“The Rules of the Game”: Analysing Ambiguity in Unsuk Chin’s "Acrostic Wordplay"

Unsuk Chin’s song cycle Acrostic Wordplay (1991) sets seven extracts from Lewis Carroll’s Alice through the Looking Glass and Michael Ende’s The Neverending Story. The texts have been altered via “randomly” swapped syllables and backwards spellings so “only the symbolic meaning remains”.[1] Chin writes that each movement is “constructed around a controlling pitch centre”, and that “all seven […] are fully differentiated from one another in their means of expression”, each portraying a different emotion or situation.[2] This analysis will address each movement in terms of these distinct moods using a flexible array of techniques, including post-Schenkerian voice-leading graphs and set theory (with a particular focus on symmetrical harmonies). This is by no means an exhaustive analysis, and some movements will get more attention than others. But, as I hope will become increasingly clear, varying degrees of resistance to traditional analysis are inherent to these miniatures' make-ups. Ambiguity is part of Chin's game.

I. Hide and Seek

The first movement is an interplay between stasis and change. It cuts between two tempi (♪=50 and ♪=92), which convey two distinct textures: exposed, sustained octave Bs and rapid, contrary-motion scales (figure 1). These Bs set up a pitch centre, emphasised by the soprano’s A♯s acting as leading tones in the tempo II sections. B is obscured as the movement progresses—beginning with the bowed vibraphone’s A♯-B dyad in bar 1—but will be played or sung on some level wherever tempo I is marked. The tempo II texture’s ascending and descending contrary motion patterns are treated differently by each instrument; most of their rhythms vary subtly, and no two play the same pitches or series of intervals. Figure 2 is a harmonic reduction, where the resulting rippling surface is summarised by chords in the harp and piano (shown on the top line) as well as bass arpeggio harmonics (shown on the bottom line). The middle line shows elaborations of the B-pedal, by the soprano and tuned percussion. With each return of tempo II, these harmonies shift, and the boundaries between the strata are permeable; the upper strings, for instance, move between all three. These strata, and their attendant functions in relation to the B pedal, are as much determined by gesture and texture as they are by instrumentation.

Figure 1: bb. 1-6.

Figure 2: Reduction of bb. 1-33.

The first harmony in the top stratum has been labelled “P”, and can be heard most clearly in the harp in bar 3. If the B pedal is taken as its root, this is an extended b-minor triad, a neo-Riemannian leading-tone F♯-G exchange away from the simultaneous G-major bass arpeggio, with which it shares the common-tones B and D. In terms of octave equivalency, chord P is symmetrical, and the F♯ in question is at its centre (figure 3). In bar 6, the second tempo II section, this F♯ is bifurcated into its two chromatically adjacent pitches (F and G), pivoting the triadic focus onto the bottom stratum and adding a minor seventh to it. When P is re-established in bar 10, the bottom stratum retains D, but the B drops a semitone and the F a tone. This departure from triadic harmony leaves a bare tritone, and follows the contours of a transposition of P up four semitones (figure 4).

Figure 3: Chord P.[3]

Figure 4: PT4.

In the middle stratum, the bowed vibraphone’s A♯-B dyad, which had originally occupied one side of P’s symmetrical divide, shifts into the similar sonority of sustained double-stopped bass harmonics after the third tempo II in bar 12. Mimicking the bottom stratum’s P4 transposition, it plays a C♯-D dyad, which in terms of P0, has simply been inverted to occupy the other side of the central F♯. The soprano’s sustained high E, a tritone away from the usual A♯ of tempo II, echoes the same tritone heard in the bass in bar 10. This pitch further invades P in bar 15, where it enters the piano’s harmony. This percolation of E across all three strata, in spite of being external to both P-transpositions, is represented with a dotted line in the graph.[4] The game of “Hide and Seek” that this movement plays goes beyond the surface level of revealing and obscuring the pedal B. Instruments are smuggled across strata, and single pitches can be passed across their boundaries, rising to prominence atop textures or disrupting their harmony from within.

II. The Puzzle of the Three Magic Gates

The second movement, like the first, makes use of a prominent pedal. Its D is partially prepared by a solo bass C♯ fermata before the coda of the previous movement in bar 50, and has only one departure (to diffuse neighbour-note C♯s and E♭s) from bar 68 to its re-establishment in bar 80. In spite of the eponymous “three magic gates” there are only two strata in this movement, because the percussive strings and woodwind almost always move together. The arrangement of pitches is whole-tonal, meaning that there are only two possible hexachords to flip between (WT-0 and WT-1). The whole-tonal permutation is established by the soprano at the start of the movement. Perhaps like a surface manifestation of the large-scale neighbour-note pedal motion, palindromes are invoked via such nonsense words such as “xenex” and “xenik”, which cross from one whole-tone scale to the other (figure 5). Maximally symmetrical across any tritone axis, whole-tone scales split the octave into two equally spaced groups of six and share no common tones; they can only be flipped between, and there is no “magic gate” between them (figure 6). “Xenik” in bar 57 particularly epitomises this whole-tonal dualism in its neat statement of chromatically adjacent sides, three-by-three. This shape is repeated across the movement and in different parts of the orchestra (see bars 71, 76, 96, and 106), and distinctively drawn out in bars 89-95 (figure 7).

Figure 5: Bar 55ff. Yellow=WT-0 and red=WT-1.

Figure 6: The two whole-tone hexachords

Figure 7: Soprano bb. 89-97.

While instruments tend to stay within one whole-tone side per gesture, hearing one hexachord across the orchestra without pitches from the other at any given time is extremely rare. Broadly, the winds and percussive strings usually employ opposite whole-tone scales to one another (see for example bars 75-77, figure 8). However, the E♭ upper neighbour motion, prominent in the soprano in bar 73 (in the same register as and semitonally adjacent to the prominent “percolated” E mentioned in my analysis of the previous movement) disrupts what would otherwise have been a rare moment of total WT-0 security. A descending chromatic scale follows, seemingly flattening whole-tonal distinction into one integrated (and indeterminate) string of equal semitones. Chin highlights differences in individual voices by writing unisons and departures from them throughout this movement, either through string glissandi (see the voice exchange between violin and viola in bars 69-70), approximate canons staggered by extremely small rhythmic units, such as the descending octaves through the percussive strings in bars 75-76 (figure 8), or capricious semitonal foils of unisons, such as the harp versus the mandolin in bar 97 (figure 9).

Figure 8: bb. 72-77. Green =WT-0 and pink=WT-1.

Figure 9: bb. 97-98.

Amid all of these blurred whole-tones, D is being surreptitiously established as a tonic. The voice-leading graph in Figure 10 shows A being treated as if in dominant preparation from bar 100, where the piano and harp make a low I-V gesture of D-A. Six bars later, the coda is signalled by a strikingly unanimous statement of WT-0 harmony throughout the orchestra, implying resolution, and accompanying a final statement of the “xenex” motif by the singer (Figure 11). Periodic timpani As continue dominant preparation underneath the D-pedal until a prominent V-I motion in bar 114, while a sustained bass C♯ (the first WT-1 pitch to disrupt bar 106’s unanimous WT-0 statement) is played by the bass in a sustained leading-tone gesture reminiscent of the first movement. In bar 115, along with D♯ in the harp, it is the last non-D pitch to be heard. Perhaps the third “magic gate” denotes these moments in which Chin puts pressure on the dualist whole-tone system, finding equivocal ways “out”, both by bifurcating D into two unresolved semitonal adjacents or by throwing wholetonality’s symmetry off by introducing a perfect fifth. Both approaches could be seen, hermeneutically, to symbolise the opening of gates.

Figure 10: Reduction of the second movement.

Figure 11: Coda from b. 106.

III. The Rules of the Game: sdrawkcaB emiT

The first irony of the third movement is that, in spite of its backwardly written title and unlike the previous movement, it exhibits no true palindromes. The score is full of implied palindromes and other unifying techniques, but they are almost all somehow thwarted. The voice’s first and last entries, for example (bars 125-26 and 220-223, figure 12), have near-identical pitch- and interval-structures, but the top G is altered by a semitone. The score, a facsimile of Chin’s manuscript, fastidiously lays out this movement alone with exactly eight bars on every page. It has a very easily locatable midpoint at bar 172, which is not in fact where the second section begins. The beginning of the second section is actually at bar 177, signalled by the soprano re-ordering (but not reversing) her opening pitches, which the bass re-orders again from bar 180 (figure 13). If this movement only seems palindromic in the superficial shapes of its lines, this begs the question of what the “rules of the game” might actually be.

Figure 12: Voice’s first and last entries.

Figure 13: Beginning of the B-section.

Allusions to unity abound. The piano plays a short-lived canon between hands in bars 181-83 (figure 13), but this is a rare example of overt organisation in its otherwise relentless streams of freely contrapuntal, completely twelve-tone triplets in both hands. Given the densely dodecaphonic counterpoint in this movement, I suggest that little insight could be gained from attempting a harmonic reduction, and the texture similarly aillusive; instruments sometimes imitate one another’s shapes or rhythms, but largely develop their own distinct material completely independently and without any strict process. The resulting densely chromatic rhythmic complexity, thick with rising and falling figures or contrary motion implying inversion or retrograde, perhaps this movement could be considered to be a kind of pastiche of the techniques and “rules” of the Second Viennese School.

IV. Four Seasons in Five Verses

Like the first movement, the fourth alternates between two tempi and their attendant textures, which are separated by fermatas. The texture attached to tempo I (♪=60) is dense, with low percussive-string chords and woodwind trills (alto flute is used, and the brightly timbred oboe and mandolin are tacet throughout; figure 14). It accompanies whispered verses—one for each season. Wordplay derives from the rejigging of singular letters, to imply other words in a sort of pidgin German. For example “im Wint wen-es-scheneit” (perhaps, “in wint’ wen-it-sunows”) becomes “im Sommer we nis scheint” (“in summer whe-net shines”). The harmony in these sections is generally static insofar as it all derives from the nonochord 9-9 (figure 15). Like the P-chord in the first movement, this chord is symmetrical around F♯.

Figure 14: The two textures.

Figure 15: Nonochord 9-9.

The eponymous “five verses” are the tempo II sections. They exhibit a glassy counterpoint between flute, upper-string harmonics, and the singer whistling. The subsets of four adjacent semitones on either side of chord 9-9’s symmetrical axis, set 4-1, are rendered linear in these sections; each voice realises a reordered four-note chromatic scale. The counterpoint, expressed in the voice-leading graph (figure 16) becomes increasingly complex from verse to verse as voices are added and their lines extended. In verse 1, for instance (bars 227-31), the flute and viola play the same transposition of the set (C to D♯) while the violin plays its tritone counterpart (F♯ to A, figure 17). Their different orderings of the set create an austere counterpoint largely based around perfect fifths. In verse 2 (from bar 234), the viola stays in the same transposition, the violin transposes up a semitone, and the flute up a tone. They now therefore no longer move at tritone poles, but as a trichord set 3-9 (figure 18). This set is in turn spelled out by the last two parallel motions of the counterpoint (figure 16).

Figure 16: Reduction of the fourth movement.

Figure 17: Sets in verse 1.

Figure 18: Verse 2’s transpositions of 3-9.

Verse 3 (bars 239-42) continues to structure the intervals between its voices around rotating trichord sets. Its surface is complicated, however, by the chromatic lines being extended to five pitches. The added contrapuntal scope of this is exploited by Chin’s use of cross-rhythm in the third verse, particularly between the viola and soprano (figure 19). From here onwards, the textures of the tempo I nonochord sections start to permeate the verses, with open fourths from the percussive strings mirroring the open fourth in the new trichord, 3-8 (figure 20). In turn, the tempo I that immediately follows opens out onto a less-dense-than-usual WT-0 subset of the nonochord, to luminous, perhaps “summery” effect. In the fourth verse (bars 244-47), however, the trichord process breaks down. Different lines have different intervallic content: the viola spans a fourth but the flute only spans a tone, and while the violin and soprano both span minor thirds, the soprano no longer completes a fully chromatic set, which imbalances her voice’s intervallic content. Progressing from the austere tritone poles of “winter” to a vibrant proliferation of complexity in summer seems to set into motion an autumnal decay. Rather than renewing the cycle of another year by inserting a new tempo I section, the nonochord penetrates the counterpoint of the fourth verse, and gives rise to a fifth.

Figure 19: Verse 3.

Figure 20: Trichord 3-8.

Throughout this movement, the bass occupies its own stratum. Seemingly impervious to the events above it, it cycles through its own subset of the nonochord, assembled from the same pitches as the dyads that surrounded the F♯-C pole in the first movement: B♭-B-C♯-D (figure 21). Towards the end of the fifth verse, however, its original pitches percolate into the percussive string tremolo (bar 252) and it shifts onto a new semitonal motion: D♯-E. These pitches imply an expressive first-inversion quality under the strikingly new B-major- and C-major-triadic sonorities of the harmonica, and the now totally diffuse and fragmented whistling counterpoint in the upper voices fades away into obscurity (figure 22).

Figure 21: Bass set.

Figure 22: End of verse 5.

V. Domifare S

When the function of the fourth movement’s fifth is revealed to be the preparation of triadic harmony for an attacca into the fifth movement, Chin makes a further revelation: that the fourth movement is not, in fact, at the centre of this song cycle’s seven. Like the thwarted palindromic centre of the third movement, or the “four seasons” being told in “five verses”, the fifth movement exploits formal asymmetry to dramatic effect. This culmination of the fourth movement’s seasonal decay is so explicitly in D major by the standards of post-tonality that it unequivocally marks a climax. The title refers to the text, which mimics solfège syllables (although, characteristically for this piece, divorces them from any compositional system) in an overt topic of what Lawrence Kramer might describe as “songfulness”.[5] Read backwards like “emiT sdrawkcaB”, as its capitalised S implies, it also invokes “serafim”; the heavenly and otherworldly.

From a lone triangle tremolo, D is established by the gradual addition of the other pitches of its major arpeggio, in hushed, repeated cycles (figure 23). Atop, the soprano sustains the dominant, before her downward arpeggio is marked by the entry of a double-stopped tonic pedal in the bass, and echoed canonically in the woodwind (figure 24). This texture will remain constant for the rest of the movement. Its harmony is almost entirely horizontal. Through-composed, this movement cycles between this arpeggio line and a secondary, V-implying A-G♯-E line (first heard in bar 264, figure 25). Both lines are led by the soprano and mimicked across the orchestra, and harmonic motion is derived from the gradual unravelling of the D-major stability which they imply.

Figure 23: The opening of movement V.

Figure 24: The texture is established.

Figure 25: Secondary line, implying V.

The unravelling process is initiated by the simple addition of pitches; once a line has descended its functional arpeggio, it might continue to taper off. Figure 26 shows the soprano enacting this unravelling in bars 268-72, and a comparison between the third and sixth pages of this movement demonstrates the extent to which harmonic ambiguity increasingly sets in (figure 27). The harmony is more fundamentally overturned, however, in bar 282, where the bass shifts from its constant tonic pedal onto B♭ (figure 28), and then E♭ in bar 290, suggesting that B♭ served something like a secondary dominant function (figure 29). As the harmonic reduction in figure 30 suggests, this E♭ bass and its attendant harmonies could be conceived as a Neapolitan tonicisation of sorts, which only nebulously resolves back to D in bar 299 (figure 31), with a register transfer up to a harmonic. This semitonal closure is reminiscent of the second movement’s “bifurcated” D tonic, with its C♯-E♭ gates; resolved only by implication.

Figure 26: Additional pitches in the descending line.

Figure 27: Increasing harmonic ambiguity. Pink=arpeggio pitches, green=secondary-line pitches, and yellow=ambiguous.

Figure 28: B♭ bass.

Figure 29: B♭ bass resolves onto E♭.

Figure 30: Reduction of the fifth movement.

Figure 31: Nebulous resolution of the Neapolitan.

VI. The Game of Chance

The sixth movement, like the fifth, refracts tonality horizontally. The soprano recites a jumbled collection of letters of the Anglophone alphabet in Sprechgesang. Apart from the last (which erupts into laughter) its four strophes all end with “Z”, followed by at least one beat of silence. In strophe 1, the soprano establishes E through repeated D♯ leading-tone motions (figure 32). Her initially E-major scale from bar 312, however, culminates in a transposition of this figure a fourth lower, now implying B in the manner of a dominant in bar 314 (figure 33) which is then resolved in bar 319. The accompanying harmony, in string scales and wind arpeggios, draws from set 7-34 bar 303 and its T2-transformation in bar 305, sharing the common tones of the D bass and the soprano’s E (figure 34). The unison Es that follow its reestablishment as tonic break into another iteration of 7-34, T7, in bar 323. This harmony remains until the end of the second strophe in bar 326, where there is a bar of silence, and resumes in bar 327.

Figure 32: Establishing E, bb. 303ff.

Figure 33: Leading-tone to B.

Figure 34: Set 7-34 with T2, bb.303 and 305.

This bar of silence falls at the precise midpoint of the piece, and is the kind of palindromic gesture that might have seemed likely in the third movement. While the surface of this movement is seemingly more playful, Chin ironically renders the “Game of Chance” altogether more strictly organised than the “Rules of the Game” had been. Gestures reminiscent of the iconic midpoint of Alban Berg’s palindromic second act of Lulu (1935, figure 35), with its rising and falling piano arpeggiation, can be heard in bars 312-13 and 325-26. The former accompanies the D♯ peak of the soprano’s rising and falling scale, making the same G and F natural adjustments on the way back down (figure 33). F and G reappear in the 325-26 figure as part of a strikingly similar set of pitches, now re-contextualised as part of T7, albeit somewhat unsettled by the A-B register shift (figure 36).

Figure 35: Palindromic midpoint of Berg’s Lulu.

Figure 36: T7 rising and falling gesture.

         

The third strophe (bars 228-335) is very explicitly in A major, except that its repeated G♯s, unlike the opening stanza’s A♯s, do not resolve upwards. Instead, they are immediately taken up again in bar 336 by the fourth strophe (figure 37). When it finally is resolved in bar 340, it is accompanied by 7-34 in its original transposition from bar 303 (with an added E♭, figure 38). Almost immediately, the soprano’s line responds in kind by re-establishing E in a recapitulatory motion, its D♯ leading-tone an enharmonic respelling of the added E♭ from bar 303. Rising and falling motions permeate the orchestra, and the harmonic organisation disintegrates into a twelve-tonal flurry. Culminating in a top B—residue from the “dominant” in bar 315—the soprano’s pitchless laughter is dissipated amid an upper-strings-to-harp canon which ricochets across every pitch except F (figure 39). The D♯ leading tone remains fundamentally unresolved in its enharmonic E♭ bass form.

Figure 37: Unresolved G♯s.

Figure 38: Resolution to A with 7-34.

Figure 39: Recapitulation.

VII. From the Old Time

As its name suggests, the first movement harks back to the first, structured around divergences from and returns to held unison Bs. This time, the texture is markedly more integrated. All of the percussive strings and percussion are tacet, so the only instruments used are those that can sustain a pitch fully, without it decaying, and they all play most of the time. While the soprano’s departures are from B to B♭ (an enharmonic twist of the first movement’s A♯), there is florid, dense ornamentation in all of the other parts between these unisons (figure 40). The reduction in figure 41 summarises the harmonies of these departures from B.

Figure 40: Departures from unison B.

Figure 41: Harmonic reduction of the seventh movement.

B♭ is the most disruptive element in this harmonic landscape. In bar 355, it imbalances the symmetry of what would otherwise have been a D-G♯ pole. The harmony in bar 359 is WT-1 apart from its B♭, the enharmonic equivalent of which pierced the foreground in the previous bar with a sudden major seventh (figure 42). It is the only constant pitch throughout the most extended departure from B in bars 370-76, and when F♯ bass in bar 365 seems to prepare a cadential motion, it foils it with its forceful fff entry in bar 370. As its spelling in this movement suggests, pitch class 10—no longer A♯ but B♭—is also no longer simply a leading tone. It almost seems like it could be the tonic after all in bar 389, the bass F implying a second inversion dominant. Unresolved ever since the first movement, in spite of all of these moods and methods, this pitch is “from the old time” in the sense that it is the “acrostic” that drives through the heart of this song cycle.

Figure 42: B♭ disrupts WT-1; A♯ pierces the foreground.

Figure 43: The final bars.

This inner workings of Acrostic can be highly elusive because its surface colours and textures are so integral to its potency. There are harmonic processes in this piece which, like the randomly rearranged syllables of some of its texts, are literally indecipherable, because they are not “ciphers” for anything. In the dramatic, story-book excesses of Acrostic’s moods, gestures implying certain harmonies and compositional processes—whole-tones, for instance, or canons—where the stricter details of pitch are subtly awry, can themselves often be as significant as that which is disturbing them. This analysis has attempted to uncover just some of the ways in which this music can embrace ambiguity, not a transitory journey from certainty to certainty, but a positive site for playfulness between them.

Bibliography

Baker, James M. "Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory." Music Analysis, no. 2 (1990): 177-200.

Kramer, Lawrence. ‘Between Words and Music: An Essay on Songfulness’, Musical Meaning: Toward a Critical History. Berkeley: University of California Press, 2001: 51-67.

Michael Brim, and American Council of Learned Societies. Janácek as Theorist. Studies in Czech Music; No.3. Stuyvesant, N.Y.: Pendragon, 1994: 78ff.

Straus, Joseph Nathan. Introduction to Post-tonal Theory. Englewood Cliffs, N.J.: Prentice Hall, 1990.

Score

Chin, Unsuk. Akrostichon-Wortspiel = Acrostic-wordplay: Seven Scenes from Fairly-tales for Soprano and Ensemble. London: Boosey & Hawkes, 1996.

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[1] Chin 1991, 2.

[2] Ibid, 2.

[3] For these diagrams see Joseph Nathan Straus. Introduction to Post-tonal Theory. Englewood Cliffs, N.J.: Prentice Hall, 1990.

[4] I use the term “percolate” to have similar resonances to Janacek’s theory, but attach it to a singular pitch rather than an “invading” chord. See Michael Brim Beckerman. Janácek as Theorist. Studies in Czech Music ; No.3. Stuyvesant, N.Y.: Pendragon, 1994: 78ff.

[5] Lawrence Kramer. ‘Between Words and Music: An Essay on Songfulness’, Musical Meaning: Toward a Critical History. Berkeley: University of California Press, 2001: 51-67.