Analysis of a work of art as an academic discipline invariably addresses the investigation of a completed (or, in some cases, partially completed) object. For composers this has been – and remains – an important activity because the processes involved necessitate asking the questions ‘why’ and ‘how an artistic decision was made’: the ‘why’ leading to a consideration of the aesthetic and historico-cultural aspects of what is under investigation, and the ‘how’ necessitating an examination of the ‘workings’, structures, and processes of the object itself. It is useful, I suggest, for composers to adopt an approach which synthesises these elements.
‘Deep’ analysis can be an important skill for a composer. Theory was once considered innovative and creative in the minds and writings of figures like Jean-Philippe Rameau, Hugo Riemann, Heinrich Schenker, Arnold Schoenberg, Paul Hindemith, Milton Babbitt, and others,1 but analysis often comes with a danger that preconceived notions regarding inherited practice(s) either precede, or go hand in hand with, the analytical approach in question, tying us down to a limiting aesthetic and technical frame. Rather, I suggest that any analysis must take an individual approach, where notions of conscious or intentional objective context or historical style are not necessarily part of the solution. When analysing musical works – including my own – I think about a sample of musical ‘DNA’ which proceeds ‘outwards’ to create a whole from a small fragment. Of course, music analysis inevitably requires such an approach when working ‘forwards’ in detail but, in my scenario, there is no a priori whole from which to work ‘inwards’. In other words, the necessary process is (re)-constructive, not de-constructive.
Two Approaches to a Major Third
Although many composers have claimed that a movement or work appears to them as a whole, often with indescribable immediacy, there are many examples of works being developed from a sample of musical ‘DNA’; the best known perhaps being J. S. Bach’s Musical Offering, which presents a series of compositional schemes (fugues, canons, etc.) derived from the so-called Royal Theme given to him by Frederick the Great. For this chapter, I want to take as the nugget on offer not a fugue subject, but one interval class: the major third. Devoid of context (and, by implication, ‘meaning’) the major third has to be considered for our purpose as being comprised of four equal semitones, and so will be referred to here as ‘interval class 4’ or ic4.
In terms of notes, several considerations arise: ic4 could be considered as one element in a number of scales/modes, or it could be the lower interval of the major triad or the upper interval of the minor triad. It might also be considered as the fourth and fifth harmonic partials above a fundamental pitch, depending on decisions concerning functionality and context. For our purposes, we are not considering the deeper acoustic potential of the dyad – for example the results of combination tones and their acoustical and structural effects – fascinating though this would be. However we proceed, context and function will need to be established and, in order to demonstrate the significance of these, we will use two case studies to think about how a composer might reconsider their intervallic approach as the compositional process unfolds.
These case studies will be two relatively brief pieces for piano, selected as springboards – not necessarily as models – for study, the word ‘brief’ itself leading to consideration of timescale and duration in relation to content. These examples will be Voiles, the second piece in Book 1 of Claude Debussy’s Preludes (1909/10), and the second piece of Arnold Schoenberg’s Sechs Kleine Klavierstucke, Op. 19 (1911), which are effectively contemporary with one another: a vital factor on our investigative journey. In both, the initial sound heard is our chosen ic4: in the case of Voiles, the notes in descending dyadic pair order are those of the whole-tone scale beginning on G♯ (Example 2.1); in the Schoenberg, the invariant dyad consisting of the notes G4 and B4 (Example 2.2).
Example 2.1 Claude Debussy, ‘Voiles’ (1909/10) from Preludes Book I, bb.1–9.
Example 2.2 Arnold Schoenberg, Sechs Kleine Klavierstucke, Op. 19 (1911), ii, bb.1–4.
Debussy presents ic4 as the first sound in what turns out to be a whole-tone scale, presented as a descending chain solely consisting of that interval class. It should be noted that the notational difference between G♯ and A♭ throughout is the result of local voice-leading rather than enharmonic function. Initially, there is no wider context, and it is reasonable to assume that a listener in real time – but not the performer, a matter which we will come to later – has no point of reference within which to situate what is heard. There appears to be no implied, or actual, harmonic root; a situation reinforced by the lack of a bass sonority which, in conjunction with the absence of a (regular) pulse, results in the ‘sound object’ being experienced in a sonic vacuum. It does not merely exist, but creates the space surrounding it by its energy, shape, and density, rather as Paul Klee illustrates the case of a line in space at the beginning of his Pedagogical Sketchbook (Figure 2.1).
Figure 2.1 Paul Klee, Pedagogical Sketchbook (1925), 20.
How then do Debussy and Schoenberg establish context and function? Debussy repeats the opening descent registrally, with a subtle metrical shift and augmentation completing a ‘classical’ underlying four-bar opening unit. Schoenberg’s use of the ic4 dyad offers a regular pulse, although, if listening without looking at the notation, the metre is (perhaps intentionally) unclear. There is an opening four-bar unit with an extension in the fourth bar, as in Voiles, but where for Debussy the material appears to be both background and foreground, in Schoenberg’s piece we realise that the left-hand dyad is an accompaniment to the entry of the right-hand melodic line on the last beat of the second bar. Where Debussy creates a static ‘bubble’ consisting of a pure ic4 descent, Schoenberg offers an ostinato ic4 accompaniment which acts as structural upbeat to his well-defined, downward-arcing melody. The latter begins with an upbeat ic3 dyad (D6/B5) which, although completing the G major triad vertically in conjunction with the G/B ostinato, not only bursts the static ‘bubble’, but also leads directly onto an F♯ an octave-and-a-half lower. This wide, downward sweep creates melodic and harmonic tension, which implies gestural and harmonic/melodic continuity and opens up the possible need for an answering phrase. Debussy’s equivalent move after the first four bars of arithmetic – if not musical – symmetry is to extend his ambitus by introducing low B♭1, thereby creating a registral gap between left and right hands of two-and-a-half octaves. To describe this as establishing a whole-tone collection ‘on B♭’ would be accurate, but as yet functionally meaningless.
Vertical versus Horizontal
There are four opening bars in each piece, both initially presenting ic4 as an important sonority. Until bar 5, Debussy has avoided any sound below C4 and has used ic4 only, whereas Schoenberg writes down to A♭3 but only as the last note of his downward melodic arc; the G4/B4 dyad remaining, so that the right hand has crossed the ostinato dyad in the left, and new interval classes have been introduced. Where Debussy sets the boundaries of his sonic space, Schoenberg does not, his ostinato behaving as a literally ‘obstinate’ invariant middle register accompaniment above and below which the arching melodic line is heard, introducing a regular pulse from the outset. Debussy does something similar in the fifth bar (the goal of the initial four-bar structural upbeat) with the B♭1 introducing a sense of pulse by means of a rhythmic pattern similar to Schoenberg’s ostinato. Whereas the sense in both pieces is of a potentially continuous, static sonority being interrupted, Schoenberg’s invariant dyad in fact eventually descends in the final three bars, offering a sense of movement, before it cyclically returns to its initial registral position at the piece’s closing cadence. Debussy does also create some contrast and a brief sense of movement in a pentatonic passage around the golden section but this leads to a slightly developed recapitulation which re-confirms the static nature of the music.
Debussy expands his aural landscape by introducing a middle register octave sonority as a textural layer, with the upper register soon being re-introduced over this as a sort of upper stream. The use of a symmetrical mode of limited transposition enables him to achieve this sonic expansion, and as the higher register repeats the initial material rhythmically and gesturally, we hear three distinct superimposed levels. Symmetry is structurally – and perhaps even viscerally – experienced in the middle layer’s A♭3 and C4 on either side of the central B♭3, which itself doubles the bass note, reinforcing the new octave sonority. We soon hear augmented triads, but with the outer pitches doubling one another and the chordal boundary retaining the octave sonority with which we have now become familiar, the two inner voices continue to emphasise the ic4 sonority. The layered result is heterophonic. There is no ‘harmony’, but a specific and limited corps sonore.
After extension of the G4/B4 pedal in the fourth bar, Schoenberg offers a multi-levelled surprise. A composer presented with only the opening four bars might imagine a wide range of possibilities compared with those in the Debussy extract: where Voiles has offered variety produced from homogeneity, Op. 19/ii does not. If we were to proceed bearing in mind a ‘classical’ Austro-German approach we might consider creating a counter-statement, perhaps transposing the invariant dyad up one octave and (re)-writing the melodic line for the left hand producing invertible counterpoint. I am not suggesting this as an artistically viable solution, but as a way of clarifying the essential differences between our two models, and the process of thought in conjunction with a basic idea. In Debussy’s case, he retains the idea of unity defined a priori by the choice of limited mode, whereas Schoenberg’s melody and accompaniment combined create a teleological gesture with local harmonic tension and release in the apparent absence of either a ‘steady state’ or functional harmonic or motivic grammar. The opening statement appears to invite a balancing/answering sentence and closes musically with the effect of what, in conventional terms, might be heard as an interrupted or imperfect cadence. However we interpret this, there is no equivalent sense of closure in Voiles due to the overlapping of, and increase in, layers which contribute to a sense of seemingly inevitable continuity.
The golden ratio of both pieces is simultaneously an arrival and a turning-point.2 Debussy achieves this with a mode switch, Schoenberg with the only hexachord thus far stated, as a vertical aggregate. Given our knowledge of both composers and their working methods, it is likely that this moment in Voiles was planned, but perhaps unlikely in the case of Op. 19/ii. Debussy’s ‘modulation’ to the pentatonic collection ‘on’ B♭ answers – retrospectively – why this has been the pedal bass note since bar 5, as the pitch classes available above it include D♭ and E♭, introducing ic3 as a significant sonority (after the pervasive use of ic4) by using this particular transposition of the whole-tone collection. These are the two complementary pitch class sets which are omitted from the modal transposition on B♭. In contrast, Schoenberg’s piece introduced ic3 in the second bar, which, as described already, completes the triad through a B♮, shared (at the octave) between the right-hand ic3 and the left-hand ic4 invariant dyad. Contextual function and ‘meaning’ of the simple ic4 interval, as we consider them alongside the planning and instinct of both composers, are now coming to the fore as compositional premises.
Climaxes and Resolutions
Both composers create long-range structural coherence in similar fashion by means of registral emphasis. Debussy, having emphasised D6 as well as introducing seemingly incidental semitones, makes us hear (retrospectively) the music ‘resolving’ into the pentatonic section; Schoenberg, likewise, stating E6 significantly as F♭, so that we hear this contextually as an upper neighbour to D6 that we earlier encountered as the upper dyadic pitch of the initial melodic arc, and will do so again at the close. Schoenberg’s hexachordal climactic bar is the only one in the piece in which the invariant ic4 (G/B) dyad is omitted; this not only emphasises the importance and uniqueness of the moment, but also creates structural tension as we instinctively await the return of the ostinato. The return duly occurs in the next bar at its expected registral level, but now ic4 is also heard as a descending whole-tone scale with a significant semitone ‘twist’ onto C3/E3 in the final bar. Various analysts have put forward background tonal theories about this piece, and a compelling idea is that the closing low dyad should be viewed as the first and third degrees of C major (a finally achieved tonic goal) above which the invariant dyad of G4/B4 act as an implied chord V, itself forming the lower third of a vertical aggregate with the pitches (reading upwards) E♭5, F♯5, B♭5, and D6 that form part of the closing hexachord.3
The compositional question here is: how does Schoenberg achieve a sense of closure? Although it is feasible to hear the closing collection of the piece ‘vertically’ as a (tonic) 15th over C3, it is, I suggest, preferable to designate it as a hexachordal aggregate, the latter defining what is a conjunction of registral layers, and the function of which being resolution. The lowest two notes are, as established, the invariant G4/B4 dyad at its original pitch level. The uppermost ic4 dyad, B♭5/D6 ‘resolves’ the opening melodic line’s anacrusic B♮5/D6 (which also form the upper notes of the climactic hexachord in b.6) and the axis ic3 dyad E♭5/F#5 creates the horizontal axis of symmetry. The closing sonority is therefore a conjunction of three dyads from different registral streams. In describing the presentation of the central invariant G4/B4 dyad of Op. 19/ii as an accompaniment to the melodic line heard from the last crotchet of the second bar, we signal acknowledgement of an historic/cultural source, continuing this perspective in hearing the fifth and sixth bars of the nine-bar whole as a concentrated development towards the climactic hexachord in the second half of bar 6, the closing three bars functioning as a condensed recapitulation and coda. Bars 5 and 6, involving the absence of the invariant dyad in the latter, have, in conjunction with the lower-register climax hexachord, created the required tension to perceive the final three bars as fulfilment of registral and tonal space and its cadential, stabilising effect.
A potentially fruitful, abstract approach to compositional possibilities inherent in our ic4 dyad could be the result of considering what we may hear as the possible background pitch class sets in Op. 19/ii. Using Alan Forte’s analytical system,4 we can see that G, B♭, B♮, D, E♭, F♯[0,3,4,7,8,11] has a horizontal axis of symmetry between [4,7] dividing the hexachord into two trichords related by inversion. We then consider two tetrachords G, B, C, E♭ [0,4,5,8] and G, B♭, D, F♯[0,3,7,11], which we find share the same designation, [4–19] in Forte’s table in addition to the two surface-level hexachords, the GS marker [4,5,7,8,10,11] and the closing cadential sonority already cited as the background and which we now hear as the goal of the music [0,3,4,7,8,11]. The ‘best normal order’ (cyclical permutation followed by transposition) of the former offers [0,1,3,4,6,7], for the latter [0,1,4,5,8,9] which reveals the invariant trichordal collection [0,1,4] giving three of the four pcs of the tetrachords. Whatever the pros and cons of set theory, there is undoubtedly more than enough contained here to whet the appetite of any composer, particularly as our compositional DNA has already opened up a wide vista ranging from the non-contextual dyad to the consideration of material within a defined historico-cultural context. In addition, [0,1,4] is the clearly audible basis of the music at surface level.
Voiles, as has been observed, marks its climax with a modal switch before closing with a clearly audible third section in which the restoration of the whole-tone background and surface is influenced by the gestural character of the pentatonic section as the music leads to its close, but is it, in the sense that we observed in Op. 19/ii, an ‘ending’? Where Schoenberg invites a dual perspective hearing (background V-I with C as ‘tonic’ in conjunction with structurally functioning registral layers) Debussy, significantly, does not. In contrast, and despite the initial statement veiling the implied symmetry of two two-bar phrases, the music creates its own parameters ex nihilo. The third part returns to the whole-tone orbit of the first section, now incorporating the textural and gestural features of the pentatonic climactic passage. Once more, Debussy presents a paradox: a recapitulation influenced by aspects of the preceding development was a common feature of the mature Classical style but, in this context, the effect is one not so much of stable return as of continuing ‘motion within stasis’ leading to an enigmatic ending. The C4-E4 ic4 dyadic close returns the music to the same pitches in the same register as at bar 5 but now, rather than B♭1 entering beneath, this pedal note has been withdrawn, reversing the procedure both literally and gesturally. Important, too, is the relationship between B♭ and C (ic2) and B♭ and E (ic6), the two intervals that, with the fading C and E (ic4), are the constituent interval classes of the whole-tone scale. A sense of circularity rather than recapitulation underlines the feeling of stasis, offering a sense of wholeness if not completion in any cadential sense.
One final point underpins the difference between compositional strategy in these two pieces. Whilst Schoenberg’s piece is written for the piano, it is not essentially ‘piano music’ in the sense that Debussy’s is. This is not meant pejoratively, but culturally, relating to the two distinct lineages of keyboard music that stem from J. S. Bach in Germany and his slightly older contemporary François Couperin in France. Bach’s music ‘works’ in various arrangements across genres and styles, driven by the pitches themselves and their interplay with one another. With François Couperin (and his uncle Louis, amongst other French seventeenth- and early eighteenth-century keyboard composers) this is not the case, with the nature of sound evolving from a specific source being the key driving compositional intention. This continuing tradition – evident in the work of French composers from the Baroque claveciniste via Berlioz, to Messiaen, Boulez, and the Spectralists – lies at the heart of Voiles, its constituent harmonic and sonic layers exploiting use of the sustaining pedal to create the veils of sound suggested by the title. In Schoenberg’s case, where the dyad is revealed as accompaniment to a melodic line (which would itself suit a clarinet or violin, for example) a different approach is revealed. The presentation of the idea is heard as predominantly linear, the individual elements creating the sound world rather than existing within it, as in Debussy’s case.
Conclusion
Using a given sample of musical DNA, it is possible to work forwards intuitively. During the compositional process I encourage composers to analyse what they have notated, using their first draft as an a priori template from which to extract and mould material further. I am not recommending that a theory is developed; rather that what has been ‘fixed’ so far is examined for coherence, cohesion (or not), shape, proportion in relation to potential duration, and use of register as a possible structural parameter amongst other possibilities. The approach outlined in this chapter supports this examination and helps offer a way for composers to develop and ‘unfold’ their material. Fruitful further examples of this in the writings and music of other composers include Per Nørgård (b. 1932), whose algorithmic process applies these ideas initially to pitch generation before application to other parameters,5 and George Perle, whose essay The First Four Notes of Lulu discusses the opening tetrachordal structure of Berg’s eponymous opera in relation to his own music and that of Béla Bartók.6
Pitches alone, as we initially posited, are ‘meaningless’, but once we begin to examine or create a context – such as the possible lingua franca and body of common practice underlying the musical syntax of a particular era and cultural climate – the framework becomes ever broader, and we can dig further into matters of manner and style and consider individual approaches to parameters ranging from quality of idea to context and practical-imaginative ‘balance’. Generalised pitch classes are interpreted and experienced as individual notes (i.e. sounds in real time) in relation to one another within a network of compositional possibilities (which include register, metre, duration, and rhythm) implying an a priori set of conditions. If there is no pre-ordained organisational principle, each parameter contributes to the formation of compositional syntax a posteriori. Throughout the entire creative process from conception to completion, the relationship between micro and macro aspects of the whole is essential for the creation of a work. The manner in which this is accomplished is a matter of a composer’s natural individuality – not intentional originality, which is a false premise – in conjunction with aesthetic, cultural, and historical conditions. While issues such as the difference between structural levels (i.e. function in relation to decoration) and the relationship between pulse, meter, and rhythm have not been addressed, what has been suggested in this chapter may, I hope, act as a springboard for invention to a composer setting out on their creative journey.
