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.
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.
