Explaining Tonality

Today I'll comment briefly on why I did not make use of Matthew Brown's Explaining Tonality in the MTS article, or at least raise a critique of the book, since it is also concerned with basic features of linear analysis, including prototypes. Simply put, Explaining Tonality hangs entirely on one idea, and if you do not accept that idea, or for some reason do not find it fruitful, then there is nothing to be gained. Brown believes that there is implicit in Schenker's work a fully adequate, rationally demonstrable theory of monotonal functional tonality that models what the expert composer/listener knows. All this precedes the book, which resembles nothing so much as a triumphal run to victory, leaping over all obstacles on the way.

And I would say that "leaping" is precisely the word needed here. As one example among many, here is Brown's treatment of the rising Urlinie notion. These "contradict the law that melodies reach maximum closure when they descend ^3-^2-^1. Since ^8 lines satisfy this and our other laws, it is hard to see how they can be rejected as Neumeyer suggests" (75). Since Brown derives his "laws of tonal motion" in such a way that they conform to Schenker's theory, then of course only melodic shapes descending through ^3-^2-^1 can be accepted. I'm not sure this even rises to the level of circular reasoning, though that is what Catherine Pellegrino calls it:

[Brown] dismisses David Neumeyer’s extensions of Schenkerian theory through a curious bit of circular reasoning. Brown introduces some of Neumeyer’s alternative prototypes, including one in which the Urlinie rises from the fifth scale degree to the tonic, but then dismisses them on the basis that they do not conform to Schenker’s prototypes, which descend to the tonic. If they conformed to Schenker’s prototypes, it would hardly be necessary to propose them as extensions of Schenker’s theory, would it? Oddly enough, Brown accomplishes this logical feat just before dismissing another critic’s charges that Schenker’s own theories involve circular reasoning. (92)

At one point, Brown says that "Schenkerian [harmonic] derivations are simply more accurate than functional explanations" (61). For this, one of his reviewers, Matthew McDonald, takes Brown to task:

Two problems arise here. First, ‘accurate’ is once again an inappropriate description of Brown’s interpretation. His ideas about chord generation rely on what is clearly a heuristic model for harmonic analysis: the notion that harmonies other than the tonic ‘derive’ from melodic motions. Such derivations might well be understood as useful explanatory tools, but they can be considered accurate only if one maintains a mystical belief in Schenker’s theory as a representation of musical reality; and such accuracy could never be demonstrated scientifically (or, to use Brown’s terminology, it is not ‘falsifiable’). Chords are not derived from melodic notes, they are composed by human beings. One can conceptualise such derivations, but this is an interpretative act, not a scientific judgement. (234)

Although I, too, have an interest in what can be called theoretical foundations of linear analysis, the MTS article should make it clear that my goal is to inform interpretation, and, implicitly, that I regard Schenkerian analysis as a mode of interpretation, not a scientific model. "Theory," in my sense, is Bordwell's "semantic field" (post) -- another way of saying an organized mode of discourse -- and my interest is in reconfiguring constructs within that field for the sake of enriching interpretative practice.

With respect at least to the idea of Schenkerian analysis as fruitful interpretative practice, I am firmly in Carl Schachter's camp.

Reviews of Explaining Tonality:

Anson-Cartwright, Mark. Journal of Schenkerian Studies, 2 p141-148. 2007.

Clark, Suzannah. Journal of the Royal Musical Association, 132(1) p141-164. 2007.

Drabkin, William M. Music & Letters, 89(2) p252. May, 2008.

McDonald, Matthew. Music Analysis, 26(1-2) p217. Mar-July, 2007. McDonald's review of Explaining Tonality is on the mark, but I think he is rather too harsh on the other book reviewed, by David Beach.

Pellegrino, Catherine. Notes (Music Library Association) 63/1 (2006): 90-93.

References:

Brown, Matthew. Explaining Tonality: Schenkerian Theory and Beyond. Rochester, NY: University of Rochester Press, 2005.

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

Schachter and the rising Urlinie, Part 13b

In Part 13a of this series, I responded to one point in the appendix to Carl Schachter's article "Schoenberg's Hat": what I regard as his misreading of a graphic from Victor Zuckerkandl's book Sound and Symbol. Here I will respond to a second point, and tomorrow to a third.

The last two paragraphs of the appendix acknowledge that two of my readings are convincing. The pieces are D779n2 and D969n7. In a footnote, Schachter says he still prefers a descending Urlinie from ^3 for D969n7, but that my version is "a plausible alternative" (341n23). The rising line ^5-^8, however, is lumped with other Urlinien manquées: "'incomplete' . . . (notably 5-^4-^3) or . . . ending on ^2 [over V]" (339), and these as a group are the exceptions that prove the rule: "their existence in no way diminishes the importance of the norms to which they form exceptions." Those norms:

(a) "tonal melodies come to rest on ^1" ---- or ^8, of course, since ^8 is equivalent (identical, really) in a modal pitch-class space system with octave equivalence. Up/down might be a schema, but octave equivalence has been an element of European pitch systems for a very long time.

(b) "complete harmonic structures end on the tonic chord" ---- but what can "complete" possibly mean apart from actual compositions, where we know that bifocal tonality (LaRue), double-tonics, and tonally meandering opera szenas or film cues can be found everywhere.

(c) "differences between rising and falling motion reflect fundamental properties of the tonal system" ---- I quite agree with this one, but with two large caveats: (1) I would change "fundamental properties" to "basic expressive properties"; and (2), as this series of posts will have shown, I don't share Schachter's particular notion of "tonal system."

Schachter and the rising Urlinie, Part 13a

Part 13 is the last in this series of posts on Carl Schachter's article "Schoenberg's Hat." In case you've lost track of them all by now, the first post was on 11 January: Part 1.

The appendix is a set of comments on my JMT article "The Ascending Urlinie" (338-39). Schachter spends most of the roughly 1000 words disagreeing with my interpretation of a graphic from Victor Zuckerkandl's Sound and Symbol, even suggesting that Zuckerkandl himself didn't take quite the right view of his own graphic. The last two paragraphs acknowledge that two of my readings are convincing, but only in the context of repeating his point about the exception proving the rule. In a lengthy footnote, it is understood that I misread Schenker's statements about the Bassbrechung (background I-V-I) in relation to the harmonic series.

I'll discuss the first of these three points here, the others in Parts 13b & c.

Here is Zuckerkandl's graphic, which Schachter reproduces:

I use Zuckerkandl's distinction between "acoustical space" [movement in pitch space] and "dynamic space" [rise or fall on a tension-relaxation scale] as a way of breaking through the conceptual fourth-species logjam, the style-statistics-driven assertion that descending melodic motions have priority because suspensions resolve downward. Why lines have to obey the same rules as suspensions is never explained, nor why the musics of the 19th century have to obey the rules of the 16th (we can't say it's to preserve a continuity narrative: harmonic practices and ideas about rhetoric and expression, after all, changed radically during the same time period).

Zuckerkandl points to the ^5-^8 "upper half" as potentially rising in acoustical space but falling in dynamic space, and of course I use that in the JMT article as one of the justifications for rising lines in a generative mode of linear analysis. Here is Zuckerkandl, cited by Schachter: "the tone ^6 still plays a double role, since it can be heard both as a state in the succession ^5-^6-^7-^8 and as bound to a pointing toward its comparatively stable adjacent tone ^5; the particular circumstances determine whether the meaning 'away from ^5' or the meaning 'toward ^8' preponderates in the step ^5-^6."

Schachter says that the graphic shows "implicitly a far greater bias toward downward resolution in the dynamics of scalar structure than his explicit formulation acknowledges" and "the pull of ^1 is much greater than that of ^8" (339). But Zuckerkandl doesn't imply what Schachter claims: instead, Zuckerkandl says quite directly that "particular circumstances determine whether the meaning' away from ^5' or the meaning 'toward ^8' preponderates." Schachter misreads Zuckerkandl in order to push a couple "greaters": "a far greater bias" and a "much greater" pull.

In any case, Zuckerkandl's model has firm style-statistical support in 19th century music, especially in the popular genres of dance music, where the play of ^6 and ^5 creates a kind of tonal androgyny that makes the identity of ^5 and ^6 interchangeable, in "particular circumstances," exactly as Zuckerkandl says. Eventually (that is, by around 1860 or so, but firmly and unmistakably by 1910), the two even fuse in the triad with an added sixth.

And it all starts early, in places like D779n13: see the graphic below, where I have written a narrative of the interplay of ^6 and ^5 in the first strain. The two identities of the scale degrees are plainly evident. (Recall that you can click on this thumbnail to see the graphic at its original resolution.)

References:

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

Zuckerkandl, Victor. Sound and Symbol: Music and the External World (Princeton: Princeton University Press, 1956).

Schachter and the rising Urlinie, Part 12

The Conclusion -- "Lewis Carroll's Trousers" (337-38) -- is decidedly disappointing, despite its apparent promise to drive the sartorial point home, from hats to trousers. Schachter does nothing more than repeat his point with a couple new images -- an art historian writing in 1969 saying much what Schachter already did but in reference to shapes in a visual field (how exactly does the visual analogy prove the validity of the visual prop for a musical analogy?). Since asymmetrical figures look different upside down, therefore it is clear that, "in tonal music, with its gravitationally charged pitch space, linear shapes are also 'non-commutative.' In principle, ascent tends to mean beginnings and intensifications, whereas descent means endings and resolutions" (337). Let the unmarked term stand for all.

I take the charitable way out: Schachter tries an argument by accumulation: repeat your point often enough and it will seem to be proven. Since he had only an opposition to work with, the pendulum could have swung at any time to the marked term (the joyful playground of the post-structuralists). Since he was wholly committed to one term, there was no real way to address the issue directly. Just as I assume he refrained from making any jokes about "upside down" to his Australian audience -- it was, after all, the experience of sailing around the world that drove home the point for once and all that gravity-as-down was a schema that cultures needed to grow out of (in favor perhaps of center-periphery, one of the schemata in Saslaw's list), or else needed to make far more complex than a simple opposition.

more to Schenkerian analysis and the New Criticism

When, Jeffrey Williams, interviewing Stanley Fish, offered the now commonplace view that, in the 1970s and 1980s especially, "[literary or critical] theory provided a kind of bridge or lingua franca for literary studies, so that somebody in Renaissance could talk to somebody in twentieth-century American literature," Fish responded with comments on the preceding generation:

New Criticism provided a vocabulary, with its notions of tension and paradox and verbal artifacts, that could be as much a part of Chaucerian criticism . . . as of criticism, let's say, of Joseph Conrad's novels. So there was always a way, I think, that the techniques in one field could be generalized. What surprises me, though, and heartens me, is the survival through all of these changes of some commitment to close reading. I know that there are many, many complaints and laments that close reading is a lost art, but I see many people who still perform it. It still remains, at least in my experience, the most powerful pedagogical tool which can really awaken students' interest when they begin to realize that they can perform analyses of texts that remove the texts from the category of the alien and the strange, and then begin to actually understand the mechanics of how prose and verse work. (22)

In music studies, Schenkerian analysis and classical pitch-class set theory did much the same during roughly the same period (allowing for an offset of a decade or so). The difference was that the "tools" and "mechanics" of particular ways of reading/auditing became naturalized: in literary studies, every device, notion, or rhetorical gambit was closely scrutinized and often contested. Something like this happened with classical pc-set theory through Robert Morris's more thorough and more sophisticated reformulation of it and, more radically of course, through Lewin's GMIT, which opened the door to a wide field of theoretical and interpretative possibilities. Despite some good critical and historical work beginning in the 1980s, Schenkerian studies advanced only so far as meeting New Musicologists in a conservative practice of hermeneutics. Thus, as he does in "Schoenberg's Hat," Schachter can say in 1999 that "Schenker's description in Part I of Free Composition reveals some of the fundamental characteristics of the tonal system" (10). And the mechanics of that "system" are the naturalized "three Ursatz forms, [which are] the simplest pieces of tonal music, so simple that they have no artistic value at all, but still fulfill some of the basic needs of a tonal piece."

Between Neo-Riemannian rewriting of the history of harmony, the Schenkerian hermeneutics that must, if carried out sensitively and thoroughly, eventually break down the notion of a common practice, and the powerful new view of musical rhetoric in the 18th century that is coming out of partimento studies, a view like Schachter's is no longer sustainable.

References:

Williams, Jeffery L. Critics at Work: Interviews, 1993-2003. New York: New York University Press, 2004.

Morris, Robert D. Composition with Pitch Classes: A Theory of Compositional Design. New Haven: Yale University Press, 1987.

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

Schachter, Carl. Joseph Straus, ed. Unfoldings: Essays in Schenkerian Theory and Analysis. New York/London: Oxford University Press, 1999.

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.)

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.

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.

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.

Schachter and the rising Urlinie, Part 1

Carl Schachter was invited to give a public lecture for the School of Music, Indiana University, in April 1988. Unfortunately, I missed it as I was in Helsinki, Finland, giving a week-long series of lectures on music analysis. On returning, I was surprised to hear that he had devoted the talk to a critique of the ascending Urlinie (my JMT article had appeared not long before). Schachter had previously written on theoretical questions in Schenkerian analysis, including a now classic review-article (1981), and perhaps he was interested for that reason -- or he might simply have been piqued to respond by my criticism of his analysis of Beethoven Op. 14n1, I (Schachter 1982).

Whether it was a case of missed opportunity or simply ships passing in the night, bound for wholly different ports, I don't know, but at the time I was on my way to film and film music studies, and, when Schachter did publish an article on the rising line problem in 1996, I didn't see it. I wasn't paying attention to the music theory literature, and he chose to put the piece in an obscure place. In the meantime, William Rothstein had articulated the main objection from a traditionalist point of view:

What Neumeyer demonstrates convincingly is that a fourth-progression from ^5 to ^8 may span an entire composition; for this reason alone, the ascending progression must at least be assigned to a deep level of the middleground. Virtually always, however, the ascending fourth-progression is counterpointed by a descending linear progression from ^5 or ^3. . . . It is probably best to assign such a three-part counterpoint to a deep layer of the middleground rather than to the background. (306)

Although Rothstein is generous in making it clear that either the rising or falling line could potentially be "superior in status to the other," in practice the traditionalist view has been (and this is the nub of Schachter's position) that the descending line has priority and the rising one must ultimately be assigned to boundary play (coherent voice-leading figures above the principal line). The very rare example that is "convincing" is merely one of those exceptions that proves the rule.

Thus was set up an opposition in which the three descending Urlinien constitute the unmarked term and the rising line the marked term. ("Thus" is a bit misleading, since the question of the rising line -- and so the binary pair -- predated my JMT article by a good long while.) Schachter defended the unmarked term; I focused attention on the marked term ("flipped" the binary, that is, in a manner familiar to literary criticism since at least the 1950s). In such cases, critique cannot proceed logically, but only ideologically, a step that Schachter has steadfastly avoided (even celebrating that avoidance (2001)). He has, instead, preferred to retreat to an argument carried out as hermeneutics (in its old sense linked to Biblical exegesis).

In a series of posts over the next week, I will examine the arguments and analyses in Schachter's 1996 article and in an earlier article on Bach (1994).

References:

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

Schachter, Carl. "A Commentary on Schenker's Free Composition." Journal of Music Theory 25/1 (1981): 115-42. Reprinted in Carl Schachter, ed. Joseph Straus, Unfoldings: Essays in Schenkerian Theory and Analysis, 184-205. New York/London: Oxford University Press, 1999.

Rothstein, William. "On Implied Tones." Music Analysis 10/3 (1991): 289-328.

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.

Schachter, Carl. "Beethoven's Sketches for the First Movement of op. 14, no. 1: A Study in Design," Journal of Music Theory 26/1 (1982): 1-21.

Schachter, Carl. "Elephants, Crocodiles, and Beethoven: Schenker's Politics and the Pedagogy of Schenkerian Analysis." Theory and Practice 26 (2001): 1-20.

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

Imaginary continuo (after Rothstein)

Is it possible to retain a sense of Schubert's risky improvisations (see posts (1), (2)) in a Schenkerian graph? Only if the graph can be made to reflect the human and fallible, not just the unerring creative instinct of an idealized notion of genius. To attempt this shift, I will start with the continuo grid. William Rothstein (296) uses the construct of the "chordal scale" (derived from Lerdahl) as the repository of tones for the imaginary continuo, his term for what I will call the continuo grid.

The beginning of the first graphic below shows the chordal scale for D779n13 with respect to its tonic triad: all members of the A major triad between the lowest and highest notes struck. Out of this scale emerge the four voices of a standard part-writing progression representing measures 1-10, or the introduction and the first eight measure phrase. The analogy to a continuo keyboard part would be better if the right hand held three voices and the left just one, but I resist that because I want to preserve the textures of this waltz as much as I can.

Resisting the idealization of textures is in fact the basic strategy of this rewriting. Note that one result is the prominent set of parallel fifths. A respect for textures suggests that the pedagogically simplified, chorale-style texture of (a) is not the best solution for this passage, which after all contains several additional voices in the left hand: these are inserted in (b), the end result looking more like the textures in orchestral settings of dances in the late eighteenth and early nineteenth centuries. Note the octave doublings that have now been added to the parallel fifths. The fullness of this texture contrasts with the three-part reduction that keeps only the two imitative upper voices and the bass (c). It is this latter that Carl Schachter uses in his durational reduction of the Waltz, but Schachter corrects the parallels by texture inversion of the two melodic voices.

Instead of collapsing the texture as Schachter does, I have removed the "non-harmonic" I 6/4 chord in (a) of the next graphic below, leaving a simple ii6-V7-I harmonic progression. Level (b) expands (a) with the closing cadence.

The contents of (b) are reproduced in the lower system of the final graphic (below) and renotated to correspond more closely to my preferred Schenkerian reading, the rising line from ^5 to ^8. The alignment is not meant to suggest an equivalence, but a replacement: if maintaining textures is thematic here, then the lower system takes the place of the upper one.

The continuo grid has a quality of concreteness about it, as if the improviser is looking at the piano keyboard and making choices about register (A major, melody in the fifth octave, accompanying voices in "standard" positions for a waltz in this key). Once the fateful decision is made (at bar 3) to model this waltz on D365n6, the parallel fifths emerge very quickly, and Schubert's decision to maintain the register despite the parallels opens the door for the sublime counter-move to the downward pull of the ancient suspension figures: the sudden lift over V in the final cadence. The graphic suggests further that, having transmuted an error into the sublime, so to speak (the parallel fifths into the rising cadence gesture), Schubert adopts the rising itself as a design in the second strain: tonicizing C# major (rather than treating it as V of vi to start a cycle of fifths sequence), then the peculiar chord progression it leads to, which facilitates another expressive moment associated with upward shifts of register (in measures 31-32--not included in the example).

References:

Rothstein, William. "On Implied Tones." Music Analysis 10/3 (1991): 289-328.

Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232.

The anticipating 6-4: background for metrical readings

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

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

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

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

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

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

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

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

Schenkerian readings with the space ^5-^8

If the readings from ^8 (presented in yesterday's post) are problematic, still it is certainly true that Schubert puts plainly before our ears the tonal space of the upper fourth, ^5 to ^8, and we might reasonably engage that as a priority in the large-scale design. The first reading built on this basis is a simple rising Urlinie ^5-^6-^7-^8 that trumps Schachter's line from ^3 in simplicity and elegance: not only is the line short but the reading also rests on what we hear readily: "the right hand plays two melodic lines written in free imitation"; furthermore, the upper voice is the lead melody, even if that voice is "generally [less] active" than the alto (Schachter, 70).

We can also appeal to style statistics: although complex compound melodies exist in abundance in the violinistic Ländler repertoire, and certainly find their way into Schubert's waltzes (D145n1 (Ländler), D146n2, D779n26, D779n29, D924n3, and D969n10 are particularly nice examples), a middle-voice main melody is rare in the early waltz repertoire (although we could, I suppose, just declare this to be yet another of the anomalies in the A Major Waltz). In D734n14, for example, "soprano" and "alto" start an octave apart; the role of principal voice is initially contested, but the soprano wins out by bar 3. D779n1 (score reproduced at the bottom of this post) and D779n19 are the only other Schubert waltzes I know in which a really convincing argument can be made for alto-priority.

The alto replicates Schachter's main melodic voice throughout. The soprano also traces a middleground form of the line from ^5 to ^8 in the first strain (not shown). The ^5 is reinstated in the upper voice in the second strain, allowing the final upward-pushing figure ^5-^6-^7 over V, in a replication of the cadence of the first strain.

Although the specific figure Schubert uses here (both ^6 and ^7 over V) seems to have been an innovation of his, play with scale degree ^6 above both I and V was a cliché of the Ländler almost from the beginning and passed into the waltz once its subgenres began to merge in the 1820s.

The other reading focused on the space ^5 to ^8 is decidedly less successful. The symmetrical treatment of the space from ^5 to ^8 takes the strongest elements of the first 8-line reading and replaces its weak ending with the rising line of the first reading above. This version puts before the eye the aurally salient parallel patterns of rising in the first and second strains-the first time through the long initial arpeggiation, the second time through the ascent of the Urlinie to ^8 -- but it suppresses the same figures in the opening of the second strain (once again, however, that could be ascribed to differences of function -- or, here, function in different structural levels). I find the parallelism appealing, but finally prefer the previous reading (^5 rising to ^8) because it puts such emphasis on an unusual stylistic feature of this waltz: its play of counterpoint.

Reference:

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).

(Score of D779n1 (click the thumbnail for the original image))

Schenkerian readings from ^8

Continuing the newly revived theme of linear analysis graphs closely hewing to the Schenkerian tradition, here are three potential readings from ^8, none of which is particularly convincing (all would fit Culler's ideas about extravagance and the implausible in (over)interpretation).

The first two are conventional readings. They require an initial arpeggiation across C#4 and E4 to reach ^8 at the end of the first strain; thereafter, each finds its own long path back to ^1. Both begin from G# (now acting as ^7) in the second strain.

The first reading finds a path through F#, as 7 in C#:V7, and so reaches the register of ^5 and descends as in the five-line readings. This requires the "mixture" voice leading to work.

The second eight-line reading preserves Schachter's G# passing between A and F#, but then the descent occurs very late--we are left to imagine a rush downward over two bars of V7; this ^4-^3-^2 is a Leerlauf, though this one sounds less like an "unsupported stretch" than like a free fall. Overall, both of these readings exaggerate the weaknesses of the reading from ^5. The only Schenkerian who might choose such lines would be a contrarian who hears a determined passage of lines through the waltz's net of cover tones.

Nevertheless, the third reading is obviously the most contrived. This Mixolydian reading rewrites the already weak octave-line to replace ^7 with ^7-natural, the motivation being that the G-natural constitutes the only truly dramatic, unexpected moment in this waltz. That a Mixolydian modal scale exists to accommodate the G-natural helps, even though such modal scales scarcely exist in the musics of this period (and certainly not in music for social dancing!).

For this reading we take an expressive, marked moment, rather as Edward T. Cone does with his promissory note in Schubert's Moment musical in Ab or Schachter with his F#/Gb in Beethoven's Symphony No. 6, but go beyond either of these authors by elevating the distinctive pitch to the status of a member of the urlinie; that is, the reading imposes a belief that such a note should not merely point to the background, it should be the background. In this case, however, the G-natural lacks any further consequences (unless you believe that the A Major Waltz was meant to act as a trio to the previous waltz in D major, in which case there certainly are consequences, for the earlier waltz foregrounds a juxtaposition of a G-natural neighbor note in the upper voice with a G# in an inner voice).

References:
Cone, Edward T. "Schubert's Promissory Note." Nineteenth Century Music 5/3 (1982): 233-241. Reprinted in Walter Frisch, ed., Schubert: Critical and Analytical Studies, pp. 13-30. Lincoln: University of Nebraska Press, 1986.
Schachter, Carl. "Triad as Place and Action." Music Theory Spectrum 17/2 (1995): 149-169. Reprinted in Schachter, Unfoldings, 161-183.