Parody (after Wheeldon)

Timothy Jackson's diachronic transformation (see earlier post) bears some similarities to Marianne Wheeldon's "parody." Wheeldon examines methodological problems for linear analysis in Debussy, whose music is well-suited to studies of ambiguity and discontinuity. She identifies several features of his late works that can be interpreted in terms of discontinuities. Of those, “parody” might be applicable to D779n13.

Wheeldon finds parody in the Cello Sonata, first movement, to lie in a contradiction of the developmental expectations of sonata form: "Despite . . . motivic correspondences that pervade the movement, the motivic material fails to develop or grow, since wholesale repetition does not constitute development. The high degree of motivic repetition creates an ultra-unified movement, yet it literally inverts the central metaphor of organicism, that of growth" (163). In this kind of context, unity does not evolve–it is imposed: "The statistical climax [in the movement's prologue] is not the point where unity is first achieved, but rather where it is overwhelmingly reinforced."

In the case of D779n13, we seem to have a reverse process. When Margaret Notley says of dances including this waltz that they "unequivocally are works" (141), she points to an attempt to break free of the constraining frame of the 16-bar social dance, to "evolve" rather than simply to repeat. Paradoxically, drawing the dancers' establishment of the beat into the piece itself (measures 1-2) begins this process. On the other hand, the echoing figures in the right hand tightly constrain the first phrase and its repetition up to the moment of the cadence, at which point the line not only ascends but for the first time fails to repeat the four eighth notes of the principal motive.

In this context, the opening of the second strain is unexpected–its insistent literal repetitions take the place of the contrasting middle of a small ternary form, where we would expect to hear motivic fragmentation and rearrangement. The parody, then, would seem to be of temporal or design expectations as much as pitch. At both beginning and end, the C# major section draws attention crudely to the awkwardness of the waltz's metric design, the point that we emphasized in the earlier post, under the diachronic transformation, in our attempts to construct a suitable contrasting middle as a simple expansion (using D365n6 as the model).

References:

Wheeldon, Marianne. "Interpreting discontinuity in the late works of Claude Debussy." PhD. diss., Yale University, 1997.

Notley, Margaret. "Schubert's Social Music: The 'Forgotten Genres'." In Christopher H. Gibbs, The Cambridge Companion to Schubert, 138-54. Cambridge/New York: Cambridge University Press, 1997.

Trouble with thumbnails

Apologies for the fact that thumbnails in most recent postings have apparently lost their links to the (much larger size) original files. I am working on it. DN

The anticipating 6-4: background for metrical readings

The foreground in Carl Schachter’s set of durational reduction graphs (cited in an earlier post but not shown, for copyright reasons) shows with particular clarity the two-against-three pattern that is basic to the interaction of right and left hands in D779n13: "the right-hand sets up a secondary meter of 3/2 against the 3/4 pattern of the left-hand part" (70). Such two-against-three patterns are by no means unknown in the waltz repertoire (they are favorites of Johann Strauss, jr., for example), but they are rare in early sets -- the first instance I have found after D779n13 is in Joseph Lanner’s opus 26, published in the early 1830s (still another reminder -– as if we needed one -- of how out-of-place the A Major Waltz seems in the Valses sentimentales).

Schachter uses the demonstration of the larger meter or hypermeter to make an observation about style. The cadences in this waltz hold an "anticipating 6/4," or a cadential 6/4 that is "in a weaker metrical position than the V7 to which it resolves." "Not frequent," these anticipating 6/4s do "occur from time to time, especially in music of the nineteenth century. Schubert and Chopin probably use them more than any other great composers, though examples can also be found in music by Schumann, Mendelssohn, and others" (73).

That cadential 6/4s might appear in both basic metric positions, strong and weak, is by no means surprising in the waltz repertoire, since, as we know, the figures of the common form of the valse à trois temps are displaced by a bar, so that one dancer's "bar 1" is the other's "bar 2."

Statistics for Schubert's dance music show that these hypermetrically weak 6/4s actually appear rather more often than "from time to time." In seventy two strains of the thirty six waltzes of D. 365, the most frequent progressions for the final three bars of a strain are I-V-I and V-V-I: these appear thirty six times. Next most frequent is the "anticipating 6/4" or "I6/4"-V-I; its sixteen appearances are nearly double those of an accented 6/4 placed in the penultimate bar (nine times). As rough statistics, these numbers hold up in his later dance sets, as well.

Among other composers, the anticipating 6/4 is a strong motif in Chopin's first waltz, op. 18, where it is used in all but two strains (see the first one below). After that, Chopin uses the device rarely, but in prominent positions (the cadence of the first strain or the first waltz) and especially–but not exclusively–in the waltzes in Ab major.

Lanner hardly uses the 6/4 chord at all; isolated instances of the anticipating 6/4 appear in later sets, such as Alpen-Rosen, op. 162 (twice). In the reduction of the first waltz below, note the ending of the second strain.

On the other hand, Strauss, sr., deploys the 6/4 at about the same rate as Schubert, and he prefers the anticipating type.

Strauss, jr., uses the 6/4 far more freely than any of the earlier composers, Tales from the Vienna Woods, op. 325, being perhaps a highpoint, as all of its waltzes use the 6/4 in at least one of their strains. Although he did occasionally use the anticipating type, most of Strauss's 6/4s appear in accented bars (fourth-to-last or penultimate). The graphic below shows the piano reduction of no. 5. The first strain uses the anticipating 6/4 (twice, actually, in its second phrase), but the second strain gives a prominent metric position to the 6/4.

Meter-as-rhythm (after Hasty)

Where London's theory respects a traditional distinction between rhythm and meter, Christopher Hasty actively seeks to break that distinction down by arguing that meter must be continually reinvented in listening: for example, he asserts that "meter, even when viewed from the perspective of metrical type, is fully particular and never 'the same'" (131). (London, on the other hand, cites cognition studies to argue that meter is internalized and therefore becomes a set of expectations that are maintained until strongly contradicted.)

Hasty's theory is based on projection: an attack and a duration project the possibility of another attack and duration, the simplest of which would be a repetition of the first (the solid arrow in (a) of the graphic shows a realized projection, the dotted slur that follows the potential of the same kind, the longer arrow marked Q a longer potential projection).

The simplest pattern in a 3/4 meter is shown in (b). As Hasty observes, triple meter is decidedly more complex than duple meter because

The third beat cannot function exactly like the second beat simply to continue the duration begun "before" there were any beats, for now that there is a second beat there is also a real potential for projecting a half-note duration (the potential Q in [the] example). In order to function as a continuation, the beginning of the third beat must deny this potential. In contrast, the beginning of the second beat denied no potential--rather, it created one projection and the potential for another. (132)

Given the consistency of temporal figuration in D779n13, a complete analysis on Hasty's terms would quickly become tedious, but his method may allow us a more nuanced view of the establishment of the hemiola pattern that is shown so plainly in Schachter's durational reduction. The familiar accompaniment pattern of bass and two afterbeats works out in a direct way through the first four beats the projection of triple meter we would expect from (b). In the next graphic, see P for quarter beats, R for the bar measure (the example is simplified as it shows only completed projections, not projective potential).

The repetition of R through bar 2 is sullied by some uncertainty as the entrance of the right hand figure creates an unusual two-beat anacrusis that sets up the possibility of an independent projection (Q). The completed projection of the left-hand figure through bar 2 eventually secures a two-bar hypermetric level (S), but the duple projections continue. Thus, the metric properties of the first three bars are all different: a simple development of 3/4 meter through quarter-note and bar-level projections (P, R); complicating the meter through a "superimposed" duple projection (Q); and establishment of a two-bar hypermeter (S) that includes both duple and triple projections.

References:
Justin London. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford University Press, 2004.
Christopher Hasty. Meter as Rhythm. New York and Oxford: Oxford University Press, 1997.

Metrical reading (after London)

Today and tomorrow’s readings are based on theories with sharply opposed views of temporality in music. In Justin London's theory meter and rhythm are distinct. Meter is portrayed as cyclical, based on entrainment and other cognitive constraints. Meter is "time-continuous," patterned cyclically: once the listener is entrained through subjective rhythmization (14-5) by a minimal number of phenomenal events (an event at a beat level within perceptible range plus one set of subdivisions), meter recycles itself and thus continues "in mind" independently of phenomenal events unless undermined or contradicted by them. The issue for analysis is how well a meter is defined, how "thick" or "thin" it is ("one may characterize meters in terms of their hierarchic depth–that is, whether a meter involves a rich hierarchy of expectation on many levels at once, or only a limited set of expectations as to when things are going to occur" (25)).

I will work through an example, using not D779n13 but the well-known theme of Mozart's K. 331, I. We start with the establishment of meter through entrainment. To simplify discussion, I assume a tempo where a dotted quarter equals 60–tempo is crucial to London's theory because it determines the possible meters and the range of their rela-tionships. The first chord (a in the graphic) cannot establish meter in itself, nor can the sixteenth that follows–the latter is a subdivision perhaps, but of an unexpressed beat in a meter not yet established (b). The second chord repeats the first, and that in one respect is a weakness–the meter is still not established because the second chord is just as likely to be the second beat of a duple meter as the third eighth of a 6/8 measure (c). Only with the quarter note chord is the meter unequivocally set (as triple or compound duple, that is): we have now heard well-defined events on two beats and at least one of the triplet eighth subdivisions (itself supported by a still smaller value as a "pickup") (d).

The meter is now set, and Mozart continues to define it effectively through the quarter-eighth rhythm. Given the ubiquity of this figure across the entire theme, and the fact that Mozart even turns to continuous eighth notes in the second section, I would describe the meter in this theme as "thick," as heavily and continuously reinforced by phenomenal events. With the measure moving at 30 bpm (or 2000 ms), the upper threshold for perception of a (hyper)metric unit (6000 ms) would be reached by the end of measure 3. Thus, it is quite easy to maintain a palpable or immediate sense of hypermeter at the two-bar level, a perception that Mozart patently encourages. Beyond that, a regular hypermeter and the symmetrical proportions that can derive from it are abstractions, constructs in memory. Beyond this distinction between the immediate and the abstract, however, there is no need to separate meter from hypermeter; as London puts it, "the number of metric levels both above and below the beat can and does fluctuate, [and thus] there is no substantive distinction between meters and so-called hypermeters" (25); elsewhere he says that "having several levels of metric structure present above the perceived beat is no more extraordinary than having several levels of subdivisions below it" (19).

I find London's cyclical conception of meter appealing, in part because it respects distinctions between rhythm and meter (or between patterns of phenomenal events and processes of metric entrainment), in part because it is intuitively more satisfying than Lerdahl and Jackendoff's hierarchical model. London's cyclical conception of meter allows one, by contrast, to see that the heads of the longest time spans, "structural down-beats," "structural accents," and similar terms as Lerdahl and Jackendoff and others deploy them, are rhythmic/metric themes for hierarchy-based readings whose central task is to sort out the roles of the various temporal units that can be distinguished in hearing a musical performance.

The results obtained for K331, I, apply equally well to D779n13: meter is "thick," heavily and continuously reinforced by phenomenal events. The entrainment of meter happens in the introduction (as the dancers would require), and once the right hand part enters the metric levels of beat (quarter beats), subdivision (groups of eighths), measure, and two-bar hypermeter are maintained consistently throughout (even the right-hand hemiolas are consistent and readily subsumed in the ongoing meter). Only at the four-bar level is hypermeter inconsistent, but by now we know that trait of D779n13 well.

Reference:
Justin London. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford University Press, 2004.

Dialectic of continuity/discontinuity (after Kielian-Gilbert)

In the MTS article, I write about Timothy Jackson’s juxtaposition of conflicting linear readings and also about similar work by Marianne Kielian-Gilbert (294). Her opposed pair, prolongational and translational relationships, can cover a wide range of event types and levels (refer to Figure 2: Tendencies of prolongational and translational parallelism, in her article, p. 70) but her interest lies particularly in contexts where ambiguous harmonies are linked with recurring themes, motives, or other figures.

In D779n13, there is no obvious instance of this kind of event, but Kielian-Gilbert's categories do give interesting results when applied to one crucial, "generative" moment and its varied repetitions in subsequent phrases, the result being what she calls an “oscillation” between ii6 and IV. The C# dissonance in measure 3 clearly belongs to a 7-6 suspension figure that stretches from the firmly established tonic triad of measures 1-2 to the ii6 chord in measures 3-4 (see the top system of the graphic below). The inversion of clichéd voice leading in the upper voices—see the top system, middle, combined with the firm bass motion from ^1 to ^4, however, enables a possible reading of a 7-8 suspension against subdominant harmony (top system, righthand side).

The 7-8 suspension itself is not unduly problematic (mid-seventeenth century theorist Christoph Bernhard already includes it as an acceptable syncopatio, though he also says it is rare, a statistic that still applies in the early nineteenth century)--but of course it would have radically different implications for the alto voice's movement out of C#5 (^3). Still, the context favors the supertonic and the common 7-6 suspension. On repetition of the figure in measures 10-12, however, the added G-natural, which replaces the C# that gave a literal, if short, preparation for the suspension figure in measures 2-3, shifts the two possible ways to hear measure 11 into balance (graphic, middle system). One can still hear A: I—ii6, but an applied dominant with deceptive resolution, A: V7/IV-ii (as if D: V7-vi), would surely be much more plausible with a bass motion from A2 to B2--it is easier to hear an applied dominant moving to A: IV (middle system, righthand side).

By the time the opening phrase reappears after the C# major section, the force of the tonic key is nearly attenuated: if ii6 was more difficult to hear in measure 12, it is all the more difficult in measure 31, after two measures of an A7 chord that is equally plausible as a German Sixth chord in C# major (bottom system). Now the subdominant seems much stronger, even to the point of raising the question whether the resolution to B5 does not invoke a triad with an added sixth (dominant ninth chords do arise accidentally over V7-I progressions in waltzes of the 1820s, but the added sixth is exceedingly rare before its appearance in French and Austrian ballet, operetta, and dance music in the 1860s). If one can indeed hear this moment as a triad with added sixth, then the implications for voice leading are again strong, as the added sixth would lead upward to C# in a return to I or would be stationary in a move to V.

Over the course of the waltz, then, the translational parallelisms of voice leading motives in the phrase openings can be heard gradually to undermine the stability, not of the prolongation (the subdominant function can be served equally well by ii or IV) but of the voice leading implications. The hegemony of the suspension-led motions is not so secure as it seemed. I would argue that, by measures 29-32, we do oscillate between one hearing and the other, first favoring IV (because of its applied dominant), and only later ii (because of the expanded context that ties the subdominant function into the cadence progression).

References:

Jackson, Timothy. "Diachronic Transformation in a Schenkerian Context: Brahms's Haydn Variations." In Carl Schachter and Hedi Siegel, eds. Schenker Studies 2, 239-75. Cambridge: Cambridge University Press 1999.

Kielian Gilbert, Marianne. "Interpreting Schenkerian Prolongation." Music Analysis 22/1-2 (2003): 51-104.