The simplicity and elegance of a reading from ^3 are nearly duplicated by a reading from ^5, which simply flips the priority of voices in the first strain and in the C#-major section of the second strain: E5 is the principal melodic tone and C#5 heads an alto voice. One would choose this reading if one was persuaded that, pace Carl Schachter's claim about relative levels of activity, traditional priority to the top-most voice is maintained in this waltz (Schachter: "The right hand plays two melodic lines written in free imitation. The lower of these lines (starting on [C#5] in bar 2) carries the main melodic motion and is, in general, more active than the upper one. The upper line, therefore, functions as a secondary part" (70).)
A stronger sense of polyphony also is preserved in a reading from ^5, as the upper voice may have priority but the music is still driven forward by the suspensions in the alto. The all-too-prominent ascent from ^5 to ^8 at the end of the first strain is explained as a fourth-line to the cover tone A5.
The only difficulty with this reading is the Urlinie descent: ^4 is assumed in the only place it can be-over the ii harmony-and ^3 follows over the cadential 6/4. This is not just an extrapolation from the chords involved: the move ^4-^3 is in the voice leading, as the left-hand afterbeats of measures 31-34. Still, it is not reassuring when we are obliged to abandon the salient right-hand voices to derive Urlinie notes from the accompaniment. In the meantime, the last recurrences of E5 are reminiscences of ^5, now as cover tones, with an ornamental but inconsequential line to ^8 at the end.
The reversal of function for ^3 and ^5 from beginning to ending phrases is not necessarily a weakness: such changes in function due to context occur so routinely as to be expected in Schenkerian analysis. But one might complain that the distinctive A7 chord in measures 29-30 is not given its due in either of the readings so far. The graphic below shows what happens when one elevates this chord to a necessary part of the voice leading. First heard as a faintly mysterious German sixth chord (see the lower staff), the A7 pulls E# down to E-natural, creating what can be heard abstractly as mixture: E5-E#5-E5.I am using the term "mixture" loosely here to refer to all chromatic mediant relations. Schenker restricts the term to alteration of the third in the initial chord (here that alteration would be C#-C-natural-C#).
The weakness of this reading is that it exaggerates the awkward way in which the Urlinie from ^5 cuts across the voice leading in the transition from the C# section to the final phrase. The chord progression is not incorrect-it is certainly possible to write E5-E#5-E5-D5-C#5 supported by I-III#-"I"-ii6-"I6/4"-but I would insist on it only if I decided that the idea of mixture was fundamental to this waltz (not an implausible notion given the alignment of form sections with the mixture elements) and that the boundary play of the right-hand line was too prominent to ignore (to demote to the status of ornament).
There is a way to have salience both in the principal melodic voice and in the transitional measures, but to achieve this feat we must be willing to sacrifice something else: the notion that a piece must end with a specific, predictable tonal formula that includes melodic arrival on ^1. In the next graphic, I have maintained ^5 as background tone but have reinstated Schachter's reading of the transition. However, once we reach F#, there is time only to descend to ^3. This can be justified by a stylistic argument: I have noticed a number of cadence formulas in waltzes that suggest incomplete endings, especially on ^3, but occasionally on ^5.
Thus, in this repertoire it may be quite enough when all features of the music other than an abstract melodic frame signal "end" clearly. To insist otherwise seems not only counter-intuitive but unmusical. In other words, I am asking you to accept the idea that style information can override even one of Schenker's most fundamental claims, that a piece is only "complete" if its Urlinie descends diatonically stepwise to ^1. Pragmatically, incomplete lines make chaining waltzes easier; affectively, they promote the same sense of sentiment, nostalgia, and the ineffable as the Romantic "fragment." (See also the Play of Thirds entry.)
All three readings from ^5 may be said to express the "everyday" belief in the priority to the traditional uppermost line in homophonic textures. On that basis, I find this last version the most satisfactory.
The only difficulty with this reading is the Urlinie descent: ^4 is assumed in the only place it can be-over the ii harmony-and ^3 follows over the cadential 6/4. This is not just an extrapolation from the chords involved: the move ^4-^3 is in the voice leading, as the left-hand afterbeats of measures 31-34. Still, it is not reassuring when we are obliged to abandon the salient right-hand voices to derive Urlinie notes from the accompaniment. In the meantime, the last recurrences of E5 are reminiscences of ^5, now as cover tones, with an ornamental but inconsequential line to ^8 at the end.
The reversal of function for ^3 and ^5 from beginning to ending phrases is not necessarily a weakness: such changes in function due to context occur so routinely as to be expected in Schenkerian analysis. But one might complain that the distinctive A7 chord in measures 29-30 is not given its due in either of the readings so far. The graphic below shows what happens when one elevates this chord to a necessary part of the voice leading. First heard as a faintly mysterious German sixth chord (see the lower staff), the A7 pulls E# down to E-natural, creating what can be heard abstractly as mixture: E5-E#5-E5.I am using the term "mixture" loosely here to refer to all chromatic mediant relations. Schenker restricts the term to alteration of the third in the initial chord (here that alteration would be C#-C-natural-C#).
The weakness of this reading is that it exaggerates the awkward way in which the Urlinie from ^5 cuts across the voice leading in the transition from the C# section to the final phrase. The chord progression is not incorrect-it is certainly possible to write E5-E#5-E5-D5-C#5 supported by I-III#-"I"-ii6-"I6/4"-but I would insist on it only if I decided that the idea of mixture was fundamental to this waltz (not an implausible notion given the alignment of form sections with the mixture elements) and that the boundary play of the right-hand line was too prominent to ignore (to demote to the status of ornament).
There is a way to have salience both in the principal melodic voice and in the transitional measures, but to achieve this feat we must be willing to sacrifice something else: the notion that a piece must end with a specific, predictable tonal formula that includes melodic arrival on ^1. In the next graphic, I have maintained ^5 as background tone but have reinstated Schachter's reading of the transition. However, once we reach F#, there is time only to descend to ^3. This can be justified by a stylistic argument: I have noticed a number of cadence formulas in waltzes that suggest incomplete endings, especially on ^3, but occasionally on ^5.
Thus, in this repertoire it may be quite enough when all features of the music other than an abstract melodic frame signal "end" clearly. To insist otherwise seems not only counter-intuitive but unmusical. In other words, I am asking you to accept the idea that style information can override even one of Schenker's most fundamental claims, that a piece is only "complete" if its Urlinie descends diatonically stepwise to ^1. Pragmatically, incomplete lines make chaining waltzes easier; affectively, they promote the same sense of sentiment, nostalgia, and the ineffable as the Romantic "fragment." (See also the Play of Thirds entry.)
All three readings from ^5 may be said to express the "everyday" belief in the priority to the traditional uppermost line in homophonic textures. On that basis, I find this last version the most satisfactory.
References:
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).
