[Smt-talk] Classical Form and Recursion
William Caplin
caplin at music.mcgill.ca
Tue Mar 24 17:27:51 PDT 2009
Dear Colleagues,
On 21-Mar-09, at 6:40 PM, Thomas Noll wrote:
> In the workshop I spontaneously summarized William Caplin's
> analysis (Classical Form, p. 149) of the core of the development of
> the 1st movement of Beethoven's F-minor sonata (Op. 2, No.1). Recall
> that Caplin interprets formal syntagmatic units with formal
> functions, such as presentation, continuation, cadence (closing
> function). If we understand the core in terms of a loosely organized
> "super-sentence", we find units with the functions presentation and
> continuation in recursive embedding - even if only with depth 2. In
> particular the presentation of the model involves a large portion of
> the secondary theme (including its presentation phrase and the first
> bars of its continuation phrase).
>
Seeing as some of my ideas were invoked at the start of this thread, I
would like to add some remarks on the topic of recursion in classical
phrase structure. As has already been pointed out, recursion in music
more obviously appears in the domains of harmony and counterpoint, and
are most fully developed (as noted by Jeff Perry and others) in
Schenkerian approaches. Identifying recursion has enormous appeal due
largely to general aesthetic and theoretical goals (typically
associated with various forms of organicist thought) of unity,
coherence and the like. I would, however, urge some caution when
extending such notions to classical phrase structure and form.
But first, I must acknowledge that in one important sense, formal
organization is highly recursive. (Warning: shameless plug to
follow.) In my essay, “What are Formal Functions?” which appears in
the recently published book Musical Form, Forms & Formenlehre: Three
Methodological Reflections, co-authored by myself, James Hepokoski,
and James Webster (ed. Peter Bergé; University of Leuven Press, 2009),
I present a number of “tree diagrams” (somewhat in the manner of L&J’s
GTTM) showing how the generalized temporal functions of “beginning,”
“being-in-the-middle,” and “ending” can be seen at every level in a
formal hierarchy (except the very top level, which comprises the
entire temporal extent of the musical work), and in so doing draw upon
Kofi Agawu’s notion of introversive semiosis. In this (highly
general) sense, formal organization is largely recursive. I then
propose that the various formal functions defined in my book Classical
Form are manifestations of these temporal functions, an obvious case
being the three functions of the sentence form: presentation (a
beginning), continuation (a middle), cadential (an end). Seeing as
the various “formal” functions represent, or express, the generalized
“temporal” functions, a sense of formal recursion is manifest. But to
the extent that the various formal functions are based on widely
diverse parametric criteria, the sense of recursion is less palpable.
For example, from bottom to top, a “basic idea,” a “presentation,” a
“main theme,” and an “exposition” each express the general notion of
temporal beginning. And their being embedded within each other
(again, from bottom to top) seems to be a perfect example of recursion
(when their accompanying middles and ends are included in the picture
as well). But the actual structure and defining elements of these
various functions are significantly different. The structure of a
presentation has little in common with the structure of a main theme,
which itself has little in common with an entire exposition. Each
formal function at various hierarchical levels has its own set of
defining criteria, and as such, it is not clear that the notion of
recursion is applicable in these cases. Indeed, I have argued
elsewhere (in my JAMS article on “The Classical Cadence”) that many
misconceptions of cadence arise precisely because theorists tend to
associate any type of “closure” (a generalized formal/temporal
function) at any level with the notion of “cadence,” a more specific
formal function, one that (in my opinion) is restricted to certain
middle-ground formations.
My sense is that the composers of the classical style tend to avoid
form-functional recursion at successive hierarchical levels. Thus,
while it is very common for an 8-bar sentence type (presentation,
continuation, cadential) to be embedded within a 16-bar period
(antecedent=sentence, consequent=sentence), and while it sometimes
occurs that a periodic design can be found within the presentation of
a sentence (esp. the 8-bar presentation of the compound 16-bar
sentence), it is rare for a period to be embedded within a period, or
a sentence, within a sentence. The case cited by Thomas Noll, where
the “model” of a developmental “core” comprises a sentence form (as in
Op. 2/1), seems to be an exception in that a sentence-like unit is
embedded within another sentence-like unit. But although we can
appreciate that the “grouping structure” of a core indeed resembles
that of a sentence, marked differences between them must be
acknowledged as well: in this case, the repetition of the “model” is
harmonically sequential, whereas the repetition of a basic idea within
a presentation phrase is normally tonic prolongational. These
differences in fundamental harmonic organization are not trivial, but
go to the heart of why a “core” is situated where it is in the formal
organization of a work, as opposed to a more genuine “sentence,” which
has its normative placements (as main theme, or subordinate theme)
within a movement’s structure.
In short, I believe that certain elements of classical phrase
structure are regularly recursive, but a view that overemphasizes this
aspect has the potential of blurring important distinctions among
units as to their precise formal functionality. I am thus more
inclined to recognize the non-recursive aspects of classical form, and
in that sense I have been strongly influenced by Leonard Meyer (as
cited in an earlier posting by Nicolas Meeùs), whose notion of
“hierarchic non-uniformity” seems highly applicable to classical form.
Finally, I would welcome any feedback on these ideas from members of
the list, especially since I'm venturing here into terrain (i.e.,
recursion theory) that is not in my area of expertise.
William Caplin
_____________________________
William E. Caplin
James McGill Professor of Music Theory
Schulich School of Music
McGill University
555 Sherbrooke Street West
Montreal, Quebec
Canada H3A 1E3
office: (514) 398-4535 x00279
home: (514) 488-3270
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