Debussy, the pentatonic, and the upper tetrachord

Jeremy Day-O'Connell has published an article in the same issue of MTS as my proto-backgrounds piece. He makes a comment that resonates with an earlier post here:

For Schenker,the tonic-dominant polarity held an almost mystical primacy: "May the musician always carry in his heart the image of the bass arpeggiation! Let this triangle be sacred to him! Creating, interpreting—may he bear it always in ear and eye!" ([Free Composition] 1979,15). That being said,the leading tone per se was of relatively little importance in Schenker’s mature theory, according to which tonal melody achieves coherence and completion only in a descent through ^2 to the tonic. (245)

His article is a sensitive, historically rich exploration of Debussy's treatment of pentatonic materials and design, with the Prelude La fille aux cheveux de lin as the principal example. Using (of all things) Schenkerian analysis, Day-O'Connell shows the layering and development of ^5-^6 figures and ^5-^6-^8 cadence gestures.

After reading the article through, I thought: over the years, we seem to have done a creditable job of the notes up to ^5, but we are just beginning to get a proper sense of the rest.

Reference:

Day-O'Connell, Jeremy. "Debussy, Pentatonicism, and the Tonal Tradition." Music Theory Spectrum 31/2 (2009): 225–261.

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 10

This post continues the discussion of Schubert's ballad "Die junge Nonne" from Part 9. First, a simple, nicely done description of the song through the poem's narrative may be found here, along with a link to a performance: Die junge Nonne.

From the standpoint of thematic reading, an Urlinie running down from ^5 misses too much of what is essential about the dramatic progress of the song in terms of motive and the play of register. "Misses" is not quite right -- what I mean is that an analysis grounded on such an Urlinie necessarily misconstrues the song and its elements.

The introduction announces three registers with distinct materials: I've labeled them Bass, Tremolos, and Bell. The voice (system 3) occupies the space between Tremolos and Bell (assuming the singer is meant to be female, a reasonable assumption given the identity of the poem's narrator). The Surprise moment comes in the second system, when to Bell is suddenly appended a motive that is a loose inversion of Bass, drawing attention to the relation of Db and C, which I regard as the crucial design element in the upper most voice, whether that line is in the keyboard or the singer's part. (L in the third system is a Leittonwechsel transformation, made directly as it could be in Tremolos.)

The static register of the voice -- as I wrote in the earlier post, if I were reading this with proto-backgrounds, ^1-^5 would be the overwhelming choice -- is pushed against by the same C-Db pair (above), and even more when Db = C# moves again, to D-natural (below). The harmony "breaks," however against "finster," where an R transformation in Tremolos is subverted by the G# in the bass. From that point the harmony moves toward a cadence; D-natural moves down again, finally reaching C; and the pinkie finger in Tremolos retraces its movements down from F# to F-natural.

When all this done, Surprise reappears, now in the voice, immediately after the keyboard's P-transformation (third system below). "Immerhin" here means "always" (or perhaps "constantly"), as the young nun introduces the comparison between the turbulence of the storm and her equally unsettled emotions. This moment of Surprise is remarkable, stands out as an island of calm, and promptly disappears as verse 2 gets underway in earnest.

A motivic detail of interest is Bell, which sounds as D5 but then is gone for several bars until it reappears at the moment of Surprise (below).

The second verse ends like the first, and the third verse, then, expands greatly on the P-transformation and the Surprise moment -- see below. The voice keeps pushing upward: C5-then D5-then E5-and-finally-F5 (circled notes), but as it turns out only the initial C5 is stable. E5 is reached at "Friede" but the harmony is C: I 6/4 that remains unresolved -- instead, an RP transformation takes it directly to A major (as V of D minor), then to Bb: V7 with the F5. This latter move is a PR transformation *if* you read only the underlying triads.

In all this, there is no suggestion of C5 (or any ^5) taking a significant role, though C4 in the middle of Tremolos does move to C# (enharmonically the Db of the beginning), which in turns drops back to C -- a nicely managed motivic statement.

The latter half of verse 3 was discussed in some detail in the previous post. Here I will note that Bell gives us a gesture C5-D5-F5 (connected boxes below), as pinkie Tremolos run from A4 up to D5 (connected circled notes). In Bell, E5 is skipped, not reached; and in Tremolos a reach toward E5 in the voice after the D5 is roundly subverted by Bass, which (finally) drops to Bb to define a functional triad plainly and then fosters the predictable patterns of voice leading to which Schachter draws attention.

Both Bell and Tremolos mark F5 as a goal, as, of course, did Surprise from the outset: C5-Db5 as Sturm, F5 as escaping, surmounting Sturm. In the partial score below, I have marked out the twin unfoldings in the voice part that bring ^6 back to ^5 before the final ascent. Note that *only* here are E5 and F5 stable tones. (Earlier in the song, F5 is in Bell at the Surprise moment, and of course the parallel cadence in 52-61 is set up the same way.)

The geography of dance music

I am using "geography" here to denote the immediate physical environment of Schubert's playing -- the piano, Schubert on a chair, anyone not dancing standing near him, the dancers coming by relatively close, the sound of the room, the shifting groupings and activities of the participants.

Given that Schubertiades took place with audiences anywhere from a few to a hundred, we have to assume that the physical spaces for dancing varied greatly, too. In a small space -- a drawing room of one of his friends' apartments -- the piano would probably be small, too, square. Chair with a back, not a modern-style piano bench. The piano positioned either along a side wall or, if there is space, angled out into the room (as in Kupelwieser's watercolor). The amount of resonance in the room would vary greatly, depending on wall coverings and the number of people, but would probably be fairly high since the floors would not be carpeted (or any carpets would be drawn back for the dancing).

Schubert playing, looking occasionally to the side at the dancers, especially the Vortänzer (the lead couple), and listening in case the Vortänzer call for a different figure, dance, or a pause (common in longer dance sessions), during which Schubert might continue to play or might stop, too. Persons not dancing, male or female, sitting or standing close by, occasionally talking to one another or even making brief comments to Schubert on his improvisations or requests to hear familiar dances. The distinct timbres of the three main registers on contemporary pianofortes would be audible nearby, less so on the dance floor, where the swishing of clothes and muffled swish-slide of light cloth dancing shoes would mingle with the music. The shapes of the dancing would have varied, from couples dancing freely within the dance space, couples moving in a "round dance" format (around the room along a line of dance) to chain dances or even something like the "parlor game" formats of the quadrille. Windows closed, perhaps shuttered against the night.

In breaks, food and perhaps the light, young Austrian white wines of which Schubert was said to be particularly fond. He was a "lively" drunk, and it would probably have been difficult to get him to return to the piano late in the evening if he had had too much. These, among others, were the occasions when his duet-partner, Josef von Gahy, would take over to play for any dancing done in the late night hours.

In larger spaces, Schubert would probably have had a correspondingly louder wing-shaped pianoforte to play, and the temptation to move back and forth between music for dancing and dance-music performances would have been that much greater, as well.

Note: In Kupelwieser's watercolor, the pianoforte appears to be a small spinet -- thus, neither the square piano one might expect in that space nor the larger instrument one sees in the Schubertiade drawings and other graphics.

Schachter and the rising Urlinie, Part 9

The third section, "Structure and Contour" (331-33), provides two readings that illustrate an assertion from the end of the second section:

Downward motion will characterise structural endings, and, as a corollary, upward motion will occur before the descents-~either at the beginning or in the middle of melodic lines. The tonal system, however, through the phenomenon of octave equivalency, provides an escape clause from these constraints of the structural background. Prolongations, in widening the field for tonal activity, will also free the upper voice from the need for uniformly descending resolutions of linear tension. (331)

The examples from Verdi and Schubert show registral repositioning upward of individual tones in a descending urlinie: the ^3 in the middle of a five-line, and the final ^1, respectively. In both cases, the repositioning is associated with figures in the text.

With respect to the structural cadence of Schubert's "Die junge Nonne" -- and therefore the Urlinie shape -- Schachter has simply gotten it wrong. His graph shows bars 52-61; these include a "cadence [that] achieves its rise to the tonic through a brief stepwise line that culminates in the notes C-D-E-F; F of course is the tonic note and E, the leading tone, can be understood as an inner-voice note of V that substitutes for ^2" (333). This is not the structural cadence -- "a variant of this same cadence" has that role: mm. 74-83. These latter measures are shown in the graphic below, with Schachter's reading mapped onto them: ^5 with inner voices ^3 and ^1 below, the structural bass elements IV-V-I and ^4-^3 (moving from voice to piano)-^2-^1 with accompanying sixths below, two lines moving up in the voice: ^3-^5, then ^5-^8.

Against that I offer my reading below. The ^5 over ^1 is clear at the outset. Note the string of unstable harmonies with parallel octaves between voice and bass at the same time the voice repeatedly outlines the octave register (C4-C5, D4-D5, F4-F5). The octave, and the space of the octave, are obviously crucial here. The clue, I think, is in the "bell sounds" -- the piano left hand crossover pitches, F5 in m. 74, C5 in m. 75, etc., The voice duplicates the piano's notes each time she reaches the word "Getön" (meaning the bell sound): the link between "Getön" on F5 and "Höh[e]n" on F5 is obvious. The piano may have to work the mundane task of the cliché cadence, but the voice has been transported -- and that, I would assert, is what this song is all about.

In the MTS article, I wrote about the Pietist concept of Jesussehnsucht (longing for Jesus) in connection with the funerary chorale "Christus, der ist mein Leben." Here it is not an expression derived from the Protestant notion of personal salvation, but from the Catholic tradition of specifically female figures (usually nuns) yearning for the "heavenly marriage" with Christ. That has been merged with simple Romantic nature imagery -- in the first verse, she speaks of her fear at a stormy night; in the second verse, the emotion is the turbulence of her yearning for Christ (at the end of this, she calls out for the himmlischer Bräutigam); in the final verse, the bell sound seems to clear and calm the air, and she can speak of peace, desire, and heaven.

Schubert obliges with a ballad style and textures and affects that remind one of Erlkönig. The first two verses are in F minor, with obsessive emphasis on C5 and Db5 in the voice (see below); the final verse is in F major.

I am hardly finished with the striking features of this song. Contrary to the suggestion in the lines that Schachter quotes, with their "sweet sound" and "eternal heights," the harmonic progressions of the F major verse remain surprisingly tense (at least, unstable) right up to the structural cadence -- it is the release in that final rising gesture, going one last time to F5, that enables the harmony to come to peace itself. Some sections of the song look very amenable to transformational readings, and the incessant right hand tremolos reveal a different version of the Riemannian hand. Perhaps I'll follow up those leads some other day.

Schachter and the rising Urlinie, Part 8

In the second section, "Ascending and Descending Motion Contrasted" (328-31), Carl Schachter offers two readings of ascent and descent in connection with text painting in 19th century songs. In the first case (Schumann), the inversion of a motive and a sequence made up of this rising form expresses "erotic excitement" (329). In the second case (Brahms), the motivic directions are reversed (death/night/rise; life/day/fall) but at the climax the expectations are righted by a change of shape in the motive (330).

From the first, because Schumann denies the erotic with a falling cadence at the end, comes the general statement that "the descending melodic impulse at a cadence is typical and is a central component of the tonal system" (329). "Typical" not "universal" -- Schachter never goes so far as explicitly to claim the latter for descending lines in cadences -- but nevertheless essential to "the tonal system," the latter, as we find out during the discussion of Brahms, being defined as Schenker construed it. Thus,

That descending melodic movement tends to create repose might be understood as reflecting our physical lives as creatures subject to the force of gravity. It takes effort to throw a ball into the air; it falls back to the ground by itself. Accordingly we might well imagine that musical descent suggests repose by analogy with physical motion…. (330)

. . . the ensemble of pitches conforms in part to the inner structure of a normal musical tone. . . . Musical motion toward the first partial -- " descending" motion -- leads to a fixed point of reference and thus tends to evoke a feeling of repose comparable to a move down through space. In the music of triadic tonality, this general attribute of downward motion is intensified by the fact that the triad is built from the bottom up. . . . In tonal music, the most stable positions of the triad are of course those where the root is grounded in the" earth" of the bass part. And in the melodic lines of tonal music, a descent from ^3, ^5, or ^8 to ^1 replicates in the horizontalized triad of the upper voice a move from an overtone . . . to the fundamental sound. (331)

Out of this recital of familiar notions comes the foregone conclusion that "for tonal music, the distinction between up and down is far from superficial, since moving down provides a more definitive closure."

David Lewin argues differently. Reacting to Susan McClary's charges about patriarchal containment of women's voices, he rejects an analogy between the spoken sentence and the sung phrase (and therefore a naturalized linkage between "coming to rest" and descending melodic movement): "Our musics are not 'natural phenomena,' like everyday speaking. All singing styles, in particular, are highly stylized in comparison to everyday speech" (275).

I would add that the notion of cadence-as-repose within a tension-relaxation model has no place in the singer's physical experience of performance -- tension in the body (diaphragm, lungs) rises to its top point before a phrase starts and is maintained till after the phrase is finished. One doesn't need to be a professional singer to experience that, either -- or a singer at all, since playing a wind instrument works essentially the same way.

Instead, Lewin associates patriarchy with priority to the bass (or fundamental), and from this it follows that "the transcendent musical voice must be a woman's voice" (271): "The female voice is typically acoustically free of what we conceive as a functional bass line—whether continuo or fundamental bass—and that is less typically true of the male voice" (274).

For Schachter, a certain set of historical practices in European tonal music may as well be universals ("fixed points of orientation [the tonic note, triadic roots]. . . important functional differences. . .the system itself"), but for Lewin they still have strong traces of cultural practices that can be interrogated. For Schachter, the difference between rising and falling melodic gestures offers wonderful expressive tensions in a balanced system; for Lewin, that balanced system may also be understood as a constraining cultural construct that can be "escaped" not just by the mad women of nineteenth-century opera but also by the transcendent female voice (pace McClary, Lewin counts Isolde and the soloist in Schoenberg's second string quartet and Erwartung among these).

However one reacts to Lewin's specific argument here, it is certainly well-established through historical narratives connected to neo-Riemannian theory that in the nineteenth century a harmonic model emerged that opposed symmetrical models to traditional "Earth-bound" metaphors. I also claim that whether through a Newtonian concept of gravity, the Romantic's exploitation of oppositions, or simply through a desire to escape from century-old, clichéd cadence figures, the opposition of rising and falling gestures was altered to contest (or to vitiate) the structural priority of descending cadence gestures.

References:

Lewin, David. 2006. Studies in Music with Text. New York: Oxford University Press.

Rings, Steven. 2006. Review of three books by David Lewin in new editions. Journal of Music Theory 50/1: 111-27.

Schachter and the rising Urlinie, Part 7

I summarized Carl Schachter's article "Schoenberg's Hat . . ." yesterday. A number of issues will be considered here, from how good is his defense of some traditional notions, to how convincing are his examples, to how effective is his criticism of my "Ascending Urlinie" article. I will take these more or less in order -- insofar as they can be separated from one another -- following the article section by section.

As I wrote yesterday, in the introduction Schachter takes Schoenberg to task for his assertions about a unitary musical space, but Schoenberg was not referring to rising or falling lines -- he was talking about musical "objects" (motives) that maintain their identity despite "viewer position" (P, I, R, or RI). Schachter cites Milton Babbitt's comment on Schoenberg's application of the idea to Beethoven as well as to 12-tone music -- "The tonal motive assumes functional meaning in a context, and becomes, in turn, a vehicle of movement within this context; the twelve-tone set, however, is the instigator of movement and defines the functional context" (cited on 329). Schachter apparently wants his positioning of Babbitt's comment as "long ago" to mean that Schoenberg's error should have been obvious to everyone, but in fact the "long ago" inadvertently highlights an anachronism: Babbitt's firmly placed wall between tonality and atonality (understood in Schenkerian and 12-tone terms, respectively) is an attitude that belongs to a generation of the twentieth century's third quarter. That wall started showing cracks as early as the mid-1970s, when Allen Forte, James Baker, and others began to explore transition repertoires (Scriabin, early Schoenberg and Webern, etc., and going back to the late music of Liszt); and it was crumbling noticeably after David Lewin published GMIT in 1987 and collapsed quickly once neo-Riemannian theory and its attendant historical narrative began its rise in the 1990s.

Furthermore, work on schemata, metaphor, and related ideas points to the complexity of musical cognition. Janna Saslaw, drawing on Lakoff and Johnson, lists the following image schemes: container [which suits motives and hats very well], up-down, center-periphery, link, part-whole, force, front-back, path, and source-path-goal (219, Figure 1). All of these, as Saslaw points out, can be understood as relevant to expressive and interpretative models of music making. There is no more reason to privilege the up-down schema than Babbitt's wall.

Schachter finishes the introduction by listing three assumptions: he understands "motion", "space", "high", and "low" in purely musical terms; these have only a "a loose metaphorical relation to our non-musical experiences of space and movement"; but these metaphors are nevertheless fundamental to music's expressive and affective potential.

To the first of these: Schachter immediately constrains the potential outcomes by his definitions. Motion, for example, "refers to the kinetic impressions we derive from tonal and rhythmic patterns," a description that pushes us more than halfway down the road to Schenker. "Motion," however, involves schemata whenever it is anything more organized than events passing randomly by in linear time -- schemata like path, force, and source-path-goal. "'High' or 'low' [refers] to sounds produced by vibrations of greater or lesser frequency" -- but here again the variety of ways in which frequency differences are understood or experienced is ignored in favor of a particular one. Indeed, high and low frequency differences may be primarily based on gender differences familiar from everyday speech but particularly exposed during singing (children, in this account, being lumped in with women). The music of the celestial spheres had all manner of interval sizes, not just ones that produced "high" notes -- and the symbolism of intervals and numbers meant far more to composers before the 19th century than did the superficial text painting to which Schachter alludes. Pianists experience music as much left to right as lower to higher; violinists, too, with an added angle of distortion; organists left to right and large to small; trombonists far to near; guitarists top to bottom; horn players -- well, round and round, I suppose. Only a handful of instruments fit the low/high model: cello, bass, oboe, clarinet. Finally, of course, the proper way to conceive frequency differences would be slower and faster.

To the second and third assumptions: Schachter tries to have it both ways, acknowledging the weakness of the metaphorical ties but then wanting those metaphors to have deep cultural significance (and, because of their historical depth, permanence). Although I suspect that in music gender differences are at the root of it, the up/down schema itself is certainly ancient and is obviously a mental model related to everyday experience. It has generated a powerful collection of related metaphors, including earth/sky, climbing/descending, standing/sitting (or lying), waking/sleeping, even living/dead (as an extension of waking-standing/lying-sleeping). In the arts, it has often been mapped onto the pair tension/relaxation.

The schema and its metaphors are easily tied to gravity, as Steve Larson does in his three voice leading "forces": gravity, magnetism (or attraction), and inertia (cited in Lerdahl, 191). Lerdahl criticizes the first of these, however, saying that "gravity appears to be dispensable: in the major scale, except for the leading tone, the strongest virtual attractions of nonchordal diatonic pitches are by stepwise descent anyway." Lerdahl finds the source of Larson's promotion of gravity as a force not in cognition but in an ideological committment: "By gravity he means the tendency for melodic lines to descend by step (as a Schenkerian, Larson is especially committed to this notion)."

Gravity (as priority to downward motion) is an "earth-bound" metaphor, but it is as primitive as it is ancient: the scientific definition (since Newton) is attraction, and thus the appropriate way to think of gravity is in terms of tension and opposition but not a specific and fixed direction. In the neo-Riemannian historical narrative, the emergence of musical thinking expressing this change happens clearly in the first quarter of the 19th century -- see Cohn 1999, where Schubert's use of symmetrical harmonic and tonal patternings undermines the "down-to-tonic" model and prefigures more systematic understandings of symmetries later in the century.

It is certainly also worth noting that Alexandra Pierce, who of all persons should have the most authoritative notion of the embodiment of Schenkerian hearing, does not tie "ending" to "sitting" " or even to "relazing" instead, resting balance and centered core match harmonic completion and a closing tonic (in ch. 2 of her book).

References:

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

Saslaw, Janna. "Forces, Containers, and Paths: The Role of Body-Derived Image Schemas in the Conceptualization of Music." Journal of Music Theory 40/2 (1996): 217-43.

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

Cohn, Richard. "As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert." Nineteenth Century Music 22/3 (1999): 213-32.

Pierce, Alexandra. Deepening Musical Performance through Movement: The Theory and Practice of Embodied Interpretation. Bloomington, IN: Indiana University Press 2007.

Schachter and the rising Urlinie, Part 6

Carl Schachter's article "Schoenberg's Hat" has the following sections:

Introduction: Schoenberg's Hat (327)

Ascending and Descending Motion Contrasted (328)

Structure and Contour (331)

The Rising Fourth (333)

Conclusion: Lewis Carroll's Trousers (337)

Appendix: The Rising Urlinie (338)

Schachter begins by criticizing Schoenberg's extension of his idea of a unitary musical space (essential to derive and justify the several forms of a 12-tone row, including inversions) to tonal music, where Schachter points to "a functional context in which the tonal motive assumes…meaning…characterised by fixed points of orientation (the tonic note, triadic roots), [and] by important functional differences between rising and falling movement (for instance in the resolution of dissonances)" (328). Schachter is careful to say that notions of high, low, and others relating to space and motion are metaphorical or analogical, but then he goes on to claim that "I do not regard the analogies between musical space and motion on the one hand and physical space and motion on the other as unimportant, inexact though they may be. A significant part of music's ability to reflect our physical and emotional lives comes from just these analogies."

He then spends considerable time exploring text painting in relation to prolongational figures in songs by Schumann ("Die Lotosblume") and Brahms ("Der Tod, das ist die kühle Nacht"). Under Structure and Contour, the examples are Verdi, from "0 Terra, Addio" from the final duet of Aida; Schubert's "Die junge Nonne"; under the Rising Fourth, Bizet, Carmen's soliloquy in the "Card Trio" of the opera's third act. In the latter section, he also looks at two instrumental compositions: Bach's C-minor Fugue from WTC 1; Chopin's Prelude in E-major. The appendix comments on what Schachter regards as problems in my rising line article and renders his own judgments about analyses that are convincing with rising line Urlinien.

I will make some comments on the analyses and offer responses to the arguments in posts over the next several days.

References:

Schachter, Carl. "Schoenberg's Hat and Lewis Carroll's Trousers: Upward and Downward Motion in Musical Space." In Brenton Broadstock, Naomi Cumming, Denise Erdonmez Grocke, Catherine Falk, Ros McMillan, Kerry Murphy, Suzanne Robinson, and John Stinson, eds. Aflame with Music: 100 Years of Music at the University of Melbourne. Parkville, Victoria: Centre for Studies in Australian Music, 327-41.

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

Eco's Limits and the conclusion of the MTS article

In an earlier post, I wrote that I regretted being unable to call on a couple constructs from Peter Westergaard's Introduction to Tonal Theory. Today I will say the same about Umberto Eco's Limits of Interpretation -- the point that I attribute to Jonathan Culler in the conclusion of the MTS article was made earlier, more forcefully, and we probably should say more famously, by Eco.

Where I seek to link the uncontrolled proliferation of themes, and therefore thematic reading, by citing Culler on the heuristic value of interpretive frameworks (319-320), Eco says that his goal in Limits is to

make clear that the notion of unlimited semiosis does not lead to the conclusion that interpretation has no criteria. To say that interpretation (as the basic feature of semiosis) is potentially unlimited does not mean that interpretation has no object and that it "riverruns" for the mere sake of itself. To say that a text potentially has no end does not mean that every act of interpretation can have a happy ending. (6)

Undoubtedly, the question has less significance now than it did fifteen years ago, when Eco felt obliged to note that "Even the most radical deconstructionists accept the idea that there are interpretations which are blatantly unacceptable" (6). If one is willing to make this acknowledgment, then one must allow that "the interpreted text imposes some constraints upon its interpreters." He identifies "the limits of interpretation [as coinciding] with the rights of the text (which does not mean with the rights of its author)" (7).

Eco's claim itself has heuristic value (a point on which he is by no means always clear). Note that he uses "unacceptable" -- the constraint on interpretation is partly the material dimension of the work, but partly also the moral dimension always implied in interpretation -- for comments to these points, see these posts: (1), (2), (3). The problem, of course, is that the moral dimension tends to be rooted in the prescriptive, which would seem to leave interpretation with no other option.

Final note: Today is the 100th entry in this blog. I have gotten a bit off the path of directly constructed close readings of D779n13 in recent weeks. After finishing up discussion of Schachter's "Hat" over the next several days and commenting on Richard Cohn's article on Schubert's Bb Major Sonata, I plan to post some of the following (in no particular order): a pitch-space reading, several recomposition exercises (including one modeled after Matthew Bailey-Shea's article in Music Theory Online), a dense motivic reading after Daniel Chua, the substitution of D779n13 for another piano piece of Schubert's in a movie scene, a reconsideration of cycles and tonality as Arthur Komar construed them for Dichterliebe, hommages to Leonard Meyer and Wallace Berry, and closer consideration of harmonic transformations (after Kopp and Hook).

Fauxbourdon

Was the C# major section a creative (and perhaps spontaneous?) response to the problem of parallel fifths in the first strain of D779n13 and the realization of an underlying fauxbourdon figure?

Readings from ^3 -- including Carl Schachter's -- inevitably include a string of parallel sixths underneath the principal line (see this post). In a recent session that included both improvising on right- and left-hand 6/3 passages and playing through a number of Schubert waltzes, especially those I know least well (that is, those written down before 1819), I realized (a) that following a tight fauxbourdon figure in the right hand frequently led to rather dull results; and (b) that, given their obvious utility in structuring the physical path of a dance improvisation, Schubert frequently uses strings of parallels in the right hand but is surprisingly reticent about the line of sixths down from ^3. When he does use the latter, he will find ways to vary it -- as with the truncation in the first strain of D365n9 (below) or the upward extension in D365n5.

I should have made an obvious stylistic point much earlier in this blog: ii6 -- or for that matter any S-type or predominant chord -- is a marker of the German dance, not the Ländler. The latter, as Litschauer documents, is characterized by alternations of tonic and dominant or prolongations of one or the other (see my Music Analysis article, 214-15). The German dance makes use of a range of progressions, including many taken from menuets. On these terms, D779n13 is a perfect marriage of the two dance types: it announces itself as a German dance immediately but is zärtlich like a Ländler -- indeed, one might speculate that the rare expression indication was meant to alert a contemporary player that, although this looks like a deutscher, it should be played more slowly and sweetly. (Virtually the same, btw, can be said of D365n2, the Trauerwalzer.)

In posts sometime next month, I will write about another right-hand figure that is quite common in Schubert's waltzes: the diatonic wedge, or ^7 to ^1 below with ^6 to ^5 above.

Postscript: One of the most direct treatments of parallel sixths in the ^1-^3 space is in the first of the two schottisches that follow the German dances of D783:

Schottisches in the first decades of the nineteenth century are often surprisingly direct, even crude (Beethoven's are good examples). With this one, the minor-key topos and pedal point announce zingarese exoticism but the second strain suddenly turns the motive into a loud march, and the dance ends with horn calls. All this in the space of 16 2/4 bars. The result is a comic portrait of Hungarian soldiers, perhaps an invitation to a parlor game rather than dancing.

Options to follow C# major

At (a) in the graphic below is a chordal reduction of the basic progression in D779n13. At (b) through (d) are three alternatives that in fact would have been statistically more likely results for a waltz that is firmly in A major in its first strain, then shifts abruptly to a C# major triad at the beginning of the second strain. Version (b) does not tonicize C# major, as does D779n13, but instead converts the triad into a seventh chord and moves smoothly through a cycle of fifths progression, devoting roughly equal time to each step. Version (c) tonicizes not C# major, but the F# minor that would have been a more likely goal of a C# chord in this context. Version (d) plays out the other implication of version (b) -- here a cycle of fifths progression leads to a close on E major. It is assumed that the close comes as the end of a contrasting middle section, because the articulation is necessary to explain an otherwise awkward retrogression to B minor for the reprise.

Version (d) follows through the implications of the hexatonic cycle and supposes a direct movement from C# major to F major (with an intermediate respelling of the C# triad as Db), and again from F major to A major.

I have worked all of these out in improvisation sessions. Not surprisingly, versions (b) and (c) are the easiest to manage, particularly in the close quarters of an 8-bar strain, but also as an 8-bar contrasting middle leading to a full reprise. Version (d) is not so successful; to make it sound plausible, I had to, as it were, override the close on E by following it with an A major triad -- that additional step on the cycle of fifths made for an uncomplicated move into the D7/b6 dissonance of the reprise. Version (e) sounded quite strange if I attempted to make it compact (fit it in 8 bars), but at least plausible if I stretched it out as a series of tonicizations.

The idea of a close look at chromatic harmonies as an addition to or corrective to linear analyses in the Schenkerian tradition was explored in a convincing way more than twenty years ago by Charles J. Smith (who was reacting to a tendency toward somewhat radically linearized -- and therefore sometimes harmonically obtuse -- readings among the first generation of American post-Schenkerists). More recently, Marianne Kielian Gilbert has given sustained attention to the issue in several articles -- see this post.

References:

Smith, Charles J. "The Functional Extravagance of Chromatic Chords." Music Theory Spectrum 8 (1986): 94-139. See also David Beach, "On Analysis, Beethoven, and Extravagance: A Response to Charles J. Smith," Music Theory Spectrum, 9 (1987): 173-185; and Charles J. Smith, "A Rejoinder to David Beach," Music Theory Spectrum 9 (1987): 186-194.

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

Kielian Gilbert, Marianne. "Inventing a Melody with Harmony: Tonal Potential and Bach’s "Das alte Jahr vergangen ist." Journal of Music Theory 50/1 (2006): 77-101.

Notational styles

The "chordal middleground reduction" below will show up again in tomorrow's post on options for progressions from the C# major area in D779n13. The style of notation here is quite similar to chordal reductions used by Douglass Green for his textbook Form in Tonal Music.

This notational style apparently derives in part at least from Felix Salzer's Structural Hearing. See the facsimile of Green's class notes for the opening of Mozart's Symphony No. 40 below. The middle system uses chordal reduction with the broken beams that are characteristic of Salzer, though he did not use one-stave reductions. All in all, Green's notes run a range of styles -- perhaps that was part of his pedagogical goal for the class.

References:

Salzer, Felix. Structural Hearing: Tonal Coherence in Music. 2 vols. New York: Dover, 1962. Original edition 1952.

Green, Douglass. Form in Tonal Music: An Introduction to Analysis. New York: Holt, Rinehart and Winston, 1965; 2d ed 1979.

Green, Douglass. Class notes, unpublished, in my possession.

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.

On Departure and the Tonal Archetype

I am returning one last time to the progression that Kofi Agawu describes as "a closed harmonic progression [that] constitutes the norm of coherent and meaningful tonal order" (109).

In a previous post I observed that this progression is not in fact "syntactically correct" because it shows the compromises necessary when melodic parsimony conflicts with a strictly maintained four-voice texture.

There is another problem with the progression, specifically with its status as a departure-return model. The first chord conflates a stable harmonic beginning point (I) with an already-departed melody (^3, not ^1). Now, this is presumably out of deference to Schenker, but that deference also means too much is taken for granted here. As Westergaard puts it near the beginning of Introduction to Tonal Theory, "pitch and time relationships are the primary stuff of the structure of any piece of tonal music" (11). If stable beginning is also to be point of departure, then only ^1 over I can be adequate to the task.

The properties are separable: in the examples below, all constitute points of departure (bar 1 of a waltz in D365) but only one of them constitutes a stable beginning (and even there, the tonally stable beginning is pre-empted metrically by the pickup note E5, which gains in salience from its mordent).

Although Westergaard, too, sets his rules out of deference to Schenker ("The first note of the basic step motion must be a tonic-triad member a third, fifth, or octave above the final note" (as cited in Peles 78)), he seems to recognize the problem at some level. Looking back at Introduction to Tonal Theory more than thirty years later, he says (59) that he would replace arpeggiation with borrowing as a basic operation (arpeggiation is melodic movement between triad members; borrowing accounts for these movements as drawing notes from other voices in the voice-leading web -- the same as Rothstein's imaginary continuo). Westergaard's example (60) begins (this is the crucial bit) with a closed position tonic triad, whose label reads "Four voices define a span by stating a C-major triad in closed position with the C doubled in the outer voices." Only after this, rearticulation confirms duration and borrowing lets the soprano claim ^3 from the tenor. Thus, the closed position triad, with ^1 at the top, is conceptually prior to the first chord of Agawu's "norm."

References:

Agawu, Kofi. Music as Discourse: Semiotic Adventures in Romantic Music. New York: Oxford University Press, 2009.

Westergaard, Peter. Introduction to Tonal Theory. New York: Norton, 1975.

Peles, Stephen. "An Introduction to Westergaard's Tonal Theory." In Theory Only 13/1-4 (1997): 73-94.

LINE, N, and Westergaard's Tonal Theory

In the MTS article, I present a small set of transformations that are applied to the intervals of the proto-backgrounds. I didn't realize it at the time, but Peter Westergaard had already done something very close to what I intended (an earlier, less careful formulation of it was behind the list of forms generated by a "criterion of simplicity" [Neumeyer 1987]). As Stephen Peles describes it:

Westergaard's set of generative operations that determine allowable within-line relations is small. Indeed, Schenkerian theorists will no doubt be struck by the comparatively parsimonious nature of Westergaard's typology of tonal transformations. A whole battery of Schenkerian operations, such as arpeggiation, unfolding, motion from an inner voice, and the like, collapse into a single operation category in Westergaard's system: namely, the arpeggiation operation. (77-78)

Westergaard's order of presentation in the section "Linear Operations and Constructs" (35-37) of his book Introduction to Tonal Theory would have served very nicely as a way to present the intervals and these transformations. He has four classes (he calls them "structures" (37)): (1) rearticulations (that is, repeated notes), which, coincidentally, introduce a whole range of rhythmic-metric issues, but which also lead to (2) neighbors; similarly, (3) arpeggiation [or, two consonant notes originally understood as simultaneous but arranged successively] leads to (4) step motion. The four of these "together with [the rhythmic devices of anticipation and delay can be used] to compose and to understand tonal lines."

What appeals to me is the simplicity of the pairings and the neat symmetry of the two groups, something implied in my Ex. 10 (the 30 backgrounds (301) but not made explicit: rearticulation --> N; arpeggiation --> LINE.

Westergaard does not introduce equivalents of my transformations INV or ADDINV; instead, he moves directly to chapters on species counterpoint and eventually introduces Schenker-derived operations he calls "doubling, borrowing, exchange, and transfer" (289).

References:

Westergaard, Peter. Introduction to Tonal Theory. New York: Norton, 1975.

Neumeyer, David. "Thematic Reading, Proto-backgrounds, and Transformations," Music Theory Spectrum 31/2 (fall 2009): 284-324.

Neumeyer, David. "The Urlinie from ^8 as a Middleground Phenomenon." In Theory Only 9/5-6 (1987): 3-25.

Peles, Stephen. "An Introduction to Westergaard's Tonal Theory." In Theory Only 13/1-4 (1997): 73-94.

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.

Schachter and the rising Urlinie, Part 2

Before I go on to discuss details of Carl Schachter's essay on a Bach prelude, I should note that Schachter did in fact write about D779n13; see comments in early posts (1); (2). This is one example in a classic essay that, with its companions, was a foundational influence on metric-rhythmic studies in the Schenkerian tradition. I commented at some length on the tonal and contrapuntal aspects of the analysis in my Music Analysis review-article, 22-24. The following is an edited excerpt:

Schachter notes that ‘the right hand plays two melodic lines written in free imitation. The lower of these lines carries the main melodic motion and is, in general, more active than the upper one. The upper line, therefore, functions as a secondary part’ (Schachter 1999, 70). The logic is uncertain: the strong linear drive created by the string of suspensions succeeds in focusing attention on the lower voice but does not therefore relegate the upper voice to secondary status: the unargued assertion that the lower voice ‘carries the main melodic motion’ in itself accomplishes that task. (22)

Furthermore, as we know well by now, the claim that the alto voice, with its suspensions, is somehow "more active" than the upper voice, with its constant play of ^5 and ^6, is simply not defensible. The characterization rests on an opposition line/boundary-play (Urlinie/Ränderspiel) that assigns structural priority (and I mean that literally as "arising in an earlier level") to a line that is internal to the texture rather than the line at the top.

Schachter's insistence on a feature that runs counter to the evident musical qualities of D779n13 is only the most obvious marker of his basic strategy, that of the symptomatic reading. As David Bordwell describes the process, the critic must first have

master[ed] a semantic field informed by particular theoretical concepts. [Then, in the work of interpretation,] certain semantic features enjoy a particular saliency. . . . The critic will pick out textual cues that can bear the weight of those semantic features [and] mount an argument, perhaps using the rhetoric of demystification, to show the significance of the semantic projections, from field to text, that the critic generated. Every recognized method . . . follows something like this routine. (12)

If large-scale descending lines have priority (that is, "enjoy a particular saliency"), then the appropriate "textual cues" are more likely to be in the alto than the soprano (which cannot "bear the weight"). The "rhetoric of demystification," then, would separate soprano/alto from main-voice/subordinate-voice by indicating how and why the alto is the carrier of the primary melodic voice. (Actually, I think Bordwell is referring to something a bit different, but in our limited context the dismantling of a cluster of binaries makes sense.)

Within the theory itself, the effacing of ^7 by ^2 is behind this particular result. More to that tomorrow.

References:

Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232. Reprinted as "Durational Reduction" in Schachter 1999a, 54-78. (Schachter, Carl. Joseph Straus, ed. Unfoldings: Essays in Schenkerian Theory and Analysis. New York/London: Oxford University Press, 1999).

Bordwell, David. Poetics of Cinema. London/New York: Routledge, 2008.

Neumeyer, David. "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis." Music Analysis 25/1-2 (2006): 201-30.

The conflict of voice leading and line

In an early article, Kofi Agawu lists three guidelines for the analysis of closure in music:

1. Closure is a function of formal principles and/or generic signs.

2. Closure is not the same thing as an ending. . . . An ending refers to local elements in the musical structure, whereas closure denotes a global mechanism.

3. Closure is a function of both syntactic and semantic principles. (1987, 4)

In his explanation of the last of these, Agawu says that "The musical equivalent of poetic syntax is the set of rules that govern the succession of notes. For example, a ^2-^1 over V-I cadence offers the correct syntax for effecting a cadence." Or as below, from his most recent book, where Agawu says much the same: "a closed harmonic progression [that] constitutes the norm of coherent and meaningful tonal order" (109).

This progression, however, is hardly "syntactically correct" -- it shows the compromises necessary when melodic parsimony (move by step whenever you can, or not at all) conflicts with a strictly maintained four-voice texture (derived from continuo practice). The problem becomes obvious to the eye and ear if we put the alto or tenor at the top and move the soprano into the inner voices:

How to solve this without changing the number of parts? You can't. In the four solutions below, melodic parsimony is maintained but the final chord is incomplete (contrary to figured bass), as at (a) and (c). Or, Agawu's "syntax" is violated because ^2 retreats to ^3, as at (b) and (d).

What this suggests is that there will always be a conflict between the two-voice structure assumed by "^2-^1 over V-I" and the archetypal four-voice texture of figured bass. There is no reason to choose Agawu's "norm" with its damaged inner voices over (a) or (c) above with their incomplete final tonics. In fact, (b) and (d) would seem to be the best solutions, as they meet the requirements of both melodic parsimony and figured bass rules -- only the assertion of a very particular melodic requirement that arbitrarily applies parsimony and unidirectionality to just one voice can unseat them.

In the Attwood Studies, Mozart voices cadence chords differently than Agawu. Mozart calls the cadential six-four "accordo di quarta consonante" and the older-style dissonant vertical that would occupy the same accented position in a cadence the "accordo di quarta dissonante" (Heartz et al 1965, 21). See his voicings of the specific verticals involved in (a) and (b) below, respectively.

In a related document ascribed to him, Mozart also contrasts the older cadence with a 4-3 suspension over the dominant to the cadential six-four: the former is "contrapunctisch," the latter "modern (gallant [sic])," the obvious implication being that the latter replaced the former in practice) (Heartz and Mann 1969, 16-17). In those examples, too, the voicing differs from Agawu's "correct syntax."

Modern use of the term "cadence galant" comes from Charles Cudworth (1949), who ascribed its invention to the early 18th century Neapolitan opera composers and in particular to Leonardo Vinci. It seems likely, however, that the change was generational, as Daniel Heartz and Bruce Alan Brown point out ([2009]) -- and, according to Lucinde Braun (2007), it can in fact be found in French claveçin composers, among others, around the same time. It was this clichéd formula that Schenker eventually took for granted as a possible component of Urlinien: the cadential dominant figure appears without comment in Free Composition, Fig. 16 (the table of bass motions under the Urlinie from ^5).

Agawu asserts that his "closed harmonic progression" "is characterized by a sense of departure . . . and return, [or] motion from one (relatively) stable point to another (more stable point)" (2009, 109). Echoing Lerdahl and Jackendoff, Meyer, and others, he explains that "departure generates tension and arouses expectations, while return provides resolution and fulfillment of expectations." A century earlier, August Halm had said much the same, although, following the Ramellian tradition, he tends to attribute the essential qualities of tension/relaxation to the dominant chord itself ("Urkeim [der Kadenz] ist die Dominante mit ihrer inneren Bewegung zur Tonika" (5) [rough translation: "the core of the cadence is the dominant with its inner motion toward the tonic"]). His example (below) is described as "die primitivste Musik" but "zweifellos Musik! Es ist das erste Geschehnis, Leben der Töne, Bewegungsanstoß and -Abschluß! . . . . Die Kadenz ist, richtig verstanden, Grundlage und Urbild des Musizierens überhaupt!" (14-15) [rough translation: "the most primitive music, but unquestionably music! It is the first event, the life of tones, the incitement to movement and the end of movement. The cadence, understood correctly, is the foundation and the basic construct of music making itself!"]

Note, however, that Halm did not require a soprano note above or away from ^1 for his first chord. And we cannot appeal to "pure melodic principles," either -- every one of the cantus firmi that Fux uses for his species counterpoint exercises begins and ends on the finalis (modal tonic).

Clearly, Agawu's archetype is not archetypical -- it is a progression strongly interpreted according to a specific bias, which, whether accidentally or deliberately, erases the significance of the leading tone (^7). In an upcoming post, I will discuss the problem of the "two leading tones" and how that impinges on the question of the rising Urlinie.

References:

Agawu, Kofi. "Concepts of Closure and Chopin's Opus 28." Music Theory Spectrum 9 (1987): 1-17.

Agawu, Kofi. Music as Discourse: Semiotic Adventures in Romantic Music. New York: Oxford University Press, 2009.

Braun, Lucinde. "Das galante Fluidum – von der Tenorklausel zur "cadence galante'." Conference paper read at the 18th Congress of the International Musicological Society, Zurich, 12 July, 2007.

Cudworth, Charles. "Cadence galante: the Story of a Cliché." Monthly Musical Record 79 (1949): 176–8.

Heartz, Daniel, and Bruce Alan Brown. [2009]. "Galant." Grove Music Online. Ed. L. Macy (Accessed 1 December 2009). .

Heartz, Daniel, Erich Hertzmann, Alfred Mann, and Cecil Bernard Oldman. 1965. Thomas Attwoods Theorie- und Kompositionsstudien bei Mozart. Neue Mozart Ausgabe NMA X/30/1. Kassel: Bärenreiter.

Heartz, Daniel, and Alfred Mann. 1969. Neue Mozart Ausgabe X/30/1: Thomas Attwoods Theorie- und Kompositionsstudien bei Mozart, Kritischer Bericht. Kassel: Bärenreiter.

Schenker, Heinrich. [1935, rev. 1956] 1979. Free Composition. Trans. and ed. Ernst Oster. New York: Longman.

Halm, August. Harmonielehre. Berlin & Leipzig: Vereinigung Wissenschaftlicher Verleger, 1920. (Reprint of the 1905 edition.)