A first narrative reading (after Edward T. Cone)

This is in part a new reading, in part a postscript to the previous entry (on the unison ^5).

Using Cone's device of the "promissory note,” I ask how the kind of musical plotting he describes for the Ab-major Moment musical can be applied to D779n13. As the "note," I choose the downbeat of measure 3: its distinctive dissonance is as close as we will come to a marked pitch event in the first strain. With the leap upward in measure 3, one might have expected a brighter sonority, such as a triadic subdominant, yet the C# unequivocally signals a B-minor 6/3–it is the leap upward, the "brightness" that is disappointed by the incessant string of suspensions. Without the suspension, the B-minor chord might have been neutral: as the first two items in the graphic below show, the voice leading from this ii6 might carry F# up or down equally well. Ironically, IV would be less successful, as rising from F# threatens parallel fifths in the lower voices (third item in the graphic).

The F#, then, is (relatively) stable at the outset as a chord member of ii6 and as upper member of a tenth with the bass (see the beginning of the next graphic, which charts the narrative across the time line of the piece); it is also in an isolated, higher register, yet its "brightness" is undermined by the inner-voice suspension figure. The F# maintains its position, but at the end of the first phrase it appears to give in by mimicking the suspensions with a soft, 6-5, accented neighbor figure.

In the second phrase, this pattern is repeated but now the neighbor figure sounds like a proper 9-8 suspension, paired as it is with a true 4-3 suspension in the alto. But suddenly--out of nowhere--our initial expectation is fulfilled, albeit with the rough voice leading of the waltz ninth, as an F# passing tone rises to G# in the cadence. (On the "waltz ninth," see Neumeyer 1987, 292-293.)

This might have been the end of it, but Schubert writes the second strain as an ingeniously intensified variation of the progress of the first. The relation of F# to E is sharpened (literally) by converting F# to the seventh of a dominant (C# major: V) and E to its resolution on E# (as ^3 of C# major). This again would appear to be the end of it–F# can only descend–except that the memory of rising is preserved in the repetitions of the cadence figure from the first strain (now a major third higher). The pitch C#6 reached in these cadences is the excuse for a remarkable twist prepared in the mysterious measures 29-30, whose G-natural will fall to F#5 as C#6 leaps abruptly up another fourth to F#6. Even more remarkably, two bars later the upper register is abandoned again, an event we might interpret either as a retreat or as a satisfied return to place (since the cadence's waltz ninth is retained). In either case, it is obviously a denouement.

A thematic statement (summary) for this "promissory note" account is most readily tied to character and progress of the narrative. (On theme and thesis and their connection to the proto-backgrounds, see the MTS article and the three web publications listed under “References.”)

Scale degree ^6 is unstable because it is not a member of the tonic triad, but it is ambivalent in directionality. Although at first pulled down by the weight of suspension figures in the alto voice, ^6 takes advantage of the cliché of the waltz ninth to rise in the cadence of the first strain. This sequence of events is repeated, in more intense form, in the second strain, but a drop in register at the end suggests a reconciliation or 'synthesis' of the scale degree's rising and falling tendencies.

This rather wordy version, however, is little more than a character-based summary of the story. We might distill it down to something like "The ambivalent directionality of scale degree ^6 is expressed at several levels." (On this ambivalence, see Day-O-Connell.) If the sense of narrative–and most of the sense of anthropomorphic character–is lost in this bland description, that is all to the good. For any reading that suggests or imposes narrative, the thesis might be the following: we are asked to believe that the parallel between the linear chronology required for reading a story and listening to a piece of music means that story-like narratives can be productively imposed on musical compositions (another way to phrase it: we are asked to believe that the story/music parallel is a strong one that permits the creative hermeneutics of narrative-building).

References:

Cone, Edward T. "Schubert's Promissory Note." Nineteenth Century Music 5/3 (1982): 233-241.
Neumeyer, David. "The Ascending Urlinie." Journal of Music Theory 31/2 (1987): 275-303.
Day-O'Connell, Jeremy. "The Rise of ^6 in the Nineteenth Century." Music Theory Spectrum 24/1 (2002): 35-67.
Neumeyer, David. Proto-backgrounds. On Proto-backgrounds: Material gathered from my UT website (uts.cc . . .) and from the blog “Hearing Schubert D779n13” (on Google’s blogspot): PDF essay on Texas Scholar Works [link updated 10 June 2016].

Neumeyer, David. Theme and thesis (Rebecca). See entry above.
Neumeyer, David. Theme and thesis (Hadas, The Genre Clerk). See entry above.

Proto-background 3: the unison ^5

Also see the proto-background introduction.

Of course, the unison ^5 forces attention away from the alto (lower right-hand voice) to the soprano, and it also (that is, like the unison ^3 from yesterday's post) aligns itself very cleanly with the formal design. The second line in the graph shows a simple harmonic transformation with one harmony for each section: first strain, contrasting middle, and reprise. In Riemannian terms, this is (L-followed-by-P) followed by the inverse (or, P-followed-by-L). L turns A major into C# minor, and P makes the latter C# major.

The third line fills in a few details for the first strain. Note that the symmetries in the harmonic patterning extend to the outer melodic voices, with the two neighbor-note figures. The inset takes this a little further by understanding the "essential" chromaticism of getting-into and getting-out-of the contrasting middle symmetrically, as well: E5 breaks up to E#5 at the beginning, but G-natural slumps down to F#5 at the end.

Proto-background 2: the unison ^3

Also see the proto-background introduction.

The unison ^3 focuses attention on the alto voice but differs from ^1-^3 (future post) in delegating its repeated linear path to later levels. As the "foreground" figure in a previous posting showed, the potent voice leading clichés invoked by the suspensions in the alto voice and the essentially stationary ^5 in the soprano are subverted at the last moment in the cadence. I have rewritten that figure below in terms of ^3 rather than ^1 (this is a thumbnail; click on it for a larger image):

Details of the first section (bars 1-18). The first line is a "middle-level" version of the second line above, relevant only to the first strain. The second line shows how the intervals unfold. Note especially the 3-6 INV pair nested inside the main pair. The third line gives even more detail, focusing on lines and the cover tone E5.

The reading with a proto-background unison ^3 can be rewritten in more traditional Schenkerian notation (the C# major section is not included here -- it's the empty space in the middle of the graph):

Obviously, one has to allow for the possibility of a background/middleground neighbor note in order to make this work. I write about that issue briefly in the MTS article (291, 297fn30) in connection with Schenkerian readings by Arthur Komar.

The A major Waltz as Trio to D779n12

D. 779 is a collection, not a cycle. The designs for functional dance music varied according to the length of the dance: the music might be arranged in a simple chain (ABCDE . . . ), in the five-part design familiar from the contredanse tradition (ABACA), as a dance with multiple trios (ABACADAEA . . . ), in the alternativo manner (ABAB or ABABCDCD), or in some ad hoc design that suited the occasion. We should also note in this connection that dances are sometimes labelled "Trio" in Schubert's manuscripts but not in print (and vice versa) (Litschauer, "Tänze," 3.)

In published works, however, the "standard" Viennese waltz design was already apparent in the 1820s: sets of five to six waltzes, usually without introductions but many with codas of varying length. The key schemes are closed, meaning that the final waltz and the coda are in the key of the first waltz. Key relations are close--the majority of waltzes are in the home key, with diversions restricted to dominant or subdominant.

The manuscript evidence and internal evidence of key sequences suggest that the A major Waltz was intended as a trio to No. 12 (in D major) ((Litschauer, 113-114); this is MS. 45 in Brown's list (Essays 237)). In the holographs, Nos. 12 and 14 appear as Nos. 6 and 8, respectively, of a collection of seventeen German dances. The first eight pieces in that set are clearly arranged in functional dance/trio groups, with the key succession: D, D, A, D, G, D, G, D. In this sequence, our A major Waltz would have taken the place of No. 7 in G major. (216-217). In the graphic at the end of this file, I have combined these three pieces in a dance-with-two-trios design: n12-n13-n12-n14-n12.

If we want to think of this design in Schenkerian terms, the waltz in A Major expresses a prolongation of an interruption on E5, or ^2 of D major (see the graphic below), a reading that resonates with--though it flips the structural priorities of--a statement by Carl Schachter as he seeks to explain the prominence of scale degree ^5 in the A Major Waltz: "A curious feature of the upper line is its beginning on [F#5] . . . A glance at the Waltz that precedes this one helps to explain: . . . No. 12 is in D major with [F#5] as its most prominent melodic tone. The [F#5] forms a link between the two Waltzes; such links occur fairly often in a chain of short pieces" (71).

References:

Litschauer, Walburga. "Franz Schuberts Tänze: Zwischen Improvisation und Werk." Musiktheorie 10/1 (1995): 3-9.
Brown, Maurice. "The Dance-Music Manuscripts." In Maurice Brown. Essays on Schubert, 217-43. London: Macmillan, 1966.
Litschauer, Walburga, ed. Franz Schubert. Neue Ausgabe sämtlicher Werke, Series 7, part 2: Werke für Klavier zu zwei Händen, Band 6: Tänze I. Kassel: Bärenreiter, 1989.
Neumeyer, David. "Synthesis and Association, Structure and Design, in Multi-Movement Compositions." In James M.Baker, David W. Beach, and Jonathan W. Bernard, eds. Music Theory in Concept and Practice, 197-216. Rochester: University of Rochester Press, 1997.
Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232. Reprinted as "Durational Reduction" in Schachter 1999, 54-78.

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The graphics below are thumbnails; click on them to see the original files.

Running Tally of Readings

Here is a link to a page I am maintaining to keep track of the readings posted to this blog: D779n13 tally.

NOTE 10 June 2016: This list has since been integrated into my PDF essay Analyses of Schubert, Waltz, D.779n13: link.

Postscript: More to Improvisation

As a postscript to yesterday’s improvisation history, here is an alternate solution that Schubert might easily have come to: a simple sixteen-bar form that resolves the hypermetric peculiarities of its model: see graphic below (NB: this is a thumbnail; click on it for the original). The roughness of its harmonic figures in the second strain is not evidence against it, as there are many precedents in the waltz repertoire for such sudden harmonic turns between the four-bar components of an eight-bar strain.

The key to the changes lies at the beginning: the two-beat (four-eighth-note) pickup has been altered to a clichéd single quarter-beat (as in D365n6), and the harmony begins "in progress," as it were, with the 7-6 suspension over ii6. The fact that this opening is plausible (and closely resembles an existing piece) tends to invalidate Carl Schachter’s claim that "to omit the first two bars [of the A Major Waltz] would be to suppress the opening tonic altogether; [this] would make the whole piece pointless and nonsensical" (72).

The prosaic clarity of the recomposed first strain serves as well as any preceding analysis to highlight the strangeness of Schubert's original, perhaps the last bit of evidence we require in order to affirm that the A Major Waltz is a poor piece of social-dance music and is misplaced in D. 779--perhaps it would have been more successful had it been expanded a bit to act as the trio to a minuet or scherzo.

My crude rewriting barely masks the most obvious metric problems, however. The A Major Waltz, with its repeated second strain, consists of 29 two-bar groups, or the two-bar introduction plus 14 four-bar phrases, or 7 eight-bar strains: a waltz in an 8+8 design has four eight-bar groups, and a waltz in an 8+16 design has six groups.

The fact of an introduction itself is unproblematic; they are not common in Schubert's own dances, but brief introductory figures or flourishes had become familiar to dancers nearly a decade earlier through their use in the "extraordinarily popular" Linzertänze by Michael Pamer, principal predecessor of Lanner (Reeser, 47)--both Strauss, sr., and Lanner had played in Pamer's orchestra. Three other waltzes in the familiar sets by Schubert include two-bar introductions: D146n10; D365n34; and D734n15. (In a performance setting for dancing, such introductory "vamping" was undoubtedly commonplace, as I suggested in yesterday’s post.)

And uneven hypermetric groups do happen, also: three of the Valses nobles, D. 969, have them. Numbers 9 and 12 have an extra four-bar group in the second strain: the former adds up to seven eight-bar groups with the repeat of the second strain, the latter to nine such groups. Number 3, however, wins the prize as the oddest design in the major waltz sets: a four-bar introduction is followed by a repeated strain of 8+8; the second strain consists of four eight-bar groups plus one six-bar group (as 4+2). Thus including the repeat of the second strain, the total is 4 + (8 x 13) + 4, or 14 eight-bar groups altogether.
According to Litschauer and Deutsch (111), D. 969 was very probably meant as a concert cycle, not a functional dance collection, and one has to wonder whether the A Major Waltz would not be better placed as a trio in that set, rather than in D. 779, whose members are otherwise all functional dances not far removed from Schubert's first published collection, D. 365.

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.)

Reeser, Eduard. W. A. G. Doyle-Davidson, tr. The History of the Waltz. Stockholm: Continental Book Company, 1949.

Litschauer, Walburga, and Walter Deutsch. Schubert und das Tanzvergnügen. Vienna: Holzhausen, 1997.

D779n13 originates in improvisation

The Opus 9 (D. 365) collection was published in 1821; as most of the waltzes of D. 779 were probably composed in 1822-23, it is entirely plausible that Schubert might have played a version of D365n6 at some point not long after the publication of Opus 9 and decided to use its distinctive opening formula to improvise a new waltz. The likelihood is increased by the fact that D365n6 was apparently among Schubert's favorites: as Litschauer reports, it is among only six Schubert waltzes that appear three times in different manuscripts and one of only two found in manuscript copies made by one of his friends (Litschauer 1995, 4). The fact that some of these are variants is all the more intriguing. The first of the three manuscript versions (in 9 Deutsche (1819)) is identical to the published version, but the second (in 2 Deutsche (1821)) is striking in that it gives a fully realized Bb minor 6/3 chord in the left hand of bars 1-2, whereas the third (in 4 Deutsche (undated)) combines the first strain of D365n6 with the second strain of No. 7 from the same set (see Litschauer 1989).

Thus, we can imagine the new waltz starting as depicted at (a) in the graphic below: as necessary, vamping to establish the waltz meter and tempo for the dancers (or to gather one's thoughts), then open with a slight rhythmic variant of the figure in D365n6. The voice leading formula (second line in (a)) is varied too from the moment that F# becomes the upper voice (by the end of the first full bar of melody), but that is also where the trouble begins (third line in (a)), also realized as an initial attempt at a complete phrase in (b), which has a rather flat ending that allows the suspensions to drag the upper-voice melody down through ^4 and ^3).

Level (c) shows this ending again with the lead-in to the repetition of the phrase. Here is the first inspired moment in what has so far been a rather dismal effort: the hemiola rhythm of the initial gesture has taken control by now and the "turn" in four eighth notes gracefully (and convincingly) gathers energy that is directed toward the F#. Finishing out this varied repetition of the first strain, Schubert brings the upper voice down from its perch on ^6 and ^5 with a conventional ländler cadence that strikes ^1 but leaves the register of ^3 open. This cadence will also close the second strain of an 8 + 8 recomposition in Example 4.34.) Like the descent to ^3 in the first statement, this cadence seems weak.

At this point, the decision has to be made whether to set the new waltz in a two or three-part form, but for our purpose here, Schubert's choice makes little difference. I will assume that he composes a contrasting second strain (in the manner of D365n5). The dancing continues, and I imagine that Schubert plays a trio (perhaps one of the Ab major waltzes from D. 365 transposed to A major), but the awkwardness of the newly invented waltz bothers him, and he returns to it. This time around, the first phrase and most of the second are as we know them in the published version, but the cover-tone-qua-melody, now much more insistent than in the first attempt, brings about the second inspired moment, the cadence that lifts the upper register to ^8 (see the lower line in (d)).

Having reached the register of ^8 (A5), Schubert decides to stay there, perhaps expecting to use G#5 to initiate a cycle of fifths sequence as in (e'). For reasons unknown (which might include a simple lapse of attention during a long evening of playing), he decides to ground the contrasting middle of a small ternary form in a tonicization of the C# major supporting that G#5. There are a few examples of this design, where the contrasting middle closes in the tonicized key, and the reprise returns to the main key without modulation, but in this case the design will not work because the theme starts on a non-tonic position one half-step above C#.The third and last inspired moment, then, is to take advantage of yet another motion upward to carry the melody into the pianoforte's thin-toned and ethereal upper octave where the reprise begins in the final version.

Schubert chose to keep the A Major Waltz and eventually found it a place in the D. 779 collection, but I fancy it was not because of its odd combination of counterpoint and dance topoi or even its dramatic tonal contrast (something Schubert is known to have liked), but instead for the sake of its charming two-tiered melody. I imagine one of his musically skilled friends, perhaps Josef von Spaun, coming over after hearing several repetitions of the Waltz and whispering, "Schön, zärtlich," while the dance continued.

References:

Litschauer, Walburga. "Franz Schuberts Tänze: Zwischen Improvisation und Werk." Musiktheorie10/1 (1995): 3-9.

Litschauer, Walburga, ed. Franz Schubert. Neue Ausgabe sämtlicher Werke, Series 7, part 2: Werke für Klavier zu zwei Händen, Band 6: Tänze I. Kassel: Bärenreiter, 1989.

Parallel fifths in D779n13

Today's reading might be described as the counterpoint student’s revenge. Schubert did write parallel fifths, those fifths are not hard to hear, and once heard it is not difficult to discern this sparse open sound scattered throughout the right-hand part as a shifting registral frame: see the example below.

In order to grasp how Schubert might have arrived at this unusual result, it's easiest to think in terms of improvisation while playing for dancing. The A Major Waltz bears a curious resemblance to a waltz in Opus 9 (D. 365): these are the only extant Schubert waltzes that open with a figure based on the supertonic harmony with a 7-6 suspension. As the graphic below shows, D365n6 (at the top) shares with the A Major Waltz not only the initial 7-6 suspension but also the subsequent 5-4 over the 6/4 initial component of a cadential dominant figure.

I discuss D365n6 briefly in the context of typical harmonic patterns here: "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis," review-article, Music Analysis 25/1-2 (2006): 215. I will expand on the idea of improvisation as a source for D779n13 in tomorrow's post.

Postscript: Nicholas Cook offers a brief but trenchant account of the problem of parallel fifths in Schenkerian theory and practice. Writing about Schubert's song "Das Wandern," he concludes that a reading including middleground parallel fifths "is less satisfactory [than readings that remove the parallels] as an expression of that structure in terms of the metaphor of Fuxian counterpoint. [The fifths make] the music look ungrammatical and, therefore, incoherent. But this is not because the middleground consecutives contravene any natural law of musical organization. It is because they run counter to the representational means adopted in Schenkerian analysis. They spoil the comparison between Schubert's song and Fuxian counterpoint" (126, 128).

In that connection, here is a thoroughly "tamed" version of the waltz as a fourth-species exercise (with allowances for bass-specific leaps, of course).

Reference:
Cook, Nicholas. "Music Theory and 'Good Comparison': A Viennese Perspective." Journal of Music Theory 33/1 (1989): 117-41.

Proto-background 1: the unison ^1

Also see the proto-background introduction.

It would have been better, perhaps, to start with a simpler reading, such as ^3-^3, ^1-^3, or the obvious ^3-^5, but the unison ^1 has the advantage of shifting the interpretive ground rather abruptly and thus emphasizing the variety induced by registrally based proto-backgrounds.

NB: The graphics are thumbnails; click on them to see the originals.

Given the alto's strong focus on ^3 and the soprano's equally dogged emphasis on ^5, a reading generated from ^1 might seem counter-intuitive, but it does a very good job of conveying the teleology in the 8-bar antecedent. After the left hand's "oompah" introduction establishes key and meter, the right hand figures unfold over unstable harmonies; the first point of stability is at the end, when the alto reaches ^1 over I (bar 9). The notation in the treble staff reflects that with unstemmed closed notes for ^5 and the line from ^3 but an open note for ^1.

The consequent repeats the harmonic progression with variants in the eighth-note groups, but its ending is a surprise as a line rises from ^5 to the upper octave (A5), overwhelming the placid repetition of the descent in the alto. The idea, then, is to make a REGistral shift, but the register of A4 is doubled -- it doesn't disappear -- and so I call the transformation ADDINV, which adds above a given interval its inverse (here, the octave above the unison).

The register change is not made directly by A4-A5, but at a later level ("foreground") by G#4 -- see the graphic below:

The density of this figure is preferable to a reading that simplifies the passage through reduction to schematic voice leading over the given harmonies.

Returning to the main graphic, I have bracketed the octave with its internal fifth (which receives direct melodic emphasis in bar 17) and then noted how the progress of the second strain takes this framework and transposes it upward twice. (These could have been labeled as diatonic transformations T2 & T3, respectively.) This is an elaboration, however: on the larger scale, the entirety of the second strain repeats (or maintains the result of) ADDINV.

D779n13 in Music Analysis article (2006)

In my review-article on Fred Lerdahl's Tonal Pitch Space, I introduce a number of analyses of D779n13. This post lists them.

1.-3. I reproduce Figure 10.1 from Lerdahl and Jackendoff, their time-span reduction or analysis of the metrical structure of D779n13. To that I add a prolongational reduction or reading of the harmonic-voiceleading structure following their rules. Finally, I interpret the prolongational reduction in terms of Lerdahl's function rule (from TPS) (Neumeyer 2006, 209-214).

4.-7. Then I introduce what I call "four contexts" into which to place the A major Waltz: (1) "functional patterns in waltzes of the 1820s as they would be known by one accustomed to playing or improvising dance music; (2) D. 779 as a collection; (3) the waltz as danced; and (4) other modes of structural hearing as represented in alternative analyses." (Neumeyer 2006, 214-221; quote edited from 214). To no. 4: I create a reading based on a germinal motive that is a registral pattern, not the usual melodic figure. This is worked out hierarchically, including a registral foreground (Neumeyer 2006, 224-226).

8. Carl Schachter's rhythmic-metric reduction is translated into standard Schenkerian notation in Ex. 7 (Neumeyer 2006, 221).

References:

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

Lerdahl, Fred, and Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.

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

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).

Signature transformations and D779n13

Jay Hook has published an essay that uses the A-Major waltz as its principal example from the era of traditional European major-minor tonality. Here is the abstract:

Two types of transposition operators may be applied to diatonic objects such as chords or melodic fragments: the familiar mod-12 transposition operators (which may be understood to transpose the underlying diatonic scale along with the object itself); and the diatonic, or mod-7, transposition operators (which shift the original object within a fixed diatonic scale). Both types of transposition are expressible in terms of signature transformations. A signature transformation reinterprets any diatonic object in the context of a different key signature. With an appropriate understanding of octave and enharmonic equivalence, the signature transformations can be shown to generate a cyclic group of order 84, of which both the mod-12 and mod-7 transposition groups are subgroups. Signature transformations therefore hold considerable theoretical potential in unifying chromatic and diatonic structures, and relate to a number of established constructions in transformation theory and diatonic set theory. Direct applications of signature transformations may be observed in the works of many composers, as illustrated by examples from composers as diverse as Schubert, Debussy, and Michael Torke.

Hook applies the signature transformations not only to the obvious case of the abrupt shift to C# major in the contrasting middle but also to the succession of four-element eighth-note motives passed back and forth between the upper voices.

Reference:

Julian L. Hook. "Signature Transformations." In Jack Douthett, Martha Hyde, and Charles J. Smith, eds. Music Theory and Mathematics: Chords, Collections, and Transformations, pp. 137-160. University of Rochester Press, 2008. Link to book page on the UR Press site.

Caplin's form functions

The form-function terminology of William Caplin, derived in part from Schoenberg and so useful for sonata movements (among others), is less well suited to dance repertoires of the early nineteenth century. Late menuets still work well, and German dances generally pose fewer problems than do Ländler-based waltzes, in which tightly unified (that is to say, highly repetitious) themes and small forms can sometimes offer little in return for the effort involved in applying the terms.

Certainly, Caplin's terminology offers no unusual insights into formal design in D779n13. The first strain is only a bit more insistent than most waltzes in its repetitions of the basic idea of mm. 2-3, and other unusual features are self-evident without additional analysis: the displacement of the basic idea through the extended pick-up; the unexpectedly stable, if tonally distant, opening to the second strain; and the ending that is convincing as a reprise even though its appearance is somewhat muddled by a transition that puts the basic idea in a tonally uncertain position. The 16-measure theme in the first strain is a true 16-measure theme in Caplin's sense (not an artefact of the awkward beginning that would make the use of repeat signs clumsy). The 16-measure theme becomes the norm in Strauss, sr., and Lanner; that is stretched to 32 bars in the next generation. The contrasting middle (opening of the second strain) as a second theme is by no means unusual in the early waltz repertoire, especially in Schubert.

Sketch of the design: first strain: 16-measure period consisting of an 8-bar antecedent (sentence in which the continuation phrase is biv + biv with an imperfect authentic cadence) and an 8-bar consequent with the same elements but a perfect authentic cadence. (biv = "basic idea varied.") Second strain: rudimentary period with a 6-bar antecedent that appears to end with a perfect authentic cadence, followed by a 2-bar transition and a reprise of the consequent from the first strain.

Reference:

William Caplin. Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York: Oxford University Press, 1998.

See also my summary of the terminology in Chapter 1 of my PDF essay Dance Designs in 18th and Early 19th Century Music: Beethoven examples in Chapter 1.   Link updated 10 June 2016.

Proto-backgrounds (introduction)

My essay "Thematic Reading, Proto-backgrounds, and Transformations" is about to appear in Music Theory Spectrum 31/2: 284-324. For that reason, several early blog posts will read the Schubert waltz in terms of the proto-background construct developed there. A PDF essay with explanation and examples may be found here: proto-background. [Link updated 10 June 2016.]

In a generative hierarchical theory of traditional European tonality (such as Schenker or Lerdahl and Jackendoff), intervals precede lines. Taking the view that intervals are therefore the proper content of the earliest level(s), I build a set of 9 proto-backgrounds within the octave: three unisons, three intervals above ^1, two above ^3, and one above ^5. For the key of D779n13, these would be:

In the essay, I use an informally applied transformational language to elaborate the proto-background intervals, but any kind of notation for linear analysis (including any of the several "dialects" of Schenkerian notation) would be appropriate, too. Some transformations work directly with intervals (ADDINV and DIVision), others with stepwise formations (LINE, Neighbor, and their directional inverses).

I will post a series of entries, each of which is a reading based on one of the proto-backgrounds. A tenth entry will take up the question of comparison and evaluation.

D779n13 score

Here is a score for D779n13: this is a thumbnail -- click on it to see a larger image.

Here is a link to the IMSLP page for D779: link.

Lerdahl and Jackendoff comment on the waltz's anomalous design, and Margaret Notley takes its oddities as proof that the A-major waltz is a true character piece, not just another waltz improvised for dancing. I discuss the formal design in detail in the review-article. In a subsequent blog entry, I will show how the striking 10+8+10+10 design can be easily understood as created through improvisation (following comments by Kofi Agawu on composition or recomposition as analysis).

References:

Lerdahl, Fred, and Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.

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

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

Agawu, Kofi. "How We Got Out of Analysis, and How to Get Back in Again." Music Analysis 23/ii-iii (2004): 267-86.

Introduction

In March 1994, I read a paper at a conference organized by Peter H. Smith. The conference took place at Peter's home institution, Notre Dame, and was called "Critical Perspectives on Schenker: Toward a New Research Paradigm." My contribution was titled "Ursatz as Narrative: Or, 32 Ways to Hear a Schubert Waltz."

"Narrative" was an overly ambitious word for my actual topic, which was alternative strategies of analysis (reading, interpretation). I chose a single composition, a waltz by Schubert that had been analyzed by Carl Schachter and also by Fred Lerdahl and Ray Jackendoff, and I added to their readings 30 others. The point of the exercise was (a) to counter the idea that, even within the general constraints of linear analysis, one was obliged to find a single, correct analysis (even if that is exactly what Schenker himself required); and (b), more radically for the earlier years of music theory as an academic discipline, to imply that other modes of analysis produced interpretations that were equally interesting.

My notions of analysis-as-interpretation were not very well formed at that time. Since then, my attention to the question has been mainly in the context of film (music) studies, but it has also recently become an important topic in the music theory literature. In 1994, I naively assumed that pointing out a variety of options would in itself create a more self-critical practice of music analysis. But such an approach can be -- and was -- too easily rejected as relativistic, as lacking the moral (prescriptive) dimension that the rhetoric of interpretation always assumes, if not necessarily highlights. An effective self-critical practice has to include, rather than simply undermine, the conventional rhetorical strategies of interpretation. (I will write directly to this point in a subsequent blog entry.)

In this blog, I will post and discuss a variety of readings of D 779n13, not only the 32 from the Notre Dame conference but many others that I have generated since, a few of which have been published in "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis," Music Analysis 25/1-2 (2006): 201-30.

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)

Lerdahl, Fred, and Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.