[Smt-talk] Classical Form and Recursion
Olli Väisälä
ovaisala at siba.fi
Mon Mar 30 04:59:26 PDT 2009
>
> I think the deep question is this: is "prolongational structure" a
> quasi-syntactical, more-or-less objective feature of the music, the
> way TSDT harmonic structure (arguably) is, or is it something we
> (perceivers, analysts, etc.) impose on the music from outside -- as
> when we interpret ABABAB... as (ABA)(BAB) = ABABA...
Yes. This is, indeed, a crucial question.
I do not think tonal music is necessarily (deeply) prolongational,
but it has the potential to be structured (and perceived)
prolongationally, and I have been suggesting that there is empirical
evidence that some composers—such as Bach—have utilized this
potential extensively. This empirical evidence relies on the way in
which features such as design, register, meter, and rhetoric/gestural
emphasis support prolongational structures in his music. In other
words, prolongational models have great explanatory power for the
arrangement of such compositional features in his music.
[I have touched upon this issue in two recent (forthcoming) studies
on Bach, and have drafted another one in which I address it more
expressly. I can send the draft to anyone interested, but at present
it is only a draft that I have already started to rewrite. I also
wrote on this issue in this list under the rubric "Why I am a
Schenkerian"—last summer, I think.]
Instead of discussing Bach, I shall again present simple examples for
illustrating that there may be varying degrees of evidence for
prolongational structuring. Consider the following progressions in
4/4 time (soprano tones in parentheses; / = barline).
Progression (1). I (1^) – V (2^) – I (1^) – V (2^) / etc. / etc.
Progression (2). I (3^) – V (2^) – I (3^) quarter rest / V (2^) – I
(1^) – V (2^) q.r. / I (1^) – V (7^) – I (1^) q.r.
In Progression (1), there is no empirical evidence that the
"composition" is affected by any prolongational patterning beyond the
most immediate level in which each V prolongs surrounding Is (as
supported by the meter). Deeper-level models have no explanatory
power in this case. (Trying to identify deeper levels would be as
nonsensical as hierarchicizing the tones in a trill.)
In Progression (2), there is considerable empirical evidence that the
composition is affected by a larger prolongational pattern, since
meter, grouping, and regular design bring out archetypal patterns
both for the harmony (I–V–I) and the top voice (3^–2^–1^). The
prolongational model has considerable explanatory power for the way
in which the music is shaped. Of course, one cannot "prove" that the
composition manifests prolongation. The features that seem to support
the 3^–2^–1^ shape might be a chance products or better explained by
some alternative model. Given the number of such features, however,
the chance explanation does not seem too likely, and it is not easy
to see ways in which the prolongational model could or should be
bettered. At the very least we can say that restricting ourselves to
a purely concatenational model would create a high risk of losing a
crucial compositional aspect.
My work on Bach relies on an argument similar to that on Progression
(2) above, even though the music and issues involved are, of course,
much more complex.
>
> 1. Representation. I understand why someone would say that the
> melody (C4-E4-D4-C4)-(D4-F4-E4-D4) has a hierarchical, quasi-
> recursive structure: a single motive is repeated at two different
> pitch levels, and similar concepts ("up by step") apply at both. I
> am much less clear about what it means to say that (C4-E4-D4-C4)
> "represents" or "stands for" (or "prolongs" or "embellishes") a
> single note on "a higher structural level." (This gets at a point
> raised by Ioannis in a previous email.)
I am not sure whether I understand your concerns here. Tonal
tradition is rich in practices in which basic skeletal progressions
are subjected to diminution, variation, embellishment etc. I do not
suppose you mean that you have difficulties in grasping this concept
intuitively—in cases such as Progression 2 above, for example.
(Naturally, when one proceeds to higher structural levels, involving
more extended temporal spans, such concepts become less self-evident
for intuition, but this does not seem to be your point.)
Instead of trying to describe "what it means to say" that something
is prolonged, it might be more useful here to concentrate on the
consequences of prolongation. If prolongational readings are capable
of revealing larger patterns that seem likely to be pertinent to a
certain composition (as in Progression 2 above), this should suffice
for justifying the concept.
> 2. Surface accent vs. Depth. Schenker emphasized that chords
> could be accented and emphasized by the musical surface in all
> sorts of ways, and yet not belong to deeper levels of structure.
> Olli's claim seems to be that accent (meter, design, register) in
> general provide a definitive recursive interpretation.
The relationship between emphasis and structural weight is complex.
The relationship between different aspects of emphasis (meter,
design, register, rhetoric/gestural emphasis) is also complex. There
are crucial syntactical rules such as dissonance treatment, that may
override aspects of emphasis. A dissonance is subordinate to its
resolution even if it is more emphasized metrically or by other
means. While the issue of analytical criteria is, indeed, complex, I
think much more clarity about it can be acheived than what is often
evident in Schenkerian literature (and I have tried to offer some
contributions in this respect in my recent work).
> Personally, I don't see why differences in strength and weakness
> necessarily imply the need for recursive interpretation. [...]
> The question is -- do we think that differences in stress and
> accent create a need for recursive interpretation of music? To
> take your example, suppose someone tells us they hear a particular
> I-ii-V-I-ii-V-I passage as a sequence of chords, with some strong
> and some weak, some short and some long, but no "embedding" or
> "representing" or "prolongation?" Can we really say that this
> hearing is *wrong* -- that it misses objective syntax-like features
> of the music?
I totally agree that differences in strength and weakness do not by
alone imply the need for recursive interpretation. My argument is
based on the notion that insofar as recursive (prolongational)
interpretations based on such aspects reveal meaningful larger
patterns, this points to the recursive model's compositional
significance. An example of a "meaningful larger pattern" is the 3^–
2^–1^ on I–V–I in the above Progression 2.
***
While I first thought that Bach examples may be too complex for this
mail, it might be useful, after all, to close it by a brief
discussion of a real Bach example. Since I mentioned the II–(V–I)–II6–
V–I pattern in my previous post, I choose an example featuring this
pattern, Invention in G Major. The pattern is to be found in mm. 20–
27 (–29).
The initial II (m. 20) is marked by an outstanding textural element,
the right-hand trill, and opens a four-bar passage with the chord
succession II–V7–I–VI. The weakness of the three latter chords is
implied by (1) the absence of change of texture or design, (2)
hypermetric weakness, (3) higher register of bass tones. After this
four-bar passage, a relatively strong change in design marks the II6
(with 7-6 suspension) in m. 24, as the trill transfers to the left
hand, which also returns to the register close to that in m. 20.
These features unequivocally bring out the II (m. 20) and the II6 (m.
24) as the two most prominent chords within span; moreover the
correspondence between the trills on C in m. 20 (r.h.) and m. 24
(l.h.) suggest a special connection between the top voice of II and
bass of II6. There are thus several compositional features that
clearly could be explained on the basis of a prolongational model in
which the II with 4^ in its top voice is prolonged by a II–II6 voice
exchange pattern. For more evidence that this pattern had
compositional significance for Bach, let us look how it relates with
larger contexts.
The II6 is followed by V4/2 (m. 26), marked by a relatively strong
design change. The V4/2, in turn, resolves to I6 (m. 27), which is
highlighted by a crucial event in the overall design, the beginning
of the recapitulatory closing section. A hypermetrically
straightforward I6–V6–I progression follows, with top voice
emphatically reaching the high B in m. 29. This, of course, suggests
prolongation of I, with 3^ transferring from the bass to the top
voice. Such an event supports the compositional significance of the
preceding II–II6 voice exchange, since the transference of 4^ to the
bass (II–II6) is followed, after a 4^–3^ resolution (V4/2–I6), by a
reciprocal transferrence of 3^ back to the top voice (I6–I),
completing a neat, strongly highlighted 4^–3^ top-voice pattern (mm.
20–29).
Further support for the 4^–3^ pattern's compositional significance
can be gained in two ways:
First, within this Invention, it participates in the overall top-
voice progression 5^–4^–3^–2^–1^. (5^ is introduced in bar 1 and
confirmed by its linear relationship with the neighboring 6^ in m. 4,
which returns to 5^ through a E5–G4 [mm. 4–9] F#4–D5 [10–14]
unfolding; the points in this structural framework are clearly marked
by changes of design. The final 3^–2^–1^ progression occurs in mm. 31–
32; observe how the B5 in m. 29 relates with the B4 in m. 31 through
similar r.h. figuration.)
Second, more or less similar prolonged 4^–3^ motions occur very often
in Bach in approximately similar points of form. The recurrence of
such a pattern speaks to its compositional significance; we need the
prolongational model for discussing such patterns. Moreover, as I
discuss in my forthcoming Invention article under the heading "The
Predictive Power fo the Urlinie", it is characteristic of Bach that
in pieces in which he first establishes the 5^ as the governing top-
voice tone (Kopfton), he later underlines a 4^ that leads to 3^ (and
further to 2^ and 1^) in some special way, in this case the trills.
I hope this suffices to give an idea why I think that restricting
oneself to "concatenational" hearing may, indeed, risk missing
objective syntax-like features in Bach.
Olli Väisälä
Sibelius Academy
ovaisla at siba.fi
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