Instrumentos

Having solved ‘The Parallel Problem’ and ‘The Top-Down/Bottom-Up Problem’ and grounded these solutions in contrapuntal princi-ples and combined linear progressions, let us now consider some analytical implications. We will try to show how particular sequen-tial patterns can be derived within the context of specific pieces. A good place to start is with Bach’s Little Prelude in C Major, BWV 924. This short through-composed prelude contains two sequences and a dominant pedal. The first sequence appears in mm. 1–3 and consists of the pattern C–G, D–A, E in the bass. This pattern leads to a second sequence in mm. 3–6 that descends A–B–C; E–F–

G–A; C–D–E–F. The long dominant pedal in mm. 7–17 eventually resolves onto a tonic chord at the final cadence in m. 18.

Schenker himself analyzed this prelude on at least two occa-sions: in Der Tonwille 4 (1923) and again in Der freie Satz.²³ His feadings are conflated in figure 3.20 (Schenker’s analysis of Bach’s Little Prelude in C Major, BWV 924). In Der freie Satz, Schenker’s main insight was to suggest that the Urlinie is composed out at the deep middleground by a pair of unfoldings E–C and B–D (see figure 3.20a–b).²⁴He suggested that the unfolding E–C is inverted contra-puntally to create an upper sixth and that this interval is filled to create a sixth progression E–F–G–A–B–C. This sixth progression is then split into two segments, E–F–G and A–B–C, with the latter segment transferred down an octave (see figure 3.20c).²⁵In Der freie Satz and Der Tonwille, Schenker derived the first sequence from the

Figure 3.20. Schenker’s analysis of Bach’s Little Prelude in C Major, BWV 924.

Adapted from Schenker, Der Tonwille, vol. 4, and Der freie Satz, Fig. 43.b.

first segment by harmonizing it in parallel tenths with the bass E/C–F/D–G/E (see figures 3.20c–d). He followed much the same strategy in Der Tonwille to derive the second sequence (mm. 3–6).

This pattern stems from a 5–6 motion between the outer voices that is subsequently elaborated by motion in the inner voice.

As it stands, figure 3.20 offers a fascinating analysis of Bach’s prelude, one that captures both the broad sweep and subtle details of the musical fabric. And yet, this reading is not without its prob-lems. Indeed, although Schenker deliberately avoided any mention of the term sequence and overcame ‘The Top-Down/Bottom-Up Problem’ by deriving both sequences from a global prototype, he was unable to avoid ‘The Parallel Problem’ because he still derived both sequences quite conventionally from the outer-voice counter-point. In the first sequence, he sidestepped the parallels by omitting the inner voices altogether; he simply claimed that any middle-ground parallels are avoided by inserting intervening harmonies to create the pattern 10–5–10–5–10.²⁶ In the second sequence, he finessed ‘The Parallel Problem’ by deriving all four voices simulta-neously. Once again, he insisted that the purpose of the foreground was to cover up the implied parallel perfect octaves and fifths of the middleground, in this case by a string of 5–6 motions.

Figure 3.21 (Alternative analysis of Bach’s Little Prelude in C Major, BWV 924) tries to overcome ‘The Parallel Problem’ in figure 3.20. Figures 3.21a–b correspond to the progressions shown in figures 3.20a–b. Unlike figure 3.20, which derives the two seq-uences from linear interval patterns in the outer voices, figure 3.21 derives them from chains of parallel thirds in the upper register.

Figure 3.21c includes a chain of ascending thirds E/C–F/D–G/E–

A/F. These thirds are elaborated in two ways: the ascent E/C–F/D–

G/E is elaborated by lower thirds E/C–D/B–F/D–E/C–G/E, and the progression from G/E to A/F is transferred down an octave and filled in G/E–F/D–E/C–D/B–C/A–B
/G–A/F (see figure 3.21d).

Once the string of thirds in the upper voices has been generated, it can be harmonized in the manner shown in figure 3.21e. Signi-ficantly, there is only one way to harmonize this string; this har-monization inevitably produces the two sequences found at the surface of the music. Besides circumventing ‘The Parallel Problem,’

figure 3.21 also reveals some interesting connections between the

Figure 3.21. Alternative analysis of Bach’s Little Prelude in C Major, BWV 924.

sequences in mm. 1–6 and the pedal in mm. 7–17; in particular, the ascending sixth progression E–C is balanced by a descending sixth progression B–D. The main difference between the sequence and the pedal is that the former harmonizes each successive parallel third with a new chord.

We encounter many of the same analytical issues when we try to analyze Bach’s Prelude in C Minor, WTC I, BWV 847. Once again, Schenker discussed the piece on several occasions. In Harmonielehre (1906), he cited mm. 1–4 as examples of a subdominant fifth and a pedal point.²⁷ Almost twenty years later, he published an extended analysis of the entire prelude in Die Musik (1923); this analysis was subsequently revised for the final portion of his essay “Das Organische der Fuge,” from Das Meisterwerk in der Musik 2 (1926).²⁸And, finally, in Der freie Satz, Schenker included a reduction of mm. 1–18 in his discussion of combined linear progressions; this reduction refines his analyses from the 1920s.²⁹

Broadly speaking, Bach’s C-minor prelude follows the same basic format as the Little Prelude in C, though it is somewhat larger in scope.³⁰Like its diminutive cousin, the C-minor prelude begins with a long expansion of the tonic (mm. 1–18) that includes prominent sequential motion. The sequence eventually leads to an elaborate dominant pedal (mm. 21–33). This pedal finally moves onto a tonic harmony in mm. 34–38. With regard to the initial tonic expansion (mm. 1–18), Schenker rightly observed that it has four distinct components. As he noted in the Harmonielehre, mm. 1–4 use a sim-ple pedal to establish the tonic C minor. Next, mm. 5–11 consist of a passing motion from E
to B
in the Urlinie. Although mm. 11–14 continue the downward trajectory of the Urlinie, they change the accompanying lines in order to avoid a premature arrival on C.

Finally, mm. 14–18 use a 5–6 exchange to complete the octave descent E
–E
in the Urlinie and return to the tonic chord.

Schenker’s derivation of mm. 1–18 is summarized in figure 3.22 (Schenker’s analysis of Bach’s Prelude in C Minor, WTC 1, BWV 847, mm. 1–18). Figure 3.22a gives the foreground graph that orig-inally appeared in “Das Organische der Fuge.” Next, figure 3.22b gives the middleground reduction that he presented in Der freie Satz. When we compare these two readings, it is clear that they both rely heavily on the string of parallel tenths that occur between

the soprano and bass. According to Schenker, the main body of the sequence, mm. 5–11, is generated from a string of descending 7–6 sequences, akin to those found in Fourth Species textures like the one cited in figure 3.14a. His view of the prototypical voice leading is given here as figure 3.22c. Notice how Schenker suggested how the line might continue in mm. 12–18; he added the hypothetical bass tones F–E
–D–C in parentheses.

Although this interpretation initially seems plausible, it seems less satisfactory when we compare figure 3.22 with figure 3.23 (Alter-native analysis of Bach’s Prelude in C Minor, WTC 1, BWV 847,

Figure 3.22. Schenker’s analysis of Bach’s Prelude in C Minor, WTC I, BWV 847, mm. 1–18. From Schenker, The Masterwork in Music 2, pp. 48–49.

mm. 1–18). In figure 3.22a, Schenker proposed that mm. 5–11 proj-ect a string of parallel first-inversion chords, separated by applied chords. For example, the motion from A
6 in m. 5 to G6 in m. 6 is elaborated by an applied harmony that tonicizes G6. But in figure 3.22b these applied chords are reduced out, leaving a succession of parallel perfect fifths E
/A
–D/G–C/F–B
/E
. Figure 3.23 tries to overcome these problems: it circumvents ‘The Parallel Problem’ that mars figure 3.22 and it maintains Schenker’s position that dissonances are ultimately passing in nature. Like figure 3.7 this der-ivation places the string of parallel tenths in the soprano and bass

Figure 3.23. Alternative analysis of Bach’s Prelude in C Minor, WTC I, BWV 847, mm. 1–18.

(see figure 3.23a) and, like figure 3.9, it repeats each successive soprano note (see figure 3.23b). Finally, instead of harmonizing the repeated tones with root chords, figures 3.23c and 3.23d support them with inversions; this strategy preserves the prominent parallel tenths between the outer voices.

One of the most interesting features of Bach’s C-minor prelude is the fact that it uses apparent sequential motion to support an octave descent in the upper voice. The descent occurs at the middleground in figure 3.22. But it does raise the possibility that such motions might occur at even deeper levels. This possibility is clearly shown in Figure 3.24 (Two analyses of the Prelude from Bach’s Partita No. 3 for Solo Violin, BWV 1006).³¹ Significantly, Schenker supported the descent



^8–



1 in the Urlinie with a sequential harmonic progres-sion I–V/VI–VI–V/IV– IV–V/II–II–V–I (see figure 3.24a). However, figure 3.24b presents an alternative derivation analogous to the one presented in figure 3.5; in particular, it adapts Schenker’s reading to

Figure 3.24. Two analyses of the Prelude from Bach’s Partita No. 3 for Solo Violin. BWU 1006 From Schenker, The Masterwork in Music 1, pp. 40–41.

highlight the chain of descending parallel sixths. This being said, it is important to stress that sequential settings of



8-line Ursätze are not common, and it is quite possible that Schenker himself would have regraphed the Prelude later in his career. One reason for this is that



8-line prototypes tend to divide



^8–



^5–



1 with an intermediate motion onto the dominant, rather than



^8–



^4–



1 as in this particular prelude.³² Nevertheless, the graph in figure 3.24 certainly captures many spe-cial features of the work, and it confirms David Smyth’s claim that



8-line Ursätze often have important formal implications.³³

Given that the preceding analyses have focused on the ways in which Bach used sequences and pedals, it seems fitting to round things off by reconsidering Minuet II from his French Suite No. 1.

As we saw in figure 3.1a, the first part of this piece has two eight-bar phrases. These phrases both begin and end in the tonic D minor, and both are built from the same sequential progression I–IV–VII–

III–VI–II–V–I. The second section also opens with another eight-measure phrase (mm. 17–25), though it ends with a clear half cadence in D minor. Motivically, this phrase develops the main material from m. 1. Bach presents this gesture three times in the bass and tenor registers on D (m. 17), G (m. 18), and A (m. 19), and twice more in the soprano on C (m. 21) and D (m. 22). Just like mm. 9–16, these motivic statements are accompanied by contin-uous eighth notes. Having reached the half cadence in m. 25, Bach brings back verbatim the entire opening section (mm. 25–40).

Unlike the first section, however, mm. 17–40 are not repeated.

Although Schenker did not publish a graph of this particular movement, we can fill this gap in the manner shown in figure 3.25 (Analysis of Bach’s Minuet II, French Suite in D Minor, BWV 812). Figure 3.25a suggests that the piece can be derived from a



5-line prototype in D minor. Figure 3.25b then shows how the half cadence in m. 24 is generated by a division of the Urlinie at the deep middleground. Next, figure 3.25c derives mm. 1–16 as a descent from



^{5 to}



1 just like mm. 33–40. Figure 3.25d then shows how the descending fifth sequences in mm. 8–16 and 33–40 are generated from third chains in the upper voices; this derivation follows the general scheme outlined in figure 3.6. Finally, figure 3.25e derives the same sequence in mm. 1–8 and 25–32 from anal-ogous chains of thirds. Unlike mm. 9–16 and 33–40, however, the

Figure 3.25. Analysis of Bach, French Suite in D Minor, BWV 812, Minuet II.

chain of parallel thirds is submerged beneath a soprano line that rises from A (m. 1) through B
(m. 2) and C (m. 3) to D (m. 4).

Once m. 4 is reached, the soprano line takes over the lower third of the chain, thereby demonstrating Bach’s fondness for invertible counterpoint. Yet again, the derivation shown in figure 3.25 avoids both ‘The Parallel Problem’ and ‘The Top-Down/Bottom-Up Problem.’

In this chapter, we have used our discussion of sequences as a pretext for considering the consistency of Schenkerian theory. We have seen that Schenker was ultimately inconsistent in the way he treated parallel perfect octaves and fifths. Although he insisted that such phenomena do not occur when a given pair of voices move between successive harmonic tones, his analyses are littered with parallels, especially when the music is sequential. When these anomalies appear at the foreground, Schenker claimed that they can be eliminated by appealing to the behavior of the middle-ground, and when they appear at the middlemiddle-ground, he proposed that they can be eliminated at the foreground. To resolve these inconsistencies, we found a new way to generate sequences, one that focused less on the outer voice counterpoint and more on the stepwise motion of the upper voices. This strategy conformed very nicely with Schenker’s own discussion of combined linear progres-sions in par. 224–26 of Der freie Satz.

Besides eliminating an important inconsistency in Schenkerian theory, this solution has several important consequences. For one thing, it suggests that, although certain aspects of tonal motion are controlled by the outer voice counterpoint, others can be under-stood only in terms of the inner voices. When graphing a particular piece, the analyst should not simply trace the motion of the soprano and bass voices; he or she should also monitor the behavior of the tenor and alto voices. This point ties in with our discussion of Ursätze in chapter 2. For another, our discussion has shown that harmonic function is intimately connected to voice leading. In particular, we found that bass motion by fifth inevitably arises when the upper voices move by step in a single direction by parallel thirds or sixths. This observation fits in nicely with our discussion of ‘The Complementarity Principle’ in chapter 1. In the same vein, we

have also noted that sequences and pedals are actually related phenomena. This point is interesting for a couple of reasons. On the one hand, it provides further justification for



^{8- and}



^5-line

Ursätze; instead of thinking of them as containing “unsupported stretches,” we can think of them as descending across a pedal. On the other hand, by showing connections between pedals and sequences we can explain why both often appear in the same piece.

As we saw in our analysis of Bach’s Little Prelude in C, BWV 924, the underlying counterpoint of both can, in fact, be very close indeed.

Another important consequence of this solution is that it under-scores a fundamental methodological difference between Schenker’s concerns and those of many other music theorists. As mentioned in the Introduction, there are important differences between describ-ing what happens in a piece of music and explaindescrib-ing why these things happen or how to make them happen. While many music theorists are concerned with describing music in “bottom-up” terms as a string of surface events, Schenker was intent on explaining how these surfaces are generated “top-down” from tonal prototypes.

This dramatic shift in perspective does not mean that conventional descriptions of sequences are necessarily wrong or that Schenker himself never took time to describe surface events. Nothing could be further from the truth. All empiric inquiries must start from careful descriptions of phenomena and, like any good empiricist, Schenker often provided the reader with extremely vivid descrip-tions of how a piece sounds. For example, in his analysis of Bach’s Little Prelude No. 1 in C Major, BWV 924, he described the music in narrative terms, suggesting that Bach wanted “to spin a tale” and create suspense by “exquisite tensions and convolutions . . . an insa-tiable desire for first-rate suspense and intricacy.”³⁴ Yet, Schenker’s emphasis on “top-down” processes underscores that there is more to understanding music than describing its local effects; describing pieces and deriving them are simply not the same thing. Derivation requires something more.

But why should “top-down” derivations mean more to Schenker than “bottom-up” descriptions? Who, in fact, needs to understand the significance of global prototypes? To answer these questions, it is helpful to take Schenker’s narrative metaphor a bit further.

Imagine, for a moment, that we have just seen a “whodunnit” at the local theater. The production involves at least three different groups of people: the author of the play, the performers, and the audience. Of these, it is clear that the author must have some “top-down” sense of the play; if not, then, it is unclear how he/she could reveal the various clues in the right order so that the final reve-lation is convincing. Equally, the audience must not know who dunnit, at least on first viewing. Such knowledge would deprive them of the thrill of deducing that Professor Plum bludgeoned Miss Scarlet with the candlestick in the library. Their response will initially be governed by “bottom-up” concerns. The actors, however, seem to stand somewhere in between. To understand a character’s motivations and personality, the actors must know who perpetrated the crime and yet they must not give the game away to the audience.

The ability to know something without betraying this knowledge would appear to be the essence of acting.

By the same token, it is composers rather than listeners who must know in advance the global structure of pieces, and it is the task of the performer to mediate between these two groups. Schenker made his point quite clear on several occasions. In his essay “Forset-zung der Urlinie-Betrachtung: I,” from Das Meisterwerk in der Musik 1 (1925), he noted that “the composer’s business is the composing-out of a chord; this task leads him from a background Ursatz through prolongations and diminutions to a foreground setting.”

Meanwhile, “It is up to the reader or player, conversely, to retrace the path from foreground to the background.”³⁵ Schenker rein-forced his point a few lines later. When analyzing the opening to Mozart’s Sonata in A, K. 331, he uncharacteristically placed his foreground sketch above those of the middleground: “The voice-leading strata are deliberately viewed from the perspective of the observer not from that of the composer—that is, they are pre-sented, as an exception, from the foreground to the background.”³⁶ The same idea was apparently behind Schenker’s claim in Der freie Satz that “the ability in which all creativity begins—the ability to compose extempore, to improvise fantasies and preludes—lies only in a feeling for the background, middleground, and foreground.”³⁷ In other words, the tension between traditional accounts of the sequence and Schenkerian derivations stems from the fact that the

goals of traditional music theory are ultimately quite different from those of Schenkerian theory. Whereas traditional music theory is often motivated by a desire to describe how we, as informed listen-ers, experience a piece as it flows from beginning to end, Schenker-ian theory is more concerned with explaining how expert tonal composers tacitly understand how their music fits together locally and globally. This does not mean, of course, that listening and com-posing are completely unrelated activities or that informed listeners understand music in fundamentally different ways to expert com-posers. If there were no points of intersection, then it is hard to understand why informed listeners are able to recognize and value exceptional feats of compositional prowess. But it is important to recognize that they may be different and that such differences have enormous consequences for the music theorist.

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