Schachter and the rising Urlinie, Part 13c2

Schachter's second criticism is that I confused levels. Here is what I wrote:

it is not just the direction of the motion but the goal of that motion that is important. Schenker accepts this implicitly with respect to the bass arpeggiation, in that he allows it to rise, rather than fall, from the V to the final I, despite his own rule of the obligatory register in the bass. Yet if any voice should be sensitive to motion toward the fundamental, it is certainly the bass! (280)

To which Schachter responds:

the placement of V below I . . . results from prolongations at later levels, which transform the underlying shape of the bass arpeggio. Through ascending and descending register transfers in the upper voice, Schenker also allows for octave displacements of the Fundamental Line's final tone at later levels.

Here I have to say that neither of us apparently understood what Schenker said. I was wrong to tie the Bassbrechung-as-expression-of-nature to the obligatory register, and it was Schachter who confused levels. In section 268 of Free Composition, Schenker says that obligatory register applies to both upper and lower voices and means a return to a voice's "basic register" (107), which he defines as "the register of the first tone of the fundamental line." His upper-voice examples do refer to the fundamental line; the two lower-voice examples, however, are both foreground details. Still, given the care with which he matches the first and last tonic notes in the bass in the abstract figures, it is reasonable to assume that he meant for the same to be true of the background bass.

Whether or not Schenker intended a background return to the register of the first bass note at the end of a piece, Schachter is clearly incorrect in isolating displacements to later levels. Schenker says on p. 107: "Nevertheless, the final tone of the [Urlinie] sometimes appears an octave lower or . . . higher." And the basses in his figures showing readings of pieces vary quite a bit, though more often holding to the configuration of the abstract examples, as in Fig. 7a: C#3-G#3-C#3. But already in Fig. 7b the position of V is reversed: F3-C3-F3. The well-known Fig. 21b (Schumann, "Aus meinen Tränen Spriessen") is interesting in this respect: in the foreground, A4-E3-A3; this becomes A3-E4-A3 in the two middleground graphs. (He does something similar in Fig. 39,2.)

All my theoretical maneuvering in that section of the JMT article was irrelevant, I now think, to justification of the rising Urlinie. Although Schachter's criticisms are off the mark, the specific justifications from Free Composition that he attacks were not very strong, that's clear, especially insofar as they tried to conform to Schenker's own poorly defined notions of the relation of acoustics and art and his equivocation about register in the background. At the time of the JMT article, I didn't have the style statistics in hand that I have accumulated since: see this PDF file with a compositions list. From Schenker all I really needed was: "In the service of art, the arpeggiation throws off the restrictions of nature and claims the right to assert itself in either an upward or a downward direction." From this follows a principle of symmetry (the up/down schema is not fundamental but expressive) that is neatly realized in Zuckerkandl's graphic of the major-key scale.

Schachter and the rising Urlinie, Part 13c1

This continues Part 13b and is the final installment in the Schachter series -- though, because of length, I have broken it in two, as 13c1 and 13c2. The latter -- the final, final installment -- will be posted tomorrow.

In a lengthy footnote (341n22), it is understood that I misread Schenker's statements about the Bassbrechung (background I-V-I) in relation to the harmonic series.

Here -- in condensed form -- is what Schenker says in the first two sections of Chapter 2 (The Fundamental Structure)

In nature sound is a vertical phenomenon [but] art manifests the principle of the harmonic series in a special way, one which still lets the chord of nature shine through. . . . a horizontal arpeggiation.

This basic transformation of the chord of nature into an arpeggiation must not be confused with the voice-leading transformations of the fundamental structure which occur in the middleground.

[Section 2 is labeled] The fundamental structure as transmitter of the primary arpeggiation

In the service of art, the arpeggiation throws off the restrictions of nature and claims the right to assert itself in either an upward or a downward direction. The following two forms represent the briefest and most direct ways for the harmonic series to be realized by human vocal organs: [Fig. 3 shows two arpeggiations through an octave: C3-E3-G3-C4, then C5-G4-E4-C4]

The upper voice of a fundamental structure, which is the fundamental line, utilizes the descending direction [from Fig. 3]; the lower voice, which is the bass arpeggiation through the fifth, takes the ascending direction [here he refers again to Fig. 1, which shows an Urlinie E5-D5-C5 against a Bassbrechung C3-G3-C3]. As in the natural development of the arpeggiation, the ascending direction is the original one; indeed, in the fundamental structure it serves as a constant reminder of the presence of the chord of nature.

And here is the first of Schachter's two explanations of my "slightly inaccurate account of Schenker's view of bass structure."

When Schenker, in Free Composition, speaks of the bass motion as upward, he refers to the ascent from I to V, but not to a continued ascent up a fourth to the closing I. His Figure 1 and the accompanying discussion on p. 4 make this clear. Thus when Neumeyer (p. 281) says that "the descending fifth from V to I in I-V-I represents what should have been a rising fourth", he is not, I think, reporting what Schenker really means.

True, as far as it goes. Schenker quite deliberately "reverses" the direction of the move from V to I, from ascending as it should do, to descending. This dictum is pointless, however, because, as we shall see tomorrow, Schenker is quite lax about the obligations of obligatory register, so to speak. Yet he is determined to make the bass conform to the principle of obligatory register, and it would seem the reason is that he wants to set up a firm wall between the harmonic origins of the tonal system -- he was unequivocal about giving priority to the bass ascent in section 1 -- and the artistic priorities of the tonal system as he conceives it and as they are contained in the Ursatz. My MTS article was concerned in part with the suggestion that the wall is permeable (intervals as non-expressive themes generate lines, etc., as expressive themes) -- or, really, that the wall is a chimera.

Postscript: It is unfortunate that Allen Cadwallader and David Gagné simply parrot Schachter's assertions in their textbook. That sort of pedagogical hardening is not good for theoretical discourse.

Reference:

Cadwallader, Allen, and David Gagné. Analysis of Tonal Music: A Schenkerian Approach. 2d edition. New York: Oxford University Press, 2006.