Postscript 2 to Berry

If only he had relaxed his insistence on recursive hierarchies, Wallace Berry might have been an early darling of musical post-structuralists. As I noted in yesterday's post, his "metric middleground/backgrounds" usually have the effect of flipping the binary in which harmonic hierarchies (and the hierarchies of formal design implied in labels like "A", "B", etc.) constitute the unmarked term. His final graph for Chopin, C-Major Prelude, Op. 28n1, for instance (Berry, "Metric," Ex. 17b), looks very much like my graphic for D779n13 in the post two days ago.

And Berry is quite willing to talk about harmony in overlapping spheres of influence rather than as exclusive, as in his characterization of the harmony in the C-Major Prelude, WTC I:

Primary tonal elements in the Bach Prelude are, in my view, best deemed a complex of overreaching foreground occurrences, anticipating and reflecting. Two occurrences of V, conceivable as one basic manifestation, enclosed by three encompassing occurrences of I, comprise a fundamental unity of linked, overlapping events which span the Prelude ("Metric," 24).

. . . the Prelude's first nineteen measures [suggest] segments marked by overreaching occurrences, prolongations, and processes, inarticulative of precise temporal spans. Particular occurrences and recurrences seeming in the graph [his Ex. 20] to mark explicit spans should be read as veiled, blinking, fading and reemerging, signals (25).

This complex treatment of harmony is, in fact, remarkably similar in its basic strategies to work by Charles J. Smith cited in an earlier post.

Berry, unfortunately, went further in his final book to assert the composer's priority, after the by-then dated manner of the 1960s and the "CMPs" (Contemporary Music Project; Comprehensive Musicianship). As Nicholas Cook puts it, "the dominant approach [to the relation of analysis and performance is] typified by Walter Berry's Musical Structure and Performance. [Its problem is] that it is prescriptive, that it proceeds from analysis to performance, [and] that it tells performers what they have to do rather than listening to what they have to play" (217). What Cook calls for is analysis that is not "monotextual," and thus Berry becomes the emblem of a (heretofore) hegemonic unmarked term.

References.

Berry, Wallace. "Metric and Rhythmic Articulation in Music." Music Theory Spectrum 7 (1985): 7-33.

Smith, Charles J. "The Functional Extravagance of Chromatic Chords." Music Theory Spectrum 8 (1986): 94-139.

Cook, Nicholas. "At the Borders of Musical Identity: Schenker, Corelli and the Graces." Music Analysis 18/2 (1999): 179-233.

Berry, Wallace. Musical Structure and Performance. New Haven: Yale University Press, 1989.

Schachter and the rising Urlinie, Part 11

Carl Schachter devotes the fourth section of his article "Schoenberg's Hat" to an assessment of one rising fourth line, ^5-^8 (333-37).

Allowing that "the fourth from ^5 to ^8 is among the most important structures that produce rising contours, sometimes spanning whole formal sections and, especially in short pieces, often forming the high point of an entire melodic line," Schachter says that its close on the tonic note accounts for its status, in part at least. Equally important, however, is the play of registers within the Urlinie and the balance of registers that complements upper with lower. It is these – and not Schoenberg's notion of unitary space -- that bring formal and expressive treatment of "inversion" into tonal music. Thus, for Schachter, "the interest and beauty [of such treatments] result as much from the structural and expressive differences between rising and falling lines as from the similarities of shape."

His examples are Bizet, Carmen, Act III, "Card Trio"; Bach, WTC 1, Fugue in C-minor; and Chopin, Prelude in E-major. In the first, contrast of direction is linked to an expressive life/death reversal. In the second, the gap opened in the subject is filled by the rising fourth line that leads to the fugue's highest pitch in the third episode; the line reappears in the structural cadence. The "^5-^8 fourth . . . serves as a foil both to the essentially descending subject and to the structural descent of the upper voice as a whole" (335). Finally, the E-major Prelude's obvious closing cadence figure is set into context as follows:

Although each phrase contains a primarily rising melodic line, the Prelude as a whole maintains a remarkable balance between upward and downward motion. This effect results from the second phrase's powerful climax on Ab (G#), which provides a focal point for the right-hand part. Thus the first phrase and most of the second seem to rise up to this tone, which then falls to the E at the end of the Prelude. The large-scale motion from climax to final note, then, is a descent, even though the immediate path to the final note is an ascent. (337)

I read the last of these the same way in my "Three-Part Ursatz" article (27-28), which Schachter does not cite.

Schachter, it seems to me, mixes together the notion of up/down with registral contrast, which can often be linked with timbral differences and functions of textural layers. In other words, rather as I have argued earlier, Schachter wants to maintain a simple opposition down/up so that he can the more easily choose the first, unmarked term and set it against an expressive marked term. As a device for interpretation, that tends to oversimplify (constrain) the treatment of register. In the MTS article, I discuss how the emphasis on balance of tension (along with a tendency to "naturalize" interpretive goals) links Schachter's practice to that of the literary New Critics.

Reference:

Neumeyer, David. "The Three-Part Ursatz." In Theory Only 10/1-2 (1987): 3-29.

Schachter and the rising Urlinie, Part 5

If the rising line is not a good candidate in the Eb Major Prelude (see previous posts), it is inescapable in the G Major Prelude. The same kind of dramatic emphasis that Carl Schachter notes and uses in part to situate his reading of the several voice leading strands in the Eb Major Prelude occurs also in the G Major Prelude, and specifically in connection with a cadence that rises to and through the leading tone: here are the final bars. [For reference, a copy of the score appears at the end of this post]

The opening bars (shown below) establish a three-part texture with great clarity; the topmost voice charts a neighbor-note figure across mm. 1-4 and even embellishes itself with little neighbor note figures along the way. The bass is a pedal point G2, and the middle voice walks sturdily on a path from ^5 to ^1 (^8): D3-E3-F#3-G3. As we shall see, the relationship of the upper two voices is simply reversed in the final cadence, the pedal point bass there being V or D3. That the topmost voice is the principal one is confirmed a few measures later, when a stereotypical (^2)-^2 brings ^3 over I down to ^2 over V (see the rectangle frame in the example). Along with this, the role of D4 is plainly identified as a cover tone, or focus of an auxiliary (secondary) voice above the principal voice.

Disruptive cadenzas like those in the Eb Major Prelude are lacking in the G Major Prelude, but there some dramatic moments before the final flourish. In the first system below, a registrally expansive gesture runs quickly across the strings from the open C2 to our cover tone D4. The latter is pushed one half tone higher to Eb4 two measures later -- that's the highest note before the run up to G4 at the end. The effect is immediately vitiated, however, by a move downward and resolution to B3 as ^3 (end of the rectangular frame), and D4 is heard again it's obviously a cover tone once more (circled in the last system).

At the end, the formation of A3 (^2) above V could hardly be clearer, and the sudden chromatic rush up to G4 is a surprise -- although the chromaticism itself is a marker of the cadenza, and that is apparently how the figure is meant to function here. The diagonal line marked in the score suggests that the figure outlines (unfolds) a sixth from A3 to F#4.

In the final bars, the circled note pairs mark the parallels to the beginning of the Prelude, but now with the voices inverted: what was the uppermost voice is in the middle, and the middle voice, having attained its tonic goal-tone, is shifted an octave higher, above the original "soprano." Thus, the opening gesture at the left of the example below turns into the closing gesture at the right.

I suppose one could argue that the stretched-out chromatic scale changes the relations of the voice leading strands to the point that the middle voice replaces the upper voice as primary, and therefore one gets a rising Urlinie from the cover tone D -- picked up in the middle of the chromatic scale -- up to G4. I am wary of these sudden reversals, however, just as I am of Urlinie ^3s that show up just a few bars away from the end of a piece. The cover tone D4 never has the kind of significance earlier that would predict such a change of role -- the rising line, then, seems an arbitrary choice. Thus, I would go with Schachter's "equals" here, the inner voice being "first among" them, and would probably notate using Channan Willner's "polyphonic Ursatz" (see yesterday's post). But there is a caveat: a descent to ^1 is plainly as forced and arbritary as a rising Urlinie would have been. The Prelude, then, ends as it began: with ^3 in the principal voice (and probably then a background shape involving neighbor notes -- see my comment on Arthur Komar's reading of the WTC, C Major Prelude in the MTS article, 291).

Postscript: Should D779n13 not be read in a similar way? Have I not said that the rising cadence gesture is a surprise? And does not the set of parallel sixths force B4 (^2) back up to C#5 (^3) rather than down to A4 (^1)? I could settle for the latter reading, but as to the rising gesture, it is only a surprise in terms of the clichéd formulas of the cadence (and, in the waltz repertoire, therefore, rather less of a surprise than it would be in most other genres). Unlike the cover tone D4 in the G Major Prelude, in D779n13 the F#5 (^6) that appears almost immediately and is touched on repeatedly thereafter forces constant attention to the "space above ^5" and sets all the conditions needed for a move further up at the end.

Schachter and the rising Urlinie, Part 4

In his article on the Prelude from J. S. Bach's Eb-Major Cello Suite, Carl Schachter makes a serious attempt to weigh the merits of a rising Urlinie, but the direction of his argument is nevertheless obvious from the outset, as he weighs the three possibilities for a reading of the upper voices in the first section (mm. 1-10). [For reference, a copy of the score appears at the bottom of this post]  He addresses the question of the rising Urlinie head on only in the closing pages, and then only briefly. Still, the answer he comes to -- the Urlinie as one among equals rather than an obvious and controlling line -- responds in a sensitive way to the circumstances of the Prelude even as it preserves the theoretical priorities dictated by Schenkerian theory. His "first among equals" construct here is in fact almost indistinguishable from Channan Willner's four-part Ursatz model: see the item "Polyphonic Ursatz" under the year 2007 on his publications page.

I don't hear the Prelude quite the same way, but mainly with respect to the middle strand on ^5 (Schachter labels this "y" -- "x" is the upper Eb, and "z" the Urlinie G3). The idea of continuing voice leading strands certainly makes sense, given the static quality of the registers (so static they have to be broken up radically by the cadenza-figures), though I might want to experiment with the five or even six voices implied by the arpeggio figures, rather than the four Schachter follows (bass plus x, y, and z).

In the graphic below, at (a) I have pulled out early-middleground/background features for Schachter's reading in terms of score fragments and at (b) have produced an analogous graphic for my own view of it. Remember that the graphic is a thumbnail -- click on it to see the original size.

I would essentially flip the priorities of Schachter's textural model, with an ^8-^7-^8 figure as the background and Schachter's "y" and "z" as the other "equals." Probably because of the lack of typical emphasis on V, a relatively common figure that combines descent and ascent (from ^8 down to ^5, then back up) really doesn't work at all here. And in any case, I can't hear the ascent in Schachter's strand "y", especially in phrases 3 and 4 (mm. 27-62), where a rise from C4 through C#4 to D seems forced, too much at cross purposes with the underlying harmonic progression.

Posts in a series starting next week will look in detail at the article in which Schachter addresses the theoretical questions of the rising Urlinie directly: "Schoenberg's Hat and Lewis Carroll's Trousers: Upward and Downward Motion in Musical Space."

References:

Schachter, Carl. "The Prelude from Bach's Suite No. 4 for Violoncello Solo: The Submerged Urlinie." Current Musicology 56 (1994): 54-71.

Neumeyer, David. "The Ascending Urlinie." Journal of Music Theory 31/2 (1987): 275-303.

Schachter and the rising Urlinie, Part 3

Today's post is a summary of Carl Schachter's article on the Prelude to J. S. Bach's Eb-major Cello Suite. I will provide critical commentary in tomorrow's post.

Here is a much condensed and (necessarily) heavily edited version of Schachter's 250-word abstract (71):

The Prelude has a quick-moving and active bass line above which ^3, ^5, and ^8 initiate linear strands: ^8 is a cover tone that begins and ends the Prelude; ^5 begins a fourth-progression ending in the final ^8; ^3 descends to ^1 at the structural cadence. Among the complex interactions is a contradiction between Db and D-natural whose resolution helps to direct the large-scale harmonic structure.

In the opening, ^3 lies below ^8 and ^5: this disposition characterizes the Prelude as a whole. The descent from ^3 to ^1 occurs in the middle of the texture: the uniformity of this texture suggests that the Urlinie is first among equals rather than the governing upper voice (that is, a two-part outer~voice counterpoint has less explanatory power here).

The essay has the following sections (headings taken from the text):

The Musical Idea. Responding to a criticism that technical analysis (the analytic graphics) may not provide real insight into a work's musical idea (here, not only a motivic germ but also a sense of movement and balance), Schachter summarizes his argument by noting the striking Db in m. 3 and its resolution through D-natural

several bars later, but in the "wrong octave" and middle of the texture. This is corrected at the end of piece but is worked through dramatically in conjunction with changes in figuration after the low C# (enharmonically Db) in m. 49.

The Opening Tonic Pedal and Underlying Shape: mm. 1-10. Three upper-voice motions are possible: the one described in the previous section, an ascent from an inner voice ^5 up to ^8, or a descent from ^8 down to ^5. The first of these, which is considered boundary play by Schenker, is preferable, and because its registral shift "exposes an inner strand of the texture--Ab-G--and transforms it into the upper voice," that G3 is ^3 of an Urlinie that remains essentially "submerged" throughout the Prelude as an array of events moves above it.

The Large Structure: An Overview. Details of the preceding (multiple strands with the Urlinie in one of the middle ones) are shown.

The C-Minor Prolongation and Parallelisms: mm. 11-28. Highlights motivic parallelisms between the topmost voice at the beginning and the bass in the following section.

The Chromatic Move C-C#-D: mm. 27-52. The more important and dramatic music follows after the C-minor cadence (in the preceding) through this section that leads to a cadence in G minor. Disturbances in the figuration gradually increase, up to the point of the full stop on C#2 in m. 49.

The G-minor Cadence: mm. 49-62. Connections are made between voice leading movements here and those of the three strands and their registral positions.

From G Minor to the End: mm. 62-91. The G-minor cadence is framed by a pattern of gradually introduced sharped notes before (shaped by the circle of fifths) and a corresponding series of flatted notes after (likewise following the circle of fifths). The several strands remain; the large-scale fourth in the upper strands resolves itself in the final two measures.

The Submerged Urlinie. The lower strand, with ^3-^2-^1, rather than the large-scale fourth, is the fundamental line because (1) it "is the primary melodic constituent of the big harmonic cadences, and these cadences clearly shape the tonal movement of the piece . . .; (2) G is a far more prominent constituent of the opening tonic prolongation than the Bb; (3) in this piece, the 3-2-1 line is representative of the melodic structure that characterizes the tonal repertory at large" (68-69). Here, at least, "the contrapuntal interplay between several upper voices is important enough to reduce the explanatory power of inferring a two-voice framework."

Oppositions. "The opposition of ascending and descending motion [,] an inescapable constituent of any music with organized pitches [,] plays an inordinately great role in the design and structure of the Prelude. Indeed if the musical idea of the Prelude involves the restoration of equilibrium after an initial disturbance, it is largely in terms of the opposition of descending and ascending that the idea seems to be conceived" (69)

Symbolism? Tentatively suggests Christian symbolism: "the change of Db into C# may symbolize the redemption of fallen humanity through the crucifixion" (70). Although the focus on flatted notes in the second half "might suggest mortality and physical death, they are mitigated by the final rise to the high Eb, the saved soul's ascent to heaven" (71)

Reference:

Schachter, Carl. "The Prelude from Bach's Suite No. 4 for Violoncello Solo: The Submerged Urlinie." Current Musicology 56 (1994): 54-71.

The two leading tones in Schenkerian analysis

This is a continuation of the topic from the last two posts, where (two days ago) a conflict between melodic parsimony and a melodic descent from ^3 to ^1 was observed to be unresolvable in four-part writing; and (yesterday) basic sets of oppositions with unequal (marked and unmarked) terms were seen operating in Schachter's reading of D779n13.

One can preserve Agawu's syntactically necessary "^2-^1 over V-I" only in three-voice counterpoint and then only by accepting incomplete tonic chords -- see below. In other words, three-part writing is no better than four-part writing at solving the conflict, but it is certainly better at revealing the basic elements of the archetypal progression that Agawu invokes: I-V-I in the bass with a progression including the descending line from ^3 and both leading tones resolving correctly.

In two-voice counterpoint, of course, the ^2-^1 is possible but not the V-I (at least, not in the Fuxian species), which is why the structural levels of a Schenkerian graph can be understand as replicating the order of the Fuxian species only conceptually, not literally (we just saw something nearer the literal in the examples above). Schenker was interested in marrying the melodic principle in the old cadence, with its 6-8 or 3-1 interval sequences, to a nineteenth-century, abstract conception of harmony, and so he resorted to a Hegelian dialectic of basic musical forces: melody vs. harmony in synthesis become the counterpoint of the Ursatz -- the rational perfection of first species, not its duplicate or imitation.

In the old clausula vera or Tenor-Klausel, there are two equal "leading tones," the equivalents of ^2 and ^7 in the major-minor scale system. Here is an example of the latter as it is expressed in the final two bars of J. S. Bach, Eb-major Cello Suite, Prelude.

As I suggested in yesterday's post, however, Schenkerian analysis has devices that remove the ^7 to later levels than the ^2. Two of these we have already seen:(1) the bias toward descending lines from ^3, and (2) the attendant willingness to give priority to inner voices if they carry such lines. The other two are, in a way, more pernicious: (3) the leading-tone third line, which provides "automatic" explanations for ^7 as subordinate to ^2; and (4) the implied ^2, which supplies ^2s even if not present in the score.

This erasure of the ^7 has some far-reaching consequences for interpretation.

Two readings after Cohn and Dempster, no. 1

Richard Cohn and Douglas Dempster criticize the treatment of motivic patterning in Schenkerian analysis as internally inconsistent: "In principle, motivic relationships must emerge as a by-product of voiceleading reduction; but in practice, voice-leading reductions are molded in part to optimize motivic relations" (171). In part as a way of respecting the directionality implied by this observation, they rethink the relationship of hierarchical levels in an ingeniously plural conception of a top-down hierarchy, according to which a given musical "surface"--a text (however construed)--"'holds together' underlying diversity by providing a compositional solution to multiple and disparate demands of harmonic, contrapuntal, motivic, and rhythmic operations" (177). As Robert Fink puts it, Cohn and Dempster “make a convincing case that viewing the musical surface solely as the product of a single generative hierarchy is too limiting; they prefer to consider it as the product of multiple interlocking hierarchies. Their revisionism does not, [however,] encompass the [more] radical step of detaching the surface from hierarchy altogether” (105).

Instead of conceiving analysis in terms of a top-down or chain-of-being hierarchy (after Zbikowski), they advance "a view of musical structure as a network resulting from a set of generative operations that are intertwined yet independent of one another" (172). Specifically, they suggest the use of product networks for "modeling music [in a way that is] simultaneously generative (in the sense of precisely specifying each event) and nonhierarchical" (174). They offer four examples. The first is drawn from David Lewin (204-6; Cohn and Dempster, 172-4) and allows for simultaneous generation in melodic and harmonic (intervallic) dimensions for organum. The other three examples set Schenkerian voice leading analysis against a "more loosely defined scheme of motivic generation" (174); a voice leading frame against a plan of figuration (in Bach, Well-Tempered Clavier, vol. 1, Preludes in C Major and C Minor); and "voice-leading designs [against] metric/figurational schemes" (175).

The last of these is of particular interest here because the authors point to topical conventions, which often "subsume conventions of meter, tempo, duration, and figuration into a higher-level construct" (175). If, following Cohn and Dempster, we want to locate D779n13 "at the intersection of voice-leading paradigms and topical conventions, [through a] product network [that] values the unifying potential of movement along either of the two axes" (175), we might exploit our narrative-topical conception of the piece as a portrait of a dancing couple (earlier post to this: link; also see "dancing" in the Labels sidebar). The topic is single (the waltz itself); the narrative consists of the formation of the couple, the dance figures (multiples of two-measure groups), and the separation of the couple as the dance concludes. For the voice leading generator, we could use any linear reading.

I have made an attempt at representing such an analysis in the graphic below. The upper line shows the initial courtesies (M = Man, W = Woman) and formation of the couple (F), the figures of the dance (D) and their multiples against each section of the music, and finally the separation at the end (F-1). The second line is a "primitive urlinie" ^3-^2-^3 (which, of course, could be easily renotated as a simple elaboration of the proto-background ^3-^3): here the graph shows all repetitions and thus a correct representation of the music in the time-line of the dance.

There is some virtue in writing out the repetitions -- as a reminder of the unifying power for (any) music of that simple process, but D and its multiples leave out two important features of the dance: the detail that each figure consists of a step by the man in one measure mirrored by the woman in the next, and the larger, contingent factor of the environment: how many figures one dances along any side of the room and how many figures may be accomplished in a complete circuit depends on the size of the room. Since Schubert's waltzes were played at house balls and parties, the spaces involved would most often have been relatively small.

By way of experiment, my partner and I managed 8-9 compact figures in circuits of a rectangular floor at 12 x 16 feet, and thus a couple could be expected to go around the room at least three times while dancing to D779n13. The surface represented in the graphic, then, is not a reading of the text of D779n13: it is the contingent circumstance of a dance to that music. In Cohn and Dempster's terms, we conceive this "complex . . . surface [not] as unified by an underlying structural simplicity [but] as a solution to the compositional problem of mutually satisfying the demands of several sets of independent formal operations" (176; their emphasis); that is to say, the dancers dancing and the music playing produce the dance. Note that the operations are in fact independent: unlike the extended figures of a quadrille, the figures of the waltz are coordinated with the music only up to the two-bar hypermetric level.

References:

Cohn, Richard, and Douglas Dempster. "Hierarchical Unity, Plural Unities: Toward a Reconciliation." In Bergeron, Katherine and Phillip V. Bohlman, eds. Disciplining Music: Musicology and its Canons, 156-81. Chicago: University of Chicago Press, 1992.

Fink, Robert, “Going Flat: Post-Hierarchical Music Theory and the Musical Surface.” In Cook, Nicholas, and Mark Everist, eds. Rethinking Music, 102-37. 2d ed. New York: Oxford University Press, 2001.

Lewin, David. Generalized Music Intervals and Transformations. New Haven: Yale University Press, 1987.