[Smt-talk] Classical Form and Recursion

Dmitri Tymoczko dmitri at Princeton.EDU
Sun Mar 29 11:46:05 PDT 2009

> I am, indeed, of the opinion that music – complex art music, at  
> least – typically accommodates different and even "conflicting"  
> aspects of organization. The relationship between prolongational  
> (recursive) and "concatenational" aspects of common practice  
> harmony and voice leading is one example of this phenomenon. [...]  
> Let us state, in somewhat simplistic terms, that Schenker made the  
> following two claims. (1) Prolongation—or multilevel patterning of  
> harmony and voice leading—is an important aspect of organization in  
> tonal masterworks. (2) It is the all-embracing aspect to which all  
> other aspects are strictly subordinate. Now (1), of course, does  
> not imply (2). I think many if not most present-day Schenkerians  
> (such as me) would approve of (1) but not of (2).

Very good point!  I describe this view as "compatibilism."  I  
completely agree that most present-day Schenkerians are  
compatibilists.  Schenker and Salzer (and maybe Beach and Rothgeb)  
weren't/aren't.  So there's been a pretty big shift here -- with  
hardly a single music-theoretical publication about the subject.  In  
fact, the only relevant writing I know of is an excellent unpublished  
paper by Bill Rothstein, who's also a compatibilist.  I wish he'd  
publish it, because I think it's a really important issue.

> I did not want to deny the significance of psychology. There are  
> wide variances in what we perceive or fail to perceive depending on  
> circumstances, predispositions, conscious efforts etc. What I  
> wanted to point out is that the ways in which chords and tones  
> relate with other parameters (meter, design, register, etc.) (1)  
> offer empirical evidence of the ways in which composers perceived  
> the relationships between the chords and tones (2) affect the  
> probabilities of the ways in which the listeners will perceive  
> these relationships.

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...
	It seems like you're claiming the former; someone like Nicholas Cook  
(or maybe Ben Boretz) might favor the latter view.  Panos and  
Ioannis, by contrast, would almost seem to want to erase the  
distinction entirely, claiming that "recursivity" is *entirely* an  
interpretive matter, having nothing to do with the underlying stimulus.
	To my mind, there are a host of complicated issues relevant here.   
For instance:

	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.)  The claim that certain  
sequences of notes "represent"/"embellish"/"stand for" others, and  
that this standing-for is ubiquitous in tonal music, is very complex  
and thorny.  It's almost a philosophy or linguistics issue, as Mark  
DeBellis has been suggesting.

	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.
	Personally, I don't see why differences in strength and weakness  
necessarily imply the need for recursive interpretation.  Nor does  
the presence of simple ABA patterns.  For example, the sentence  
"Americans care only about Americans" does not "prolong" or  
"represent" or "embellish" the word "Americans" even though it has  
the structure ABA.  Nor do differences of emphasis, or pauses:  
imagine reading "Americans care only about Americans" while strongly  
stressing the first and last words, or drawing them out in length.
	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?
	Offhand, I'm more inclined to think that recursive conceptualization  
is optional rather than required -- a feature of the way many people  
like to think about music, rather than an interpretation mandated by  
the music itself.  This is perhaps the way Nicholas Cook thinks about  
Schenkerian interpretation.

	3. "Hearing" vs. "hearing as."  	We know that it is possible to be  
wrong about what one hears -- for instance, one might incorrectly  
think that one could hear long-range tonal closure.   And we also  
know that there's an important difference between "hearing  
as" (knowing through perception that X) and "hearing plus  
thinking" (hearing while thinking "that's X").  So how could we  
establish that Olli (or other listeners) hears the sequence in the  
way he's described, rather than just hearing it while thinking "this  
prolongs that"?  In other words, what reason do we have to believe in  
the reliability of statements like "I hear these chords as prolonging  
this one?"
	I don't mean this rhetorically, by the way.  I'm very interested in  
whether there could be empirical tests of this very issue.  I've  
tried to come up with some, without much success.

In any case, I don't think I have the answers to these questions, but  
I do think they're really interesting and not-much-discussed.  They  
almost lie at the border of philosophy, cognitive science, and  
music.  The role of recursion in tonal music is really, really  
fundamental here ... and it would be great if we as a community could  
work toward some clarity about the issues involved.  There's clearly  
a huge amount of interest in the subject, judging by the flurry of  
email activity on the list.


Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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