[…] indem wir dem Leben von unserem Leben geben, das nur durch die geringe
Verbindung, die wir mit ihm haben, vorläufig für uns tot ist.
Arnold Schoenberg[1]

Es ist somit nicht allein die Hingabe, der Genuß, den wir vom Meisterwerk abziehen,
wir empfangen darüber hinaus Vorteile für die Kräftigung unseres Lebens.
Heinrich Schenker[2]

1. Once More on the Organic in Music

After decades of standing for regressive or repressive ideology in the eyes of many music scholars,[3] the notion of the organic in music has taken on new pertinence in light of recent research on non-human cognition and networks in biology, ecology, and philosophy. The organic in music “challenges us to think anew about what our bodies, our sociality, and our creativity share with other living entities and the ecologies in which they are enmeshed.”[4] As Holly Watkins proposes, “the problem is not with the thesis that certain musical processes create a semblance of the organic, but with the models of the organism brought in to give content to that semblance.”[5] Above all, the model of an organism producing itself out of itself and forming a unity of parts and whole, ubiquitous in nineteenth- and twentieth-century organicist discourse, is inaccurate and hence potentially repressive, because “the ‘parts’ of organisms […] are not self-contained, independent units”; rather, according to Niklas Luhmann’s systems theory, “each so-called part of the body is a meeting place for interconnected but functionally independent systems,”[6] and these bodily systems can be further coupled with psychic and social systems. All such systems operate and maintain themselves through recursion, the iterative looping of output back to input.[7] From this it follows, as Watkins argues, that music, a “subsystem of the social system of communication,”[8] can evoke the organic (the bodily and the psychic)[9] through the “internal recursiveness” of musical works, their external “recursiveness vis-à-vis other music” (that is, their intertextuality), and – crucially – “the knowingness the music displays toward its own operations,” as it were, by influencing its recursion from a particular standpoint.[10]

Despite Watkins’ recognition that life, even just bodily speaking, involves multiple systems, when it comes to interpreting music in terms of life, she analyzes only a single system of “melodic and rhythmic discourse,”[11] and – following the lead of other writers on musical discourse[12] – focuses on “referring back to and elaborating material already presented” or already existent as its mode of recursion.[13] In a parallel way, Stefan Rohringer analyzes music in terms of a single Luhmannian system of tonality.[14] By way of contrast, I adopt the premise that music evokes the organic most vividly not through recursive processes in individual systems but through the as-if intentional integration of such processes in multiple systems, of which I concern myself particularly with the harmonic, contrapuntal, and formal domains (or, more precisely, the motivic).[15] For in a piece featuring these domains (especially in eighteenth- to early-twentieth-century music), every note generally has at least one coherence in at least each of these systems,[16] somewhat as virtually every part of the body involves, say, the cardiovascular, musculoskeletal, and nervous systems. If Arnold Schoenberg is right that every detail of a work reflects the whole, just as wherever one cuts the body, blood comes out,[17] then it is also generally true in such cases that the flesh is injured and pain ensues.

This study bears comparison with one by Ariane Jeßulat, who somewhat similarly finds that an impression of the organic arises through the interaction of counterpoint and form,[18] but unlike Jeßulat I find it necessary to offer correctives to both the theories that I draw on and their reception. In particular, I build on and critique the organicist theories of Arnold Schoenberg and Heinrich Schenker,[19] which similarly concern the harmonic, contrapuntal, and formal domains.[20] And I explore this direction through an analysis of Bach’s Prelude No. 7 in E major from book 1 of The Well-Tempered Clavier, BWV 852, a singular piece that billows forth like an unfathomable blossom. Analysis of Bach’s prelude concretizes and supports the proposal that a piece of music can evoke – perhaps even provoke? – the organic through recursive processes in the harmonic, contrapuntal, and formal domains not only individually but especially in combination.

2. Harmony, Counterpoint, and Form

Each of these domains has its own mode of recursion that focuses on a different dimension of an abstract musical space, as outlined in Example 1, such that a piece’s logical paths of recursion knit together, helping it to fill out the form as if it were a body. The ‘harmonic domain’ is a world of abstract relations of tones, mediated explicitly or implicitly by generative ‘ground tones’ (Grundtöne) – fundamentals, roots, and tonics.[21] That is to say, generated partials and tones in chords, scales, regions, and ‘pitch fields’ (Tonfelder) are recursively ground tones for other tones (sometimes cyclically).[22] This domain focuses on the vertical dimension, or pitch. The ‘contrapuntal domain’ consists of voice-leading relations and recursive transformations. This domain operates in the dimension of depth, from background to foreground.[23] The ‘motivic domain,’ or – loosely speaking – the ‘formal,’ consists of association of parts through repetition and variation, especially development and unravelling, which I understand differently than many writers; I will say more about them later. (For now let me just clarify that unravelling involves ‘polyphony,’ which I am distinguishing for the present purposes from ‘counterpoint.’) This domain focuses on the horizontal dimension, or time, which is why its recursive associative processes are the most intuitive and historically the most commonly associated with organicist analysis,[24] as well as – ironically – the alternative of “‘mechanist’ analysis.”[25]

Example 1: The harmonic, contrapuntal, and formal domains and their interpenetration

But each of these domains evokes the organic in its own way through its recursiveness: unrest, contrapuntal drama, and motivic character and drama. Contrapuntal drama is relatively well understood;[26] the other two are less so, and I will have much to say about them. Yet despite their separate principles, these domains are not quasi-“empirical” parameters, where one “should proceed one domain at a time” and then add a “dimension” of interpretation, as James Webster advocates with respect to “numerous different ‘domains.’”[27] Rather – and this is a key point – like all systems, they are intrinsically interpretive, and they are best understood in conjunction, because they ‘interpenetrate’: they mediate and condition each other’s recursion. Recursion “presupposes […] not yet fully determinate possibilities,” and only the “interpenetration” of domains allows for “selections that can cut off other possibilities (more or less definitely).”[28] In music, such selection in interpenetrating domains can be understood as presenting a particular ‘musical idea’ – the content of the musical mind – somewhat as when a sculptor removes chips from all sides of a block or log to reveal a form.

Schoenberg and Schenker likewise conceive of music as presenting an idea or vision,[29] and they somewhat similarly call attention to the interpenetration of certain musical domains, as well as an “Abbreviationsgesetz,” whereby art selects from “alle denkbaren Fälle.”[30] However, their limited model of a musical organism as a self-contained unity of parts and whole prevents them from recognizing the full scope of this interpenetration,[31] which is likewise outlined in Example 1.[32] I cannot treat these matters exhaustively here, but if “ideological biases on both sides” are to “give way to a meeting on common ground,”[33] then we must try to find that common ground.

Schoenberg’s greatest insight (which will become clear when I explain unrest), is that the harmonic and formal domains are bound through ‘Grundgestalten,’ or basic shapes.[34] ‘Binding’ is “the determination of how […] open possibilities will be used, through the structure of an emergent system.”[35] His greatest oversight is supposing that variation of Grundgestalten and their motivic components accounts for the entire contrapuntal domain as well. He defines ‘counterpoint’ in a traditional manner as “die Lehre von der Stimmführungskunst mit Rücksicht auf motivische Kombination,” and he says unequivocally “daß die einzige Veranlassung, der einzige Motor für die selbständige Stimmenbewegung nur die Triebkraft des Motivs […] sein darf.”[36] Schoenberg does not recognize the dimension of depth as something altogether separate from the dimension of breadth, although he is too honest to reject the possibility altogether. Soon after studying Schenker’s writings, he speculates that “der musikalische Gedanke spielt sich im zweidimensionalen Raum der Höhe und Breite […] ab,” but then he writes in the margin: “dreidimensionalen?”[37]

Schenker’s greatest insight is that the harmonic and contrapuntal domains are bound through an ‘Ursatz,’ an originary statement – or, as revisionists have it, more generally a background of some kind.[38] For the Ursatz is itself a transformation of a Klang into a contrapuntal unit.[39] His greatest oversight is supposing that contrapuntal transformation of the Ursatz accounts for the entire formal domain as well. He posits the “Ableitung aller Formen als eines äußersten Vordergrundes von dem Hinter- und Mittelgrund.”[40] Schenker does not recognize the dimension of breadth as something altogether separate from the dimension of depth. He writes, “Der Tiefe-Zusammenhang vom Hinter- zum Vordergrunde ist auch der Breite-Zusammenhang in der Horizontale des Vordergrundes.”[41]

The greatest insight in the reception of Schoenberg’s and Schenker’s work is that certain types of formal components theorized by Schoenberg and others, such as themes, correspond with certain contrapuntal patterns theorized by Schenker.[42] The greatest oversight is supposing that there is nevertheless a “conceptual gulf” between a Schoenbergian “paradigm of association” and a Schenkerian “paradigm of derivation,” i.e., transformation, a stance that merely reproduces Schoenberg’s and Schenker’s own blind spots.[43] There is no such gulf, because association and transformation are entirely separate modes of recursion in different domains. They no more contradict each other than longitude contradicts latitude.[44] This error has needlessly constrained analytical inquiry and left Schoenberg’s and Schenker’s theories vulnerable to dismissal as overreaching formalist systems.[45] This error is closely related to a false characterization of the Grundgestalt and the Ursatz as an “initial idea” for Schoenberg and Schenker, respectively.[46] Schoenberg and Schenker strenuously reject such a conflation of elements of the idea’s presentation with the musical idea itself.[47] This exaggeration of the tension between Schoenberg’s and Schenker’s theories is also related to a gross misunderstanding of Schenker’s conception of motives, which I will address in due course.

3. Bach’s Prelude as Allegory of Vitality

3.1 Overview

Bach’s Prelude in E major, BWV 852, is exemplary and exceptional, in both of the main senses of these words. It is the sole example in The Well-Tempered Clavier of a sectional praeludium, but “its sophisticated French harmony, glorious spacing, and density of contrapuntal argument” set it apart from Bach’s earlier works of this type.[48] The most conspicuous design element is the development of the subject of the first section (mm. 1–10, a prelude) and the subject of the second section (mm. 10–25, a ricercar) into the subjects of the third section (mm. 25–70, a double fugue; Ex. 2).[49] Gestalt-form a¹, the subject of the first section, made up of two statements of motive x, is developed into a² and incorporated into Gestalt A, the first subject of the third section. Meanwhile, Gestalt-form b¹, the subject of the second section, made up of two statements of motive y, is developed into Gestalt-form b², the second subject of the third section. It has been said that the prelude is “typical of Bach’s maturity in creating a union of opposites.”[50] Nevertheless, for this particular kind of union of Gestalten, “we possess no persuasive parallel compositions by Bach.”[51] Joseph Kerman catalogues the “many free, improvisatory, ‘irregular’ features” of this fugue and notes that “the tonal equivocation in this work becomes a nice problem for the music theorist who might wish to engage with its network of nuances.”[52]

Example 2: Motives, Gestalten, and development in Bach, Prelude in E major, BWV 852

While most analyses of the piece have focused on its fugal techniques[53] or its form,[54] I take up Kerman’s invitation to explore the network of harmonic nuances, and I examine its expressive connection to the other two domains. I will show that the fugue subjects in the third section are not simply prefigured by the earlier subjects; rather, Gestalten a and b transfigure and invigorate each other in tandem with the music’s working out of its unrest and dramatic unfurling of its tonic triad.[55] The music’s recursive processes are thereby synthesized into an awe-inspiring allegory of vitality that betrays an apparent thought behind the music, a musical idea. Although I do not claim to exhaust either the musical idea or the music’s meaning more broadly, I do believe that this unparalleled piece, with its flamboyant rhetoric and irregular syntax, invites an equally audacious interpretation.

3.2 Unrest

I begin with the crucial concept of a ‘problem’ (Problem) or ‘unrest’ (Unruhe). Both Schoenberg and, to a lesser extent, Schenker discuss problems.[56] A problem is broader than what Patricia Carpenter calls a “tonal problem,” meaning a “challenge to the tonic.”[57] Although Schoenberg at times describes problems this way, this description does not differentiate between different kinds and degrees of unrest, nor does it account for problems in non-tonal music.

Very briefly, I define a problem or unrest in a basic motive or at least in a Grundgestalt as a new, remote, unclear relation of tones that leads to movement aimed at “clarify[ing] this problem.”[58] By “new,” I do not mean irregular but marked, yet susceptible to accommodation.[59] These relations are primarily harmonic but also contrapuntal on account of the way the harmonic and contrapuntal domains are bound through the background. “Der Verlauf des Stückes dient dazu, alles, was beim ersten Hören nicht erfasst werden konnte durch oftmalige Wiederholung und mannigfaltige Darstellung dem Verständnis näher zu bringen,” by means of either development or unravelling.[60] In other words, logical paths of generation (and transformation) leading out from a ground tone to the problematic tones are gradually reconstructed, together with logical paths of association leading out from a Grundgestalt, and this clarification quells the unrest. (This is what is meant by the binding of the harmonic and formal domains.) This profound principle applies to both tonal and non-tonal music, albeit in different ways.[61] In tonal music, marked problems often involve chromatic tones (marked with accidentals), and that is indeed the case in the Bach.

D in mm. 1–2 poses a problem (Ex. 3). In one respect, it is unclear whether D in m. 1 is an octave-displaced step from E, as suggested by the middleground, thus an “independent ground tone” (fundamental),[62] or whether, since E is sustained in the foreground, D is merely part of the resonance of E (that is, a missing fundamental an octave below the written bass). In this respect, D imitates the seventh partial of the ground tone E, a remote overtone beyond the ken of the major-minor system.[63] To be sure, a compound minor seventh is almost a third-tone sharp from the seventh partial, but that is why Schoenberg, Schenker, and I all call such a note an imitation rather than the thing itself.

Example 3: Bach, Prelude in E major, BWV 852, section 1, mm. 1–4

In another respect, D is the subdominant degree of the subdominant region, which is touched on in mm. 1–2. If the subdominant degree of the tonic region, being the only tone not derivable by ascending fifths, is the “representative of an earlier system,”[64] i.e., the subdominant region, then the (recursive) subdominant of the subdominant is the representative of a still more “remote” system.[65] In this respect, D is unclear, because it obscures and undermines the tonic region and could draw the music “into a foreign region of still deeper underfifths.”[66] This “centrifugal” force (leading away from the tonic) is evident in mm. 1–3, where the accented notes in the upper voice form an apparent D-major triad.[67] I am aware that this triad is contradicted by the actual chords; that is why I call the triad apparent, and why I refer to a force rather than an actual movement.

Speaking of this contradiction, in a third respect, there is a juxtaposition of D in mm. 1–2 and D in mm. 3–4, such that it is unclear which is the rightful seventh degree. Although the subtonic has been part of the gamut since time immemorial, in the context of the major mode, the leading note has always had the upper hand, and to that extent, the subtonic remains new.[68]

The reader may object that the allegedly unrestful D is simply part of a quiescenza, a schema with a -–––-scale-degree progression, which is a common opening ploy in early eighteenth-century preludes, toccatas, and the like.[69] It is indeed part of a quiescenza. But in a quiescenza, a leap from to - such as we find in the Bach is somewhat unusual, except as embellishment added to a stepwise –- motion.[70] This leap, which as I will explain shortly is extremely marked, calls attention to D as a thing in itself and not simply as a passing tone per the schema. Here Schoenberg’s protestation comes to mind: “Man löst Probleme, um eine Unannehmlichkeit aus dem Wege zu räumen. Aber, wie löst man sie? Und daß man überhaupt meint, sie gelöst zu haben!”[71]

As I will show, the piece clarifies D in these respects by presenting it as (1) an independent ground tone (even a root), (2) the subdominant degree of the subdominant region, but channeled into a “centripetal” movement (toward the tonic), and (3) being “equal in rights” with the diatonic seventh degree D.[72] And this “working out” of D versus D corresponds with the piece’s motivic drama of Gestalten a and b.[73]

3.3 Motives and Gestalten

According to Schoenberg, a ‘motive’ (Motiv) is “der jeweils kleinste Teil eines Stückes oder Teilstückes, der trotz Veränderung und Variation, als überall vorkommend erkennbar ist,” while a ‘Gestalt’ is a part of any size, but typically an immediately perceptible unit, that has a “charakteristische Eigenschaft” such as “ein auffallendes Intervall.”[74] It has been entirely overlooked that Schenker makes a parallel distinction between “der Ableitung von Tonfolgen aus dem Einfachsten” and “sofort erkennbare[n] Wiederholungen.”[75] On the one hand, many tone successions derived from the simplest element are entirely on the surface,[76] yet they have been discussed almost exclusively in terms of repetitions beyond the surface.[77] On the other hand, Schenker – like many others to this day – refers to immediately recognizable repeated Gestalten as ‘motives.’[78]

Indeed, Schenker distances his elemental, “mehr verborgene[] Wiederholungen” from what he calls ‘motives’ so vehemently,[79] that it has contributed to the widespread but erroneous beliefs that (1) there is a gulf between a Schenkerian paradigm of transformation and a Schoenbergian paradigm of association, and that (2) to discuss motives in a strict Schenkerian context, it is necessary to define them as fixed diminutions.[80] I have already argued that the first of these beliefs is unjustified. As for the second, regardless of what Schenker may seem to imply about entities needing to be diminutions,[81] he also says quite plainly (and sensibly): “jede Art von Wiederholung ist an ihrem Platze gut und fördernd.”[82] And in his analyses, it is not just that Schenker sometimes identifies motives that are not set diminutions.[83] Eighteen of his twenty-six examples of more concealed repetitions (Table 1) involve variation of diminution (sometimes slight, sometimes drastic) or even no diminution. Sixty-nine percent of his examples cannot be dismissed as aberrations. While ingrained and seemingly elegant, the notion that a Schenkerian motive should be a set diminution is undercut by his text and contradicted by his examples.

Table 1: More concealed repetitions in Schenker 1956. Those with variation of diminution or no diminution are highlighted.

For the most part, then, a Schenkerian motive (a more concealed repetition) is simply a Schoenbergian motive. The main differences are that (1) unlike Schoenberg’s motives, Schenker’s supposedly elemental repetitions are made up of still simpler repetitions in a couple of cases,[84] and that (2) unlike Schenker, Schoenberg is minimally interested in repetitions beyond the surface. I consider these differences to be oversights stemming from Schoenberg’s and Schenker’s preoccupation with association and transformation, respectively, and I look for both motives and Gestalten beyond the surface.[85]

Robert S. Hatten advocates “expanding the concept of […] Grundgestalt,” with its “emphasis on pitch and rhythm,” “by defining it in more comprehensive terms as a thematic gesture,” so as to allow “insight into […] expression.”[86] However, Schoenberg’s definition of a Gestalt is already virtually identical with Hatten’s definition of an ‘aural gesture’ as a “significant energetic shaping of sound through time.”[87] Most importantly, Gestalten are “grounded in human affect,” for their features “können auch immerhin [Merkmale] des Ausdrucks, des Charackters, der Stimmung, der Farbe, des Klanges, der Bewegung etc[.] sein,” in addition to purely musical parameters.[88] As mentioned, Gestalten are typically “in the perceptual present (typically within two seconds)” but “may be hierarchically organized” or nested in the form.[89] And a Gestalt “may be marked as thematic” but “muss nicht notwendigerweise mehr als lokale Bedeutung haben.”[90]

Because Gestalten are already gestures, Hatten’s ideas about the expressivity of gestures can supplement Schoenberg’s and (the early) Schenker’s principle that a piece of music is a drama showing the destinies of its Gestalten and motives (the smallest possible Gestalten) according to their character.[91] Hatten shows that gestures can combine into ‘tropes,’ composite signs whose meaning emerges from the way their elements are blended. Tropes must meet three conditions: there must be “(1) two incompatible or contrasting gestures that (2) ‘come together’ in a single functional location, and (3) there [must be] a compelling reason to consider the trope as motivated by a higher-level expressive intent.”[92] I will show that Bach’s prelude dramatizes one grand gestural trope, tying together the contrasting Gestalten a and b in the culminating third section for an expressive purpose that bridges the three domains: to allegorize vitality as relational, and as a synthesis of exuberance and endurance.

Gestalt a, the subject of the first section, is characterized by exuberance. This trait is projected especially by its characteristic feature: the large, ascending leap E–D in motive-form x² in m. 1 (please refer back to Ex. 3).[93] This leap is marked by pitch, harmonic, rhythmic, metric, registral, and textural accents, and it is emphasized by repetition and intensified through a rise in register. It is the most prominent element of the entire first section, and it invites interpretation. This unusual leap to a drawn out dissonance is marked as impassioned in comparison with the features of stile antico,[94] which – as I will discuss momentarily – is referenced in the second section. More specifically, this leap projects a sense of impulsive, overextended movement, in that the leap lands on an unprepared dissonance and extends beyond the anticipated point of repose.[95] The music cannot even pass down from G to E in m. 1 without first burbling up to B, as it were – an instance of enlivening “passagio.”[96] The ebullient Gestalt a, being “an improvisation hand-shape figure,” is somewhat unsteady.[97] This unsteadiness comes through first of all in the variability of the ascending leap in x², which ranges between a fourth (mm. 1–2) and an astonishing eleventh (m. 43, to be discussed).

This leap to the problematic D in m. 1 initiates a series of such impulsive, overextended movements on a large scale in the first section (Ex. 4). The upper voice delineates an initial arpeggiation from G in m. 1 through B in m. 6 to E () in m. 7. But the upper voice first shoots up far above E to C in m. 5, the highest note in the entire piece, not least on account of the octave displacement of D in m. 1, which leads to a parallel displacement of A in m. 3. The expansive initial arpeggiation pushes E in the Urlinie out of alignment with E in the bass arpeggiation in m. 1 and onto a mere passing tone C in m. 7. The consequently top-heavy music comes crashing down like a wave on V in m. 8, and the thirty-second notes spill out like foam. Just as the centrifugal force of D requires counterbalancing, so the audacity of Gestalt a requires counterbalancing, which is initiated in the second section.

Example 4: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 1, mm. 1–10

Gestalt b, the subject of the second section, is characterized by endurance. While a features an immoderate, dissonant leap to the problematic D, b features the opposite: a moderate, consonant leap to the tonic E (Ex. 5). Like the former leap, the latter is marked by harmonic, rhythmic, registral, and textural accents, and it is emphasized by repetition and intensified through a rise in register, and it too invites interpretation. In comparison with the former leap, the latter projects a sense of determined, restrained movement. If a luxuriates by transgressing the limits of stile antico, then b perseveres by sticking to them.

Example 5: Bach, Prelude in E major, BWV 852, section 2, mm. 10–14

The music evokes stile antico through the quasi-vocal texture, the longer note values, the constant oblique motion, and b itself with its leap of a fourth and gentle syncopation.[98] The further softening of the meter through the shift of y¹ to a weak beat in m. 12 also contributes to this effect.[99] Yet the music is also “untypical of true stile antico in being a solid, sustained block of counterpoint with no rests after the voices have entered.”[100] The music does not actually embody stile antico but rather alludes to it for the sake of its comparative sense of restraint.

The section is both archaistic and arc-shaped (Ex. 6): it prolongs B in the bass in m. 8 by means of a third progression D–B in mm. 19–24 with an incomplete neighbor note E in m. 12, a hidden repetition of b¹. With these bass motions matched by parallel tenths in the upper voice (another hidden repetition of b¹), the section abides in over V. Starting with E–G in m. 14, every tenth in the section is approached from a sixth in contrary motion.[101] The reference to stile antico, the restrained harmony, and the steady intervallic alternation combine to give the music the feeling of a solemn procession, the antipode to the free-wheeling movement in the first section.

Example 6: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 2, mm. 10–25

Neither of these Gestalten alone, with their character traits of exuberance and endurance, can fulfil the calling, as it were, of the prodigious – Urlinie (Ex. 7).[102] For D, associated with a, pulls away from the tonic with seditious intimations of its own triad and region, while D, associated with b, pulls back towards the tonic, threatening to prevent the Urlinie from descending any further than .[103] The third section shows these Gestalten overcoming this challenge by exchanging qualities, growing closer, and cooperating by means of development (into A and b²) and unravelling (of c, the combination of A and b²), thereby acquiring vitality, in such a way that the centrifugal and centripetal forces of D and D are brought into balance and the Urlinie descends to .

Example 7: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852

3.4 Development and Unravelling

Motives, Gestalten, and their forms are connected through ‘development’ (Entwicklung) and ‘unravelling’ (Abwicklung), especially in homophony and polyphony, respectively.[104] Development, also called ‘developing variation’ (entwickelnde Variation), has nothing to do with the so-called ‘development section’ in sonata form (Durchführung),[105] nor is it simply “the continuous transformation or reshaping of musical material.”[106] Rather, development is variation of melodic Grundgestalten (or their basic motives) that “produces all the thematic formulations,” i.e., new motives, Gestalten, and forms of these, needed for “elaborating the idea of the piece,” whereas unravelling is such variation applied to polyphonic Grundgestalten, which are “taken asunder and reassembled in a different order.”[107] This difference is purely a matter of the type of Gestalten and the methods of variation; development is not inherently more linear than unravelling.[108] Indeed, development is very frequently non-linear, directed “backwards” toward earlier appearing formations.[109] Developing variation is often thought to be epitomized by the music of Johannes Brahms.[110] But Schoenberg repeatedly stresses the omnipresence of development and unravelling in the entire bodies of homophonic and polyphonic music, respectively.[111] He also specifies that Bach, straddling a historical juncture between polyphony and homophony, uses not only unravelling but also developing variation to a certain extent.[112]

Analysis of development or unravelling should demonstrate not merely the derivation of all Gestalten from a Grundgestalt,[113] nor a generic condition of “musical prose,”[114] but the specific “logic of the whole image,” which “depends on the analogous and appropriate utilization of the musical coherences.”[115] The development of a and b as melodic Grundgestalten into A and b² shows them to be coherent, while the unravelling of A and b² as a polyphonic Grundgestalt similarly demonstrates a coherence between them. These coherences are utilized in the gestural trope mentioned above, which gives a certain sense to the three-dimensional image of the piece as a whole.

At the beginning of the third section, Gestalt a takes on some of the restraint of b when it incorporates motive-form y³ in Gestalt A in m. 26, tempering the leap in the overlapping x² (Ex. 8). Meanwhile, Gestalt b takes on some of the liveliness of a by sequencing y¹ in b². (In the abstract, the two leaps of a fourth in b² add up to a seventh, the leap in a¹.) Moreover, A and b² are complementary in contour, A being framed by <3120> and b² being framed by <0213>, the inverse (or retrograde).[116] Thus, in a trope of gestures, a and b as transfigured by one another in A and b² acquire the shared character trait of vitality, the intersection of exuberance and endurance:[117] they are energetic yet disciplined.

Example 8: Bach, Prelude in E major, BWV 852, section 2, mm. 25–28

This exchange of qualities initiates a permanent partnership, in which a and b in the guise of A and b² continue to grow closer. For the unravelling of c, the polyphonic combination of A and b² in mm. 25–26, establishes a further coherence between them (Ex. 9). Gestalt-form c² in mm. 35–36 extends the original interval pattern 2–6 to 2–6–3 while substituting an additional statement of b² for A.[118] Gestalt-form c³ in mm. 38–40 inverts this pattern to 7–3–6 and momentarily employs a variant of b².[119] Gestalt-form c⁴ in mm. 41–43 adds A back to this combination. In a shocking turn of events, c⁵ in mm. 47–48 and 49–51 (and again in mm. 68–70 in the codetta), removes one of the statements of b² and hands over its 7–3–6 pattern to A.[120] Gestalt-form c⁶ in mm. 58–61 inverts this pattern back to 2–6–3. A restatement of c³ in mm. 65–67 reverts to prototypical statements of b², clarifying the chain of Gestalt-forms. The unravelling spells out how A and b² are coherent in that they can counterpoint b² in the same way. And this unravelling, we will now see, tracks with (1) junctures of the broader form, (2) stations in the descent of the Urlinie, and (3) the spinning out of tonal relations implicated in the problematic D.[121]

Example 9: Unravelling in Bach, Prelude in E major, BWV 852

In the first elaboration (Durchführung),[122] mm. 25–35 (which introduce c¹), and the first part of the second elaboration, mm. 35–41 (which introduce c² and c³; Ex. 10), the upper voice states a vast enlargement of b¹ in mm. 25–33, as it did in the second section of the prelude. But this time, an equally vast enlargement of the invigorated b² in the bass in mm. 24–36 instead of the staid b¹ provides consonant support for the Urlinie to descend from D () to C () in m. 37. However, this descent introduces the disturbing parallel fifths G–D in mm. 33–34 and F–C in mm. 36–37 in the deep middleground.[123] This disturbance is exacerbated by none other than the dissonant chromatic passing tone D, for “its temporary independence increases the value and power of the unity of both voices” in the consonant fifths.[124] The appearance of this D on the surface in mm. 36–37 is the most emphasized instance since the opening, bearing harmonic, rhythmic, metric, and registral accents. But in the near middleground, the parallel thirds B–D and A–C in mm. 36–37 are first unfolded into sixths, which helps to break up the surrounding fifths.[125] Much as the recklessness of Gestalt a is sublimated into vigor for both itself and Gestalt b, D is turning out to be both a source of unrest and ultimately a means to a more harmonious whole.

Example 10: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 3, elaboration 1 and elaboration 2, part 1, mm. 25–41

In the second part of the second elaboration, mm. 41–49 (which introduce c⁴ and c⁵; Ex. 11), the Urlinie descends another step from C () to B () in mm. 47–48, as the bass concludes a prodigious arpeggiation through F in m. 36 (not shown) to B in m. 49. This arpeggiation is mediated by the interpolated fifths C (from F) and E (to B) in the bass in mm. 41 and 42, which make the inner-voice passing seventh E consonant. Mm. 41–49 unfold the thirds E–G in the bass and G–B in the upper voice and compose out these thirds with Züge (linear progressions), giving this passage the thickest diminution in the piece. Correspondingly, it also has the thickest polyphonic combination, c⁴ in mm. 41–43, which is the crux of the piece’s unravelling.

Example 11: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 3, elaboration 2, part 2, mm. 41–49

Mm. 41–49 are also marked as the most impassioned, featuring elongated and unresolved dissonances, an unnatural leap, a chromatic step, and a cross-relation (Ex. 12).[126] Several of these features involve the problematic D as an alternative to D. From now on, D and D appear together in A when it is stated at its original pitch level.[127] The unnatural leap of an eleventh B–E in m. 43 places D in the same register as the preceding D. When D appears in m. 44, it pulls the music away from an unresolved minor ninth E–F, and the bass, as if dazed by this strange move, elongates and leaves the harmonic diminished fifth E–B unresolved, leaping instead to A. F, the resolution of E, finally appears two measures later (in m. 46), but in the wrong octave. The upper voice is correspondingly waylaid in reaching A, the parallel tenth of this F, and to do so, it has to lead four augmented fourths in parallel motion and induce a chromatic step and a cross-relation between D and D in m. 45, where “counterpoint loses hold and the voices coalesce into a singular outburst of regal passion.”[128] When the upper voice finally reaches A in m. 46, it forms a dissonance with B in the bass, which threatens to derail its ascent to B. But a variant of Gestalt-form b² dutifully resolves the seventh itself with G in the bass in m. 46. This resolution allows Gestalt-form a², with one last heave, as it were, to boldly reach over to B in m. 46, catching it at the last minute before the soprano tumbles, exhausted, into its original register. While D is implicated in a host of irregularities here, at the same time, by helping to tonicize F, it serves as a reminder that the F minor triad in mm. 36–49 is deeper than the interpolated E-major triad in mm. 42–49 (as can be observed in Ex. 7). In this respect, D actually helps to clarify the thicket of diminution that connects this passage to the background tonic triad. Once again, D is turning out to be a boon for E.

Example 12: Bach, Prelude in E major, BWV 852, section 3, elaboration 2, part 2, mm. 41–49

In the third elaboration, mm. 49–61 (which introduce c⁶; Ex. 13), the Urlinie descends from B () in mm. 47–48 through A () in mm. 58–59 to G () in m. 59, as the bass completes a gargantuan arpeggiation from E in mm. 1–3 through B in mm. 8–10 to E in m. 59. The passing seventh A in mm. 57–59 is made consonant by the interpolated fifths F (from B) and A (to E) in the bass in mm. 56 and 58, just as the inner-voice passing seventh E in mm. 41–42 is made consonant by the interpolated fifths C and E in the bass in mm. 41 and 42.[129] The interpolated fifth A in m. 58 is secured by an auxiliary cadence involving D in m. 58, which finally comes into its own as the subdominant degree of the subdominant region, supporting its own major triad. But instead of being simply overlaid upon the tonic triad as its antithesis, as in mm. 1–4, here the D-major triad is plugged into a sequence of IV–V⁷–I in the subdominant and tonic regions in mm. 58–59, which redirects the centrifugal force of D toward E.

Example 13: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 3, beginning of elaboration 3, mm. 49–59

The register transfer of A () in mm. 58–59 is a special event that involves processes in all three domains. In the contrapuntal domain (looking still at Ex. 13), A in mm. 57 is unfolded from F in m. 56, which is reached via a fourth-Zug from B in mm. 47–48. Amazingly, A in this Zug in m. 52 is itself unfolded from F in m. 51, which is reached via another fourth progression from the same B in mm. 47–48. Within the broader fourth progression, the intervals C–G in mm. 52–53 and C–F in mm. 55–56 are unfolded, and C–G is simultaneously inverted into a fourth, which changes the register of the upper voice. This fourth is motivated by a subsurface statement of b². In the motivic domain on the surface, there is a rising sequence of b² starting in m. 54 that carries the whole texture up with it (Ex. 14).[130] This chain establishes an abstract loop of tones in the harmonic domain that remarkably includes both D and D and no other chromatic pair, demonstrating in an inspired way how D and D are on a level and work together to drive the music forward. The completion of this loop bursts upon the music like a sunrise with the dramatic bass entry of b² that begins the fourth elaboration.

Example 14: Sequence of b² in Bach, Prelude in E major, BWV 852; adapted from Zacher 1993, 41

In the fourth elaboration, mm. 61–70 (which elaborate upon c³; Ex. 15), the Urlinie descends from G () in m. 59 through F () in m. 67 to E () in m. 68. A series of simple motions within the tonic triad in mm. 59–64 brings the upper voice back down into the lower octave, from which point an unfolding of the thirds E–G and D–F in mm. 66–67 brings it back into proper register. This unfolding is a trick the music learned from D in mm. 36–37, as confirmed by the parallelism between the chromatic passing tone D in m. 36 and the chromatic passing tone G in m. 66.

Example 15: Harmony, counterpoint, and form in Bach, Prelude in E major, BWV 852, section 3, end of elaboration 3 and elaboration 4, mm. 59–70

This parallelism becomes more obvious upon reviewing the Urlinie (Ex. 16), which, thanks to the elevation of A () in mm. 58–59, is arranged in a motivically and harmonically significant way that diffuses out contrapuntally into the rest of the piece. (The Urlinie is referenced in the bass in m. 65 as a shout of encouragement, so to speak, just before the final cadence.) Motivically, the Urlinie forms superimposed statements of x² and b¹, emblematizing the partnership of a and b in the proclamation of the tonic triad. But as the reader may have noticed, only the stalwart Gestalt b saturates the piece from background to foreground. For example, a polyphonic combination of b¹ (or a variant) and b² is varied from section to section in the deep middleground (please refer back to Ex. 7).[131]

Example 16: Urlinie in Bach, Prelude in E major, BWV 852

Harmonically, D embellishes the first leg of the Urlinie as a chromatic alternative to D, while G embellishes the second leg by analogy (looking again at Ex. 16). The chromatic step D–D, the most frequent chromatic relation in the piece, becomes more and more direct in the third section as Gestalten a and b similarly draw closer, appearing in the deep middleground in mm. 33–36, the near middleground in mm. 35–36 and 43–44, and finally the foreground in mm. 68–69, at the close of the Ursatz, where it hints at a completely chromatic tetrachord E–B. This last appearance unscrambles and clarifies the opening quiescenza, mm. 1–4, which it echoes (Ex. 17).[132] The result of all these explanations is that D is an enrichment of the tonic major region rather than a threat, and the chromatic step D–D appears throughout the following jovial fugue.[133]

Example 17: Instances of quiescenza in Bach, Prelude in E major, BWV 852

***

The development and unravelling of Gestalten a, b, and c, the transformation of the Ursatz, and the generation of the harmony: the weaving of these logical strands of recursion evokes the organic in the sense of a three-dimensional body and mind. This evocation entails a model of an organism not as a self-contained unity but as a plurality of systems – in this case, the harmonic, contrapuntal, and formal domains. Accounting for this plurality requires a revision of Schoenberg’s and Schenker’s theories and especially of how they are to be understood in the first place, specifically with respect to the musical idea or vision, unrest, motives, Gestalten, development, and unravelling.

Appropriately enough, the content of the music’s mind – the musical idea – includes a notion of vitality, of life, but not just in terms of interacting systems. It includes a notion of life as relational, as seen in the mutual transfiguration of a and b. Relationships involve trust in the personhood of the other: “the partner is conceived not simply as a sum of traits or qualities but as an individualized world-relationship” with his or her own “internally steered selection” of recursion.[134] In exchange, this “complexity of the other […] is obtained as a moment of one’s own life.”[135] It is the same with music. One trusts that its inflected recursion reflects a certain specificity and particularity not unlike our own, and this individuality, perceived through close reading,[136] augments one’s own life.

One is welcome to situate the prelude’s allegory of vitality in whatever context is most meaningful, but I like to think of the free-wheeling a, found on the surface, as the association-focused Schoenberg, and the law-abiding b, found throughout the voice-leading layers, as the transformation-focused Schenker,[137] since Bach’s music confirms that their estranged theories can interface for the greater good. It is a strength of Schoenberg’s and Schenker’s theories that they provide footholds for their own critique, and of Bach’s music that it helps to turn theory back on itself.