Postscript 1 to Berry

This is a postscript to yesterday's post on Wallace Berry, where Robert Fink's notation was adopted for part of the analysis graphic. Fink demonstrated the extent to which ascending linear gestures are present in Beethoven's Missa solemnis and the Fifth and Ninth Symphonies (1994, 88-216; 1999, 108-13). Although many of these are long-range patterns (in the sense that their elements are distributed over large segments of the music), they differ from Urlinie forms, as Fink carefully and deliberately avoids tying the gestures to harmony and voice leading hierarchies, his goal being to show how what he calls "energies," or the irrational movement of desire, can play out independently of the "logic" of harmonic functional hierarchies. Hearing an "arbitrary" rising chromatic gesture in the close of the Credo of the Missa solemnis, for example, Fink generalizes to say that "Even in a tonal work ultimately ruled by a voice leading hierarchy, this way of hearing drives a transgressive wedge between the surface and the depths" (1999, 113).

Rising gestures are appropriate (perhaps even the simplest and most direct) figures for Fink's theory, which avoids universal forms. Setting the image of a ball on a hillside against the experience of goal-directed motion in listening to a piece of music, Fink says that "In the case of the ball, the surroundings are the earth and its gravitational pull; in the case of a musical piece, the surroundings are the listener's musical consciousness and the pull of expectations and desire" (1994, 30). The "crucial difference" between the two is that: "the pull of desire is for each musical experience essentially self-created, unlike gravity." This is basically another example of flipping binaries: depths/surface in linear analysis necessarily favors the first term; the "transgressive wedge" shifts attention to the unmarked term, and one ends up with a cluster: surface/desire//depths/[design].

Fink's "flat hierarchy" is not an attempt to reconcile "surfaces" with Schenkerian practice but to displace (do away with?) the latter. His mode is essentially polemical and as a result he can offer no defense against long-standing scientific demonstrations that hierarchy plays a fundamental role in cognition, even though in hardly so monolithic a manner, perhaps, as Lerdahl continues to insist in Tonal Pitch Space.

References.

Fink, Robert. "Arrows of Desire: Long-range Linear Structure and the Transformation of Musical Energy." PhD diss. University of California, Berkeley, 1994.

Fink, Robert. "Going Flat: Post-Hierarchical Music Theory and the Musical Surface." In Nicholas Cook and Mark Everist, eds. Rethinking Music, 102-137. 2d ed. New York: Oxford University Press, 2001.

Lerdahl, Fred. Tonal Pitch Space. New York: Oxford University Press, 2001.

Wallace Berry

Detaching rhythm and meter from harmony rather in the way that Meyer prioritizes melody (but, like Meyer, preserving a loose sense of hierarchy), Wallace Berry proposes that rhythm merges into meter at larger spans and thus multiple accent streams can be read hierarchically, with a layering of accents analogous to the layering of structural levels in a Schenkerian analysis – the difference being that the accents at the upper end of the hierarchy acquire their position by cumulation, rather than syntactical differentation.

Such expressive accent groups have the advantage that they can model the dramatic or emotional curve(s) of a composition's unfolding far better than analyses that rely on metric regularities or the hierarchies of harmony. As a matter of method, however, Berry demands too much of the analyst – every level requires considerable, intuitive gathering and sorting of accents, and the resulting analysis graph can never reflect the complexity of those decisions. In the case of D779n13, reasons for the choice of the "primary" accent are not likely to be obvious, because one element of the decision is a denial of expectations: our structural highpoint or highest-level accent, m. 31 (see the graphic below), should have been as loud as the forte of the C#-major phrase, and it should have received a strong hypermetric accent (which we can confer on it but only with the help of explanations such as those engendered by Lerdahl and Jackendoff's various preference rules). The measure is marked partly by these notable absences, and in both cases, the preceding bars of A7 chords rob m. 31 of those features. Thus, even at the end there remains residual doubt about whether the primary accent belongs to the C#-major chord of m. 23, the A7 chord of m.29, or the B-minor 6/3 chord with its suspension in m. 31. The deciding factor, I think, is register, as depicted in the lower part of the example, where a steady progress of the initial F# across the piece obtains, and the moment of arrival coincides with an inversion of the initial soprano-alto interval. After this moment, the reprise and final cadential ascent sound "anticlimactic" – in Berry's terms "reactive" and recessive. (Berry's priorities resemble Robert Fink's, a fact which has motivated my notation using the angled arrow/beam.)

Berry's conception of musical hearing is the endpoint in a line that began with Schenker and moves through Meyer. All believe in hierarchy: Schenker's is the strictest, with its single generating structure determining priorities throughout the levels; Meyer loosens this to permit multiple simultaneous patterns but he clearly believes in relative significance based especially on a shorter-scale/larger-scale distinction; Berry believes in multiple, autonomous streams which establish hierarchies by statistics, the accumulation of coincident accents (one might say that this concept of meter is at the top of the hierarchy). Its combination of multiple streams of activity and dramatic accent makes Berry's method the most cinematic of any mode we have considered so far – indeed, his notion of levels of metric accent as applied to music is indistinguishable from Michel Chion's "audiovisual phrasing" as applied to a film soundtrack.

References.

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

Berry, Wallace. Structural Functions of Music. Englewood Cliffs, NJ: Prentice Hall, 1975; reprint ed. New York: Dover Books, 1987.

Fink, Robert. "Going Flat: Post-Hierarchical Music Theory and the Musical Surface." In Nicholas Cook and Mark Everist, eds. Rethinking Music, 102-137. 2d ed. New York: Oxford University Press, 2001.

Chion, Michel. Claudia Gorbman, tr. Audio-Vision: Sound in Film. New York: Columbia University Press, 1994.

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.