One of the most memorable treatments of ^5 and ^6 is in the first waltz of An der schönen, blauen Donau. Johann Strauss, jr's opus 314 was published in 1867, at the height of his success as a dance composer and conductor and not long before he turned to composing operettas. The design is standard: five waltzes, each of which consists of two strains with both repeated to create a double reprise (waltz-trio-waltz-trio) effect, plus a substantial introduction and a coda that quotes all but the last waltz. The tonal design of the set is also not unusual:
See the piano score for waltz 1, first strain, below. The circles show the expanded treatment of ^5 and ^6, including the "last second" retreat from a tonic with added sixth at the very beginning of the third system. The rectangles sketch my view of the design, which is based on the registral pattern established immediately, then shifted into the upper octave midway through the third system. I would read the strain as derived from a proto-background ^1-^5.
Schenker's desire for a unified, teleological tonal motion leads him to mis-read the first waltz in Free Composition: he maps onto the piece a waltz-trio-waltz design with the expected interruption covering the second strain (which is in A major). In fact, the waltz ends in A major because both strains, not just the first, have their reprise (the alternativo design already common in Mozart's generation [Note 19 June 2017: see my comment on this in the updated blog post for 3 March 2010]).
William Rothstein uses the first strain as a study object for his exploration of the meaning of the term "phrase." Along the way, Rothstein presents a foreground reduction with bar lines and four-bar "phrase" markings, two levels of durational reductions (after Schachter), and a "standard" Schenkerian graph. He describes the figures of this last as follows:
The first sixteen measures are ultimately static, ending where they began, with only minimal motion along the way. The gradual ascent that follows picks up from this same point, without which it would lack a firm beginning. The complete tonal motion therefore comprises the entire excerpt: all of it is to be performed "...figuratively, in a single breath."The most striking feature of this larger motion -- and what elevates this unpretentious waltz to high artistic rank -- is the broad melodic arpeggiation from the initial ^5...up to the climactic ^3....One can see how this large arpeggiation mirrors and fulfills the smaller arpeggiations of the several upbeat measures. The ascending sixth [A4-F#5] in mm. 27-28 summarizes the entire ascent in a burst of melodic energy....The concluding melodic descent then gradually dissipates the accumulated tension.
Rothstein's reading does a good job of following the broad contours of registral (and dynamic) change through this first strain. It certainly improves on Schenker's reading, which ignores the melody of the inner voice to choose ^3 from the repeated quarter note figures in the upper voices; when these figures cease in m. 24, the voice-leading moves into the arpeggio-based melody. This in itself, although peculiar, is not damning because there is indeed a distinct change of texture (and orchestration) at mm. 24-25, but Schenker flattens out the large registral shape that Rothstein shows so clearly -- Schenker locates the first Urlinie note at the beginning (m. 3-4) and describes the broad figure reaching F#6 (and then dropping back to F#5 for the cadence) as unfolding, although the far more likely label would be coupling, or middleground registral doubling.
Note: establishing the "priority" text for this famous composition is something of a problem, believe it or not. An der schönen, blauen Donau was issued first in May 1867 in an arrangement for solo piano; from August to October of the same year, editions appeared for orchestra, men's chorus and piano, piano four-hands, and violin and piano. In all, between May 1867 and August 1869, fifteen versions were published. The preponderance of early public performances were the version for men's chorus, whose original text is a light inducement to enjoy the Carnival season: it begins "Wiener seid froh," to which the upper-voice ornaments (in the tenors) answer "Oho, wie so?" This banter continues till all the voices join forces for the final phrase and cadence, "Was nutzt des Bedauern, des Trauern? Drum froh und heiter seid!" (Very roughly: What good is sadness? Have fun!")
Reference:
Rothstein, William. Phrase Rhythm in Tonal Music. New York: Schirmer Books, 1989.
