variant images of the same idea, and the detail of the transformation is correspondingly less clear, particularly without some prior knowledge of its unfolding. The question again arises as to whether such a process might be expected to be followed ‘in time’. Abrahamsen seems to play with this very idea, as details of the construction – in particular, the use of a repeated A♮ – mask the clarity of overlap. Instead, the overall trajectory becomes the focus: gradually changing one melodic strand into another is a musical device that, like many others, determines the overall shape and the smaller scale simultaneously – the process unfolds the form, and vice versa.

A more complex use of this same compositional technique can be found in Let me tell you. The first, fourth and sixth movements of the cycle – which explicitly mark the progress of time, from ‘Let me tell you how it was’, to ‘how it is’ to ‘how it will be’ – present differing views of the same musical ideas, and again, despite their spaciousness and direct expression, they are, as Abrahamsen describes, as constructed as anything in Schnee – indeed, they start from the same material.Footnote ¹⁶ Taking the first movement, the long, sinewy lines that appear first of all on two piccolos answered by two oboes before charting a gradual descent in register to end on violas and cellos again involve two closely related melodies, shown in Example 2a. As is immediately apparent, the upper lines are transposed and slightly inflected versions of the material from Canon 1a of Schnee, now without note repetitions.Footnote ¹⁷ Again the melodies gradually interpenetrate by overlapping two bars at a time before passing entirely through each other, but here this process is further complicated by a twofold switching process. The first takes place between the lower, quasi-harmonizing voices: as Example 2b shows, with each run-through the upper voice remains the same, but the intervals forming each dyad are exchanged so that perfect fifths become major thirds/diminished fourths and vice versa. Thus, in effect, each statement presents a long chain of incomplete minor triads – for line a: B♭ minor, G♭ minor, F minor; and so on. These triads are rooted on six pitch classes (B♭, D♭, D♮, E♭, F♮, G♭), and the resulting tonal sense hovers around a B♭ centricity, with the F♮ that sounds throughout the movement – first from the celeste, then from the harp and xylophone/marimba – being continually recontextualized by those shifting harmonic sands. The second process involves the rhythm given to each melody: a' uses the rhythm of b, and b' that of a (subject to very small changes, principally to accommodate the different number of notes); the web of similarities between the two melodies is thus denser than the comparable music of Schnee. This time, as the two phrases are of different lengths, the interlocking process is necessarily somewhat asymmetrical, but Example 2b illustrates the emergent sense of consistent pacing: line 2, for instance, shows how b' enters after six dyads, and is divided into 1, 2 and 11 dyads by the interlocking; the comparable reverse process is in line 5, where a enters after six dyads and is divided into 1, 2 and 10 dyads.

Example 2

Abrahamsen, Let me tell you, I: (a) opening melodies; (b) crossover process. Let me tell you, music by Hans Abrahamsen, © Copyright 2013 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

As with Canon 1a of Schnee, the working out of the transformation defines the length of the movement, although here two further important musical features also shape the overall form. The first is the appearance (from bar 6) of the vocal line, which uses the lower pitches of the second melody (b/b' in Example 2b) and presents them twice during the course of the movement (in the order b'–b, b–b', with a brief ‘coda’ after each pair which takes the last few pitches of the other melodic strand). The second is the introduction, at bar 25, of lower brass and woodwind – a striking moment in this movement, not only underpinning the high treble register used so far but also creating the movement’s distinctive harmonic sound-world. Given Abrahamsen’s concern with structure and extracting the most from limited material, it is not surprising that these harmonies are also derived from the same source: an inversion of a' and then b' around B♭, again presented in its entirety.

Other types of transformation are less closely tied to the generation of musical form, instead providing control of the note-to-note details of larger gestures. For example, the second movement of the Double Concerto, Schnell und immer unruhig, uses two distinct processes to create much of its material. The first of these is a type of permutational approach most conspicuous in the second half of the movement, though it is also found in a more limited form earlier on. From bar 109 the ensemble is divisi into 22 solo lines, and the violin sections play alternately as blocks. Each block involves the superimposition of equal divisions of the bar into three, four and five or eight, nine and ten sets of notes (effectively six different tempo layers), and the bar length itself alternates between 2/2 and 10/8. (This type of compression/rarefaction is almost a signature of Abrahamsen’s music of this period.) Initially these blocks traverse an octave between A♮3 and G♯4, and each constituent line uses several different modes in order to do so. Thus, a four-note line might, as in bars 109 and 111, divide the octave most simply into four minor thirds, creating a diminished-seventh chord, or might use one of many other alternatives (for example, in bar 110 a similarly symmetrical (0167); see Example 3a). The situation is at its most complex with the division of the bar/octave into ten (violin 1 and 2, first desks), and the mechanism through which those pitch structures are created is shown in Example 3b. For each bar a different mode is used (usually running A–G♯, but also, once each, B♭ –A♭ and A♮–G♮), in every case dividing the notional octave into semitones interspersed with two steps of a tone. The order of these pitches is permutated according to a straightforward process: in relation to the initial ascending line in bar 109, each subsequent bar involves reversing the order of a group of pitches which gradually increases in size. Thus, bar 110 (line 2 of Example 3b) switches four two-note and two one-note groups (which therefore retain their original position); bar 111 (line 3) switches two three-note and two two-note groups, and so on, working up to a simple switch of all ten at the halfway position. Here the retrograde of the original is achieved, and the process resets and repeats, finally leading back to a straightforward ascending scale. A similar system is used for all of the six ‘levels’ of bar subdivision.Footnote ¹⁸

Example 3a

Abrahamsen, Double Concerto, II, bars 109–11, score. Double Concerto, music by Hans Abrahamsen, © Copyright 2011 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

Example 3b

Abrahamsen, Double Concerto, II, bars 109–11, transformation process.

The overall effect of this superimposition of multiple tempo layers and divisions of the octave is to create a perpetually changing kaleidoscope of chromatic material. Two processes give this a larger-scale direction, however. The first is the way in which the starting unison note of each new bar is controlled: these duplicate, in augmentation, the ten-note pattern just discussed (rising A–B♭–B–C–D, then falling A♭–G–F♯–F–E♭), and are reinforced by repeated notes from violas and cellos – an application of the same material to different temporal levels. The second is the control of the solo parts: the violin initially takes a chromatic scale (12 notes played over two bars) and subjects it to a comparable permutational process. At bar 119, as the orchestra repeats the material of the last ten bars transposed a tone higher, piano and violin continue their ascending lines, now doubled at the tritone. As the movement draws towards its close, the two solo instruments reach higher and higher, with extra parallel notes added, before being left alone over sustained harmonics from lower strings. The permutational techniques in this section of music are most apparent within these solo lines: it is hard at the given speed to ‘track’ the orchestral layers as they pass by, but the global effect of heterophonic chromaticism throughout the ensemble comes through clearly, and the gradual thinning and overall ascent in register imparts forward momentum. The details here might not be as clearly foregrounded as they are in the passages from Schnee or Let me tell you discussed earlier, but the emphasis on clarity and logic is retained.

Earlier in the movement, a further type of process is involved. At its heart is a kind of rhythmically elastic, tetrachordal melodic line that takes as its starting point the first two gestures of the entire work. Appearing initially on solo violin doubled by muted piano, it transfers as the movement progresses into the orchestral parts before returning to just the solo instruments, thereby acting as a kind of cantus firmus for the first 107 bars. Its rhythmic complexity is increased by Abrahamsen’s technique of compression and rarefaction, so that bars of nine quavers in the time of ten alternate with nine in the time of eight, laid over a constant quaver pulse from the accompanying strings. To begin with, it seems that an alternating five-/six-bar ‘tactus’ is at work: transpositions of the tetrachord (G–B♭–C–E♭ to D–F–G–B♭, then to F–A♭–B♭–D♭) take place at bars 6, 12 and 17, coupled with changes in orchestration to the accompanying open fourths; an ‘extra’ bar is added before the triggering of an ascending/descending modal line from the solo violin at bar 22 (prefiguring bar 109). In fact, the construction here cuts across these much more obvious markers, creating a kind of larger-scale rhythmic counterpoint whereby the realignment of recognizable rhythmic patterns with these textural changes occurs only occasionally, most obviously at bars 33 and 65.

Example 4 shows (a) the 48-quaver pattern which opens the movement and illustrates how the passage of music in bars 17–37 (b) is derived from it. The statement beginning at bar 17 is the result of the following transformation: after transposition down a perfect fourth, the uppermost two pitches remain, all F♮s become rests, D♮ is mapped onto F♮, and any new notes introduced are D♮, thus completing the tetrachord. The next line applies an inversion of this process to this new iteration: D♮s and F♮s remain, G♮s become rests, B♭ maps to G♮, new notes are B♭. This is expressed more formally in the boxes on the right side of Example 4, with the notes of the mode, reading upwards, notated 1–4; as can be seen, the next two lines then derive from the initial statement. The first part of this movement is made up of 18 statements of similar patterns. The final two, bars 97–107, not only present a straightforward inversion of the opening but also mark an obvious return to the opening sonority of solo violin and muted piano. It would be tempting to see this as the inevitable outcome of the preceding manipulations, but the music does not support such a reading. Instead, Abrahamsen presents a perpetually changing, rhythmically charged line which is overlaid with more obvious markers of formal contrast such as texture and scoring.

Example 4

Abrahamsen, Double Concerto, II: transformation of melodic line, (a) bars 1–6; (b) bars 17–38. Double Concerto, music by Hans Abrahamsen, © Copyright 2011 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

This approach, where processes generate pitch material which is then sculpted into larger structures, is found in both parts of this movement. However, as we have seen, Abrahamsen may apply such processes on different temporal levels, and there is thus in so much of his music an underlying sense of continual transformation. It is this characteristic dynamism that forms a creative counterpoint to the crystalline purity that is also so clearly projected – a perpetual negotiation that seems one of the defining features.

Doubles

Repetition is a key strategy in Abrahamsen’s recent works. As Christopher Chandler observes in his examination of the relationships between Walden and Wald, a number of different forms of ‘recomposition, recontextualization, and varied repetition play a prominent part in his compositional language’.Footnote ¹⁹ Processes of variation – which, of course, imply a certain level of repetition against which change can be judged – will be examined in more detail below, but another very important part of how Abrahamsen structures his music across multiple timescales, from individual cells to larger sections, involves restatement. Particularly distinctive is the way in which, in many cases, material just heard is immediately repeated, as if being re-presented, a procedure best thought of as a type of ‘doubling’. Of course, any repetition, even if literally ‘note-for-note’ in the score, happens within a different context from the first appearance, but Abrahamsen also seems to play more self-consciously with ideas of identity. This is comparable to a kind of game using mirrors, which can either replicate the image exactly or distort it to a lesser or greater degree. With the inevitable passing of time that separates any such doubling, this game becomes also one of memory: is what we have just heard in fact ‘the same’ as the previous presentation?

The most obvious examples are the medium-scale repetition of sections of music, often involving a systematized number of bars. A conspicuous instance comes in Canons 1a and 1b of Schnee, where each statement of the two melodic strands is immediately repeated; it might at first appear counterintuitive to ‘freeze’ the gradual transformation in this way, but this allows each new alignment to be clear, to be fully assimilated, before moving on to the next. A similar approach occurs at the beginning of Wald. Again, a call and answer gradually move through each other so that they end by exchanging places, and again, each alignment is repeated in its entirety. The repeated passages oscillate between nine and eight bars in length – a grid-like approach to musical construction that has already been observed in respect of transformation processes. The first part of this work involves four smaller-scale sections, each of which recurs in what Abrahamsen calls ‘Variation 1’, and this opening section is there repeated in a modified form, and now with the grid structure compressed. Example 5 shows the comparable passages. Alternating between eight and seven bars and with the repeat marks removed, the effect at bars 111–34 is to present the original call-and-response material in a rescaled form – more condensed, with the transformation happening at a faster rate.

Example 5

Abrahamsen, Wald: call-and-response material, (a) bars 3–28 and (b) bars 111–34, and alignment with grid structure. Wald, music by Hans Abrahamsen, © Copyright 2009 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

Example 5

(cont.)

This interest in grid structures, scale and the associated use of repetition is reminiscent of Morton Feldman’s music, in particular that composed in the late 1970s and the 1980s, and this technique of combining repetition with rhythmic rarefaction and compression is significant within all of Abrahamsen’s works under examination here. An example of the type of elasticity that can result has already been identified in the second movement of the Double Concerto (the alternation of bars of 9:10 and 9:8 against a common quaver pulsation); in the fourth movement, a similar use of repetition in relation to a modified grid structure is the primary structuring mechanism. The main ideas are quite simply described: a series of ascending and descending scalic figures, played pp on very high harmonics, accompanies a long melodic line involving many repeated notes, heard twice from the solo piano and once from the solo violin. Example 6 shows the beginning of each melodic statement. The first time through (Example 6a), the time signature alternates between 9/8 and 2/2 (thus nine then eight quavers), and the whole statement is structured across a grid which divides the music into groups of seven and five bars, using a symmetrical pattern (7–7–5–5–7–7 bars). This structuring device is not readily apparent from the melody itself, but directly affects the accompanying ensemble lines, which move in a consistent quaver motion and are controlled through another alternating (eight then nine) series. The second run-through (starting at bar 40; see Example 6b) initially appears somewhat more complicated: the barring grid is a mirror of the first (5–5–7–7–5–5 bars), now alternating between 4/4 and 3/4, and the basic underlying pulsation is a quintuplet/triplet quaver, the same speed (through a metric modulation) as the initial quaver motion. Abrahamsen now notates this as two alternating tempos, although this is perhaps again more an effect for the eye than for the ear, and bars thus alternate between ten and nine quintuplet/triplet quavers.What this means is that this whole statement is almost exactly the same total length (325 semiquavers rather than 323), and musical events also happen in approximately equivalent places within that structure: for example, a running semiquaver figure from first violins appears in bars 10–11 of the first iteration and in bars 9–10 of the second.

Example 6

Abrahamsen, Double Concerto, IV: statements of piano/violin melody, (a) from bar 1; (b) from bar 40; (c) from bar 75. Double Concerto, music by Hans Abrahamsen, © Copyright 2011 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

The third version of the melody (starting at bar 75) is less rapid (with a stepped meno mosso as the passage continues), the accompanying scalic material in triplet quavers is taken over by the solo piano, and the orchestra creates a sustained backdrop from more slowly moving harmonics. The solo violin – having previously played the descending scalic patterns and, the first time through, two five-note motifs taken from the first movement of the work – now takes up the basic melody (Example 6c). Despite having exactly the same underlying construction as the first two iterations, the change in scoring and the feeling of a slower unfolding in this third section of the piece means that there is a clear contrast. In effect, this movement is a bipartite form created from a tripartite structure: the final section acts as the modified ‘double’ of the first two. At the same time, this movement is a kind of variation form (also important within Abrahamsen’s compositions, as we shall see); controlled by small manipulations of scale, it plays with ideas of repetition and identity in a subtle and allusive manner.

Extensive use of smaller-scale repetition at the level of individual cells can be found in music such as Canon 2a of Schnee. Here again, this is coupled with a direct control of scale, with similar material being redistributed in such a way as to occupy more or less time. This canon presents a remarkable sound-world, combining winds with muted piano to create a fast-moving whirlwind of a movement: precise, rhythmically pointed and crystalline. The basic material involves rapid repeating loops initially given to flute and clarinet, with piano and cor anglais providing an accenting rhythmic counterpoint.Footnote ²⁰ It is again tightly constructed (Example 7a shows the beginning of the movement, with each looping pattern labelled), and there is again a characteristic alternation between two ‘neighbouring’ time signatures; in this case the underlying quaver pulsation is kept as the constant. Example 7b illustrates the systematic way in which the patterns occur in this first section (bars 1–28), as well as the mirroring that takes place every seven bars. At the midpoint, bar 15, the articulation of the two lines swaps over and the pattern repeats. Cutting across this somewhat is the ‘repetition grid’, which behaves palindromically: repeats take place at one-bar, then two-bar and finally three-bar intervals before being reversed. The duplication of the 8/8 bar at the midpoint means that on the second run-through the flute and clarinet material is placed differently across the barring; at bar 28 the unfinished lines are simply cut off by a sudden, sustained silence.

Example 7

Abrahamsen, Schnee, Canon 2a: (a) opening; (b) repetition grid of first section. Schnee, music by Hans Abrahamsen, © Copyright 2008 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

The remainder of the movement is constructed similarly, with a gradual reduction of bar length to five/six and then three/four quavers before the process is put into reverse. The use of small-scale doubling is key to generating the music, with the effect of the repetition grid creating something of a paradox. Far from providing familiarity through rehearing the same material, the cutting across of the predictable melodic cells creates instability, as it becomes extremely difficult to grasp any clear rhythmic pattern. The interaction of two related systematic processes gives rise here to an overall sense of non-systematization, of a lack of clear structure.

Larger-scale doubles abound. Within Schnee this is particularly clearly pronounced – each canon has its own. As Abrahamsen explains:

In other pieces, whole sections from the same work or even from elsewhere can be re-sited.Footnote ²² For example, as has already been noted, in Let me tell you there are three different versions of the music that introduces each large-scale section of the piece. While they use the same underlying construction, they progressively reduce in length (the last is quite considerably shorter), and one conspicuous change is that the second version is constructed around a sustained G♭ rather than retaining the F♮ centricity of the outer two.Footnote ²³ The Double Concerto draws on a wider range of music. The third movement is a recomposed version of Efterårslied (Autumn Song; 1992, rescored in 2009), which itself incorporates pre-existing material from Bach’s The Art of Fugue and a song by Oluf Ring, ‘Sig nærmer tiden’ (‘My time to leave approaches’),Footnote ²⁴ while the first movement directly reworks Abrahamsen’s more recent Liebeslied (2010). In this opening, the first five bars of Liebeslied are first rescored for the new, larger ensemble, and then repeated transposed down a tritone – with gestures redistributed orchestrally. The remainder of the movement continues with a rescored Liebeslied at the original pitch, although as that itself involved a large degree of internal repetition, the form that results appears as a set of reflections of the opening bars. While Liebeslied articulates a (pseudo)-ternary A (5 bars), A' (3 bars), A (5 bars), this new form is more unbalanced: A (5 bars), A transposed (5 bars), A' (3 bars), A (5 bars). The whole movement is thus generated from a single melodic gesture, which itself – in a moment of internal referral – becomes the departure point for the process in the second movement: the first nine notes begin the repeating pattern which structures it (see again Example 4).

In this way, Abrahamsen’s use of repetition appears as an approach to material that is inherently ‘economical’ – whereby the maximum potential is extracted from a deliberately restricted starting point. But these doublings, which, as we have seen, may take place on different timescales, do not just extend that material (although that can be the effect, with considerations of scale an important aspect here), they also transform it. As a result, the music manipulates ideas of similarity and difference that inform the more explicitly transformational approaches examined earlier. How identity is shaped therefore emerges as an important broader concern within these works, with Abrahamsen’s use of process tending towards a questioning of apparent stability. It is the way in which these individual processes can be combined and deployed to broader expressive ends that now needs to be considered.

Variations – Wald

Abrahamsen describes Wald – scored for 15 players distributed in balanced groupings of two or three instruments to form seven ‘half-circles’ around the conductor (the piano/celeste placed in the middle) – as a ‘series of variations’.Footnote ²⁵ The concept of variation is implicit in much of Abrahamsen’s approach, with material often evolving and being re-presented in always changing versions, but now that also becomes a focus for the whole work. As a result, Wald is a particularly good example through which to examine the interaction of processes to create larger-scale form, and to illustrate the ways in which Abrahamsen employs those techniques of transformation and doubling already discussed alongside a range of other compositional strategies.Footnote ²⁶

Wald sets out to evoke an experience of the forest, both directly and, as Abrahamsen discusses in his note to the piece, mediated through Thoreau’s Walden and nineteenth-century conceptions of that experience such as those found in Schumann’s Waldszenen, op. 82:

This is not the place to undertake a detailed discussion of the multiple interesting parallel strategies between this work and Schumann’s, but rather to note the way in which Wald hovers ambiguously between evocation and representation. Much of the piece is very quiet and still, with horn-call fourths initially exchanged between bass flute and French horn. After a section that Abrahamsen marks as Nachtmusik (‘Night Music’) there is an outburst of activity ‘like a sudden awakening’, before the galloping music to which Abrahamsen refers and a concluding return to a more serene sound-world. How this maps onto the composed variation form can be seen in Table 1. The theme and the first two variations use the same palette of four types of material, labelled i–iv, although there is a complicated network of relationships both between the initial statements and in the ways in which those are subsequently modified, as will be discussed below. Variations III and IV use very closely related material to create the ‘Night Music’ section, whereas Variation V is tripartite – again involving internal relationships and connections to material heard elsewhere. The closing section is once more made up from two notionally distinct ‘variations’, and we thus have one of a number of paradoxes with this work, as the theme-plus-variations conception of the piece conceals itself within an emergent four-part form, creating a large-scale ambiguity which mirrors the smaller-scale processes of allusion and restatement.

TABLE 1

ABRAHAMSEN, WALD: FORMAL SKETCH

These twin processes start right at the beginning. As Abrahamsen observes in his note, the piece grows out of the opening of his 1978 wind quintet Walden (the link to Thoreau is explicit there);Footnote ²⁸ thus, rather as with the Double Concerto, this piece reuses – doubles – previous music. The original material (the first 16 bars of Walden) acts as a kind of progenitor to a variety of different versions of the motif. In Walden, a horn-call fourth, B♭–E♭, is initially answered by a rising third, D–F, from flute, clarinet and bassoon. In a manner comparable to that employed in Canon 1 of Schnee, the response gradually ‘moves through’ the call, so that on the fourth iteration their positions are completely exchanged.Footnote ²⁹ In Wald, this material is simplified to involve only two pitch classes. (The D–G call heard alternately from bass flute and horn is answered by the same rising fourth from harp and kalimba, alongside pulsed sustained notes from horn, bass flute, double bass and cello, the whole underpinned by a combination of sextuplet and quintuplet D–G double stops, quasi-tremolando, from the violins.) Important here, however, is the interplay between a conventionally tuned and a microtonally inflected dyad; the difference in pitch is equivalent to a sixth of a tone, as would be produced by playing the seventh harmonic on, for instance, a natural horn. As a result, the initial response from harp, horn and double bass sounds lower (see again Example 5).

Part (ii) of the ‘theme’ expands this initial dyad a semitone outwards in both directions, employing a C♯–F♯, D–G, E♭–A♭ hexachord. Now each fourth call is answered by a rising, apparently rhythmically elastic hexachordal figure – initially a straightforward scale, but gradually transformed through another ‘shifting’ technique. As Chandler has shown in some detail, each of the fourth intervals embedded within the line is subject to its own systematic ‘displacement process’. For example, in moving from the first to the second statement the C♯–F♯ dyad moves one crotchet earlier, while the E♭–A♭ comes one triplet crotchet later; the result is a pitch order that runs C♯–D–F♯–E♭–G–A.Footnote ³⁰ The overall effect of this passage is of a doubled, distorted version of the opening – Abrahamsen marks it poco grottesco e ironico. This leads to a sudden ‘clarification’ in part (iii): now using only a tetrachord D–F–G–A (the D–G dyad remains embedded), rapidly moving even-note patterns in several simultaneous subdivisions of the beat are dispersed across the ensemble, punctuated by occasional sforzando pitches from strings. More of a contrast is presented by the final type of material, bars 91–108, with a slower-moving sense of gradual flow created through the total chromatic, and much use of paired semiquavers to build oscillating lines which appear slowly to descend. A low B♭1 from the piano provides a clear anchor – a contrast to the predominantly treble register used to this point. The fourth motif is still present, though now forming part of longer and more lyrical three- or four-note lines; otherwise, the relationship between this music and that heard at the very beginning initially seems tangential, as if from a different place altogether.

These four types therefore make up what Abrahamsen calls his ‘theme’, and as Table 1 shows, in the two variations that follow they are again presented in the same order. However, they are also subject to variation. Part (iv) is the least transformed, as each time the basic gestures remain intact and the sound-world strongly defined (for instance, each version arrives on the same low accented B♭ from harp and piano), but the others undergo some significant changes, which are briefly outlined in Table 2.Footnote ³¹ One approach used in both Variations I and II is the transformation of scale through the manipulation of grid structures that was observed earlier in this and a number of other works. Table 2 shows the barring: while Variation I has a similar total number of beats, Variation II is significantly shorter.Footnote ³² However, this is complicated by the way in which either similar material is spread across an altered barring structure – as mostly happens in the theme and in Variation I – or a significantly different amount of material is involved. For example, part (i) in the theme involves four call–response gestures, each aligned with the repetition grid and each immediately repeated. In Variation I there are six such gestures spread across the gridlines, now involving eight fewer beats, whereas Variation II presents just one call and one response – a kind of ‘slow motion’ version. For part (iii), Variation I involves exactly the same amount of material as in the theme, arranged similarly within the barring, but the different repetition structure modifies how that appears on the micro-level. Variation II, by contrast, consists of 20 bars without any repetitions, which means that, in something of a paradox, more musical material now takes up less time. It is this complex relationship between different versions of a limited palette of ideas that gives the first third of Wald a particularly elusive and intangible quality – while individual gestures are straightforwardly defined, the ways in which they return and the sense of progress and scale that are involved are all rather more complex.

TABLE 2

ABRAHAMSEN, WALD: INITIAL THEME AND VARIATION PROCESS

	(i)	(ii)	(iii)
THEME
Tempo	= 88	= 66	= 100
Phrase structure	2-bar ‘introduction’ 4 × call–response, each repeated	2-bar ‘introduction’ 4 × call–response, each repeated	horn–trumpet/violin alternation: 4-2, 3-2, 3-4 (bars)
Grid (bars)	3/8 | 2 |: 9 :|: 8 :|: 9 :|: 8 :|	2/4 | 2 |: 8 :|: 9 :|: 8 :|: 9 :|	12/8 | 1 |: 2 :|: 3 :| 4 |: 3 :| |: 2 :| 3 |
Length	70 (2 + 68) (36 bars of material)	70 (2 + 68) (36 bars of material)	28 (18 bars of material)
VARIATION I
Tempo	= 92	= 77	= 100
Phrase structure	2-bar ‘introduction’ 6 × call–response	8 call–response (intertwined)	horn–trumpet/violin alternation: 4-2, 3-2, 2-3 (bars)
Grid (bars)	3/8 | 2 | 8 | 7 | 8 | 7 | | 8 | 7 | 8 | 7 |	2/4 | 7 | 8 | 7 | 8 | | 7 | 8 | 7 | 8 | 7 |	12/8 | 2 |: 2 :|: 1 :| 1 |: 2 :| | 1 |: 1 :| 1 |: 2 :| 3 |
Length	62 (2 + 60)	67	24 (16 bars of material)
VARIATION II
Tempo	= 94	= 82	= 100
Phrase structure	6-bar ‘introduction’ 1 × call–response (‘slow motion’)	7 × call–response (intertwined)	through-composed (horn throughout); sustained pitches added
Grid (bars)	3/8 | 6 | 6 | 6 | 6 | 6 | | 6 | 6 | 6 | 6 |	2/4 | 8 | 7 | 8 | 7 | | 8 | 7 | 8 | 7 |	12/8 | 20 |
Length	54 (6 + 48)	60	20

The two principal types of material remaining are those that make up the ‘Night Music’ section (Variations III and IV) and the ‘sudden awakening’ that leads into the invocation of the hunt (Variation V). The first of these is much more straightforward: it is predominantly monophonic, involving in Variation III a slow-moving melody from cello and double bass, with Variation IV adding interpolations from bassoon and bass flute; long sustained pitches, initially in the bass and later in the high treble register, support the melody, with occasional notes from celesta, piano, trumpets and horns punctuating the texture. This passage clearly evokes Bartók’s night music, and in particular the fourth-saturated cello and double bass solo line of the Concerto for Orchestra. It begins at the B♭1 which is the end goal of the fourth part of the theme and first two variations, and is built from a hexachord of the type used in part (ii) of the theme: two three-note chromatic clusters separated by a perfect fourth, here D♭–D♮–E♭–A♭–A♮–B♭ (the initial fourth motif permeates many aspects of the music). The melodic line at the heart of these variations is a prime example of transformation by gradual process. Example 8 shows a way in which this can be understood as a set of modifications of an initial statement. Pitches are interpolated and removed; their order is reversed or re-permutated; and in Variation IV (from bar 443) retrograde versions of a decreasing amount of the line already heard are inserted (and marked by the change in instrumentation). The result is the creation of a meandering melodic line where much remains familiar, but again Abrahamsen plays with identity and difference, presenting a kind of variation in miniature, indicative of the type of ambiguity achievable even when the most apparently straightforward material is presented in a clear, unadorned way.

Example 8

Abrahamsen, Wald: Variations III and IV, bars 408–73, ‘Nachtmusik’. Wald, music by Hans Abrahamsen, © Copyright 2009 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

In complete contrast, what follows is dense both on the surface and in terms of its deeper construction, and connects with the types of pre-compositional pitch structures on display in Abrahamsen’s work of the 1970s.Footnote ³³ Variation V is tripartite, with the first part most clearly evoking the agitated flock of birds that Abrahamsen mentions in his programme note.Footnote ³⁴ The initial ‘sudden awakening’ combines fast, rising-fifth gestures from strings – strongly reminiscent of the basic motif of Schumann’s ‘Vogel als Prophet’ from Waldszenen – with sforzando falling fourths from the remainder of the ensemble. Each of the stacked-fifth lines (for example, A♭–E♭–E♭–B♭–F♮) is built on one of the pitches of a diminished tetrachord A♭– C♭–D♮–F♮; changes of pitch-centre mostly align with new gestures, creating a shifting harmonic underpinning. The descending fourths delineate a rather more complex underlying structure, which is comparable to those used to generate the lydstyrt (‘diving sounds’) that occur in works such as Winternacht or Lied in Fall. Footnote ³⁵ This pitch material is shown in Example 9, along with the principal instruments involved in presenting each of the seven layers: there are two fixed-octave sets of pitches, built from stacks of perfect or augmented fourths. In an effect somewhat reminiscent of a Shepard tone, the continual looping back of each instrumental line gives the effect of descent without any overall motion – an illusion that again connects to Escher’s visual art, and specifically lithographs such as Ascending and Descending (1960) and Waterfall (1961). Each instrumental pairing shown in Example 9 plays the material in canon, with complete statements of each set occurring through the texture as a whole (two such examples are indicated by diagonal lines). The music begins ‘in flight’, already some way through articulating Set 1, perhaps a result of working from the midpoint – the two clearest complete statements of each set – outwards. The rhythmic complexity that results from the overlaying of the instrumental strands, involving the simultaneous use of multiple tuplet divisions of the beat and unpredictability as to the appearance of individual fourth pairs, means that the underlying structural principle is not immediately obvious: the density and rapidity of the result mitigates against tracking the process involved.

Example 9

Abrahamsen, Wald: pitch structure, bars 474–89.

The next part of Variation V, marked ‘vielleicht eine Jagd’, thus represents something of a clarification. Held together by a fast, continuous semiquaver pulsation, it emphasizes three adjacent fourths (A–D, B–E and C–F♯), each of which forms part of a fixed-octave pitch collection made up of stacked perfect/augmented fourths; the first of these, in descending order D–A–E♭–B♭–F, is a subset of Set 2, used previously. Each sonority is projected for only a few bars at a time – the clarity of the uppermost pitches and the swift alternation between them results in a greater sense of diatonicism. Strings continue to play rising arpeggios of stacked fifths, and now the trumpets also emphasize another pitch collection, E–D–C–A–G–F, and it is this set that comes to the fore in the final and most extended part of this variation. This music is again constructed around alternating time signatures: initially 10/16 and 2/4, with bars mostly subdivided into even groups of notes (six, five and four; and seven and four, respectively), then, from bar 562, 10/16 and 6/8, with subdivisions of four, five and six. Example 10a shows the way in which three strands of material are overlaid: while harp, piano and marimba maintain a continuous, even oscillation between chromatic sonorities, again made up predominantly of stacked fourths, trumpets project a more complex rhythmic pattern continuing with the six-note diatonic pitch collection. Much clearer, however, is the pentatonic material introduced initially by bass flute, horn and violins which gradually transfers to most of the rest of the ensemble. This idea is derived from part (iii) of the ‘theme’ section, as is the underlying tetrachord – as it progresses, that is revealed directly, and it will be no surprise that the continually changing melodic profile is the result of systematic transformation. Example 10b illustrates how the ten-note resultant pattern of each bar undergoes a switching process which spreads from the inside out, producing a series of ‘variations’ of the original, including retrograded and rotated forms. Although the alternation between transpositions from bar 532 onwards cuts across this, making it more difficult to track its progress aurally, the process here generates an evolving series of patterns which, in combination with the other instrumental layers and the final più mosso, propel the music forward until its sudden interruption mid-flow.

Example 10

Abrahamsen, Wald: (a) layered material, bars 522–4; (b) transformation process, bars 521–40. Wald, music by Hans Abrahamsen, © Copyright 2009 Edition Wilhelm Hansen. All Rights Reserved. International Copyright Secured. Reproduced by permission of Hal Leonard Europe Limited.

What follows – the ‘aftershock’ of Variation VI – returns us to the world of the theme, with bars 589–94 presenting a thinned-out version of part (iv), bars 91–108. (The descending chromatic material from piano, harp and percussion are now missing, leaving the bass clarinet and viola lines much more prominent.) Before that, a brief passage combines longer, angular melodies with accented stabs from piano and harp, echoed by kalimba. (The A♭–D centricity suggests both a stretching of the opening perfect fourth by a semitone and the condensing of the first two parts of the theme – the fourth and its chromatic expansion – into just a few bars.) The emphasis placed on an E♭–G♭–A♭–B♭ tetrachord characteristic of part (iii) in the subsequent four bars reinforces this idea of compression. All this can be seen as yet another type of transformational process: a simple recall reaching back over almost the whole length of the work. As Chandler puts it, ‘This is a different sort of recontextualization […] it is clearly not repeated material, but it does have its origins in the contextual criteria of earlier material.’Footnote ³⁶ The final section, which in the score Abrahamsen identifies as a further variation, thins the music down even more. From an initial E♭ centricity via a number of accented pitches which reinvoke the ‘Night Music’ of Variations III and IV, the piece ends on an implied cadence, where a rare triad, G♭ major, ‘resolves’ onto an open fifth, F–C. As a result, this final sonority is given new ambiguity – is it the point of resolution itself, or does it form a quasi-dominant of B♭ minor? And how might it relate to the D–G sonority with which the whole work opened?

So Wald ends almost where it began, but, of course, during the last 20 minutes our understanding of its initial material has been changed, distorted, subjected to sudden interjections and taken in new and unexpected directions. Everything might appear calm again, but, in line with a romantic conception of the natural world that is self-consciously evoked here (and the model of Schumann’s Waldszenen is once again useful in this context), we are changed internally by that confrontation as our ‘farewell’ takes place in a context that is radically altered in relation to our ‘entry’. Key here is the allusive sense of form that Abrahamsen creates in this work, allowing for straightforward repetition of clearly identifiable material, more complex transformation processes that take that material in unexpected directions, and sudden contrasts and dislocations which grow unpredictably from common seeds. The bringing together of multiple perspectives and techniques in this way creates a complex and challenging view of a traditional formal practice (the variation), and Abrahamsen’s music in Wald therefore once again reinvents and reinvigorates, drawing a new and enchanting world out of those familiar building blocks.

Paradoxes and illusions

Several creative ambiguities thus emerge from an examination of Abrahamsen’s recent output. The first turns upon the relationship between the intuitive and the systematic. While smaller-scale systems abound (and common processes are often found across a number of works), on the larger scale there is rather less of this self-conscious framing of the systematic, with solutions to the question of developing form being more varied and specific to individual pieces. Somewhat paradoxically, perhaps, Abrahamsen himself has expressed this the other way around: ‘The tighter I now shape the form, the more freedom remains for the detail. Form and freedom: where possible I want to try to unite these two levels with my music.’Footnote ³⁷ However, the ‘tightness’ of form of which he speaks should not simply be equated with systematization, and the reuse of material and of particular compositional techniques suggests that the originality or otherwise of the detail is subservient to larger-scale concerns of shape and expressive potential – it is perhaps those, after all, that remain the primary compositional questions to be solved in any individual work.

Bound up with the use of systems, however, is the relationship that develops between the apparent simplicity of some of the compositional approaches adopted here and the complexity of the resulting music. Although the New Simplicity label may no longer be useful (if indeed it ever was), Abrahamsen continues to pose the question of how music can be complexly simple, or simply complex. First of all, there is an apparent willingness to juxtapose passages of straightforward clarity with those whose form is much harder to grasp on an initial acquaintance – compare for example the second and third movements of the Double Concerto. More profoundly, however, his works suggest the interplay and ambiguity inherent in such ideas. Abrahamsen comments that his return to composing after nearly ten years represents the finding of an answer to exactly this problem of how to combine the complex and the ‘naive’. His recent output, he says,

Abrahamsen suggests here how the complex and the simple are intertwined (in fact, that they coexist within the same space), rather than being manifestations of contradicting aesthetic positions, as they have sometimes been held up to be.

Such a paradox may not be unique to Abrahamsen’s music, but it is one that he appears to embrace. Particularly characteristic of his recent output is the creative use of such apparent contradictions. Thus there are games played with repetition, where material is re-presented, doubled, sometimes refracted so that issues of identity are put into question. There are passages where literal restatement is destabilizing rather than stabilizing, or where gradual, consistent change produces outcomes that are inherently unpredictable. And there is the interaction of multiple structuring devices to create forms that remain ambiguous and resistant to any straightforward characterization or overall sense of trajectory.

Writing some 25 years ago about compositions that preceded Abrahamsen’s ‘hiatus’, Gavin Thomas commented on the creation of what he called – going back to the visual work of Escher – ‘illusions’. He suggested that in a piece such as Winternacht, the way in which different types of music were used meant that they became ‘simply images in a potentially infinitely reflecting hall of mirrors’.Footnote ³⁹ Examination of the more recent works indicates that, despite changes in compositional technique and a tangible shift in sound-world, this idea remains a useful lever in understanding their construction. These illusions operate on two levels. The first is more obviously comparable to the visual devices in some of Escher’s graphic art, and involves setting up analogous aural structures to manipulate perception; these include the control of pitches to create a pseudo-Shepard tone, and the interrogation of the status of questioning and answering phrases. The outcome is the creation of a music that misdirects the ear, with part of the delight it produces coming from recognizing that process while submitting to it nonetheless. But there is also a deeper level in which illusions are created – illusions that are not necessarily mapped directly onto audible structures. Instead, key here is the idea of illusion as a kind of deception, in which a false impression is initially created – and for the mind as much as for the ear. The music can thus call into question what constitutes simplicity and what complexity, or can undercut distinctions between rational system and subjective intervention, or between repetition and variation. This continual, ongoing suspension and deferral of first appearances is a recurrent and important idea here. In his discussion, Thomas praises Abrahamsen’s works for their ‘precision, clarity, and originality’,Footnote ⁴⁰ and those are certainly terms that apply to the pieces examined here. But, as we have seen, they can also involve the exact opposites: processes are neither always wholly precise nor always consistent; large-scale forms need not remain clear; and works often draw upon existing repertoire in a complex and self-conscious way. It seems that it is the creative interplay of those many paradoxes that go some way to giving the music its undeniable strength and maybe also finally its strange and revealing beauty.

Thus, Abrahamsen’s work allows a number of differing perspectives to come together and cohabit. It negotiates its own particular territory between apparently distinct categories and illustrates how a music can be immediately appealing and yet still reward detailed attention to its construction. It provides a space in which directness of expression can combine with a delight in the use of rational processes, and where that immediacy of emotional response is sublimated into a framework which shapes it and gives it additional meaning and depth. On the other hand, it illustrates the ways in which those apparently logical and coherent processes can give rise to instability and puts into question the predictability of straightforward systems. It also engages with concepts of identity (with material repeated, modified and transformed), suggesting a fluidity that seems characteristically twenty-first century in outlook. All this tends towards a common concern with the potential released by finding multiple solutions to complex questions. While intimations of the broader cultural work that Abrahamsen’s music can undertake must remain only tentative, as examinations of its poetics, cultural context and wider reception are essential for any such understanding, it seems that, in our current, seemingly fractured societies, a music which can suggest ways in which apparently competing narratives can coexist, recombine in creative ways and finally reach new alignments and accommodations is something that we increasingly need.