[Smt-talk] Classical Form and Recursion

[Dmitri Tymoczko]

Fred wrote:

> Dmitri writes:
>
>> For me, the single biggest issue with TPS is that it seems to  
>> operate with the assumption of complete perceptual accuracy.   
>> Tension values (etc.) are calculated on the basis of complex  
>> relations found in scores -- suggesting that the unconscious mind  
>> is accurately perceiving 100% of the (relevant) musical  
>> information aurally.  (It has to have this information in order to  
>> calculate in the way the book describes.)  As someone with a fair  
>> amount of experience with introductory music students, I find this  
>> implausible.  We lose an awful lot of information when listening  
>> to music.  It can be genuinely hard, for introductory students, to  
>> tell whether they're hearing a V chord.  (To say nothing about  
>> returning to the tonic key at the end of a long piece.)  This is  
>> an area, I think, where the model of linguistics has not had a  
>> salutary influence -- the assumption of perceptual accuracy is  
>> much more plausible in language than in music.
>> 	So, as I see it, it's really an open question how much of the TPS  
>> formalism would survive a more realistic appraisal of the  
>> perceiver's limitations.  Maybe this issue of inaccuracy isn't  
>> such a big deal; maybe it is.  We simply don't know right now.
>
> This issue concerns the competence/performance distinction in  
> linguistics and, more generally, the status of scientific models.  
> The world is messy. To make progress in understanding it, one must   
> break the object of study into manageable parts and adopt  
> idealizations that simplify it. Physicists say they build models.  
> That is my attitude, and I think that most music theorists share it  
> implicitly. One can't study the loss of information because of  
> wandering attention while listening to music unless one has already  
> developed a theory about what that information is and the  
> principles by which the information is received.

I was wondering whether you'd say that!  My own view is that the  
uncritical exporting of the performance/competence distinction from  
linguistics to music is highly problematic -- in fact, I'd say it's  
the very root of our disagreement.  My view is that in the linguistic  
case, most people approach idealized "competence" at least for  
relatively uncomplicated sentences.  The idealization, in other  
words, is small.

In TPS, I think the idealizations involved are very large -- actual  
listeners are not close to having the abilities attributed to them by  
TPS, for instance because they can't hear the return to the tonic  
after about a minute and a half.  (Among many other issues: they also  
can't reliably hear the V chord.)  Furthermore, and more  
interestingly, the very definition of "competence" involves delicate  
aesthetic questions that do not arise in the linguistic case.  Is the  
listener "competent" who loves Beethoven but does poorly on ear  
training exams?  What about the one who hates music but passes every  
test?  Does the ideal listener have perfect pitch?  Etc.
	The interesting observation here is that semantics (non-obviously)  
helps to underwrite the definition of "linguistic competence";  
operationally, our only access to syntactic competence runs through  
semantics.  Absent semantics, the notion of "competence" becomes thorny.

In fact, I've been giving a talk entitled "Why linguistics is a bad  
model for music theory" in which the basic points I make are:

	1. The problem of information loss in music perception is large, and  
should not be idealized away.
	2. The notion of a "performance/competence distinction" in music  
theory is highly problematic, and should not be assumed automatically.
	3. Without semantics, it's very hard to set a non-controversial  
lower threshold on "competence."

Even if we disagree about these issues, it's good to know that we  
seem to agree about what the issues actually are.

> The study of musical tension is attractive partly because  
> intuitions about it are so spontaneous. The average listener cannot  
> name a V or a I chord but nevertheless responds to a progression in  
> terms of degrees of tension. Put another way, a chord has a  
> particular location in tonal space; the listener has implicit  
> knowledge of the space and feels motion and force as patterns of  
> tension.

I think there's more of a difficulty here than you do.  Consider:

	1. TPS assumes that listeners can reliably tell whether something is  
a V or I chord, because this information is an input to its various  
algorithms.
	2. We all agree that ordinary listeners cannot reliably name whether  
something is a V or I chord.

Now there's a friction between #1 and #2, one that the TPS-defender  
has to explain away.  You don't make this vanish by changing the  
topic to "tension" -- at least, not if the tension-calculation  
requires knowledge of whether something is a I or a V.  (In other  
words, talking about tension hides, but does not resolve, the  
contradiction.)  As far as I can see, your only option is to say that  
the difficulties labeling I and V are entirely the result of trying  
to retrieve the relevant information from the unconscious -- it's  
there, but we don't realize it.  Thus, on your view, when we learn to  
apply Roman numerals, we're not learning to perceive more accurately  
-- instead, we're learning to *label* perceptions that we already  
have.  (The is reminiscent of Meno's Socrates.)

I, for one, do not find this to be compelling -- it seems more likely  
that when we learn Roman numerals, we're learning to perceive more  
accurately.  But this then weakens my credence in those parts of TPS  
which depend on your implicit-knowledge hypothesis.  And this, in  
turn, makes me want to hold TPS as a whole to a higher standard of  
empirical vindication (see below).

All of this is methodologically mundane: if you give me a theory  
whose assumptions seem plausible, I'll be more favorably disposed to  
empirical evidence supporting that theory.  If you give me a theory  
whose assumptions seem implausible, I'll require a higher burden of  
proof.  This is not abstract philosophy-mongering; it's meat-and- 
potatoes science.

> Again, to make progress one must idealize and break apart the  
> phenomena. In the project with Krumhansl, we equalized speed,  
> loudness, and timbre, and we neutralized rhythm as best we could,  
> given the current lack a theory of rhythmic tension. For the most  
> part, then, we were able to present the subjects with materials  
> that isolated tonal tension from other kinds of tension. As for  
> comparisons, only a philosopher would demand that a proposed model  
> succeed better than all other hypothetical models. Scientific  
> inquiry doesn't work that way. One makes a theory to explain and  
> predict the phenomena in question. If there are alternative  
> theories, one tries to find out which one works better. In the case  
> of musical tension, an alternative theory does not yet exist, so  
> how is one to compare?

Again, very fascinating issues.  But I don't agree with your claim  
that "only a philosopher" would ask whether there could be  
alternatives to a given theory.  I think this is the question every  
scientist always has to ask when considering whether to accept any  
theory.

Accepting a scientific theory is a matter of balancing the accuracy  
of its predictions against our judgments about the plausibility of  
its assumptions.  When Einstein predicted gravitational redshift, or  
Julian Schwinger calculated the anomalous magnetic moment of the  
electron (with an agreement of about 6 decimal places), this was very  
convincing.  The quantitative agreement with the experiments was  
extraordinarily precise, and it was very difficult to come up with  
alternatives, and the assumptions seemed to make sense.  So the  
theories were accepted pretty quickly.

On the other hand, the theory of continental drift took a long time  
to be accepted.  Mere data about the agreement of the continents'  
shapes was not compelling; it took a very large amount of evidence,  
and a very long time, for geologists to come around.  Someone who  
claimed, in 1912, to have "proven" the theory of continental drift,  
would have been exaggerating.  It would not be enough to say --  
"look, science doesn't progress by asking whether there could be  
alternate theories ... I've explained why Africa seems to fit into  
South America, and nobody else has, and that shows I'm right!"  (In  
other words, "only a philosopher would care about alternatives to  
continental drift ...")

For that matter, the theory of Ptolemeic theory of epicycles fit the  
data pretty well; in fact it was better than the initial heliocentric  
theory with circular orbits.  Here a good match to the data existed  
despite the fact that the theory was fundamentally wrong.

I think TPS is closer to the case of continental drift than to the  
Einstein/Schwinger case.  Given that one can legitimately question  
its assumptions, given that some of them are clearly false (such as  
the assumption that listeners can perceive long-term tonal closure),  
it's going to take a lot of data to convince us that the book is  
fundamentally right.  That doesn't mean it's wrong ... and it's not  
necessarily a criticism of the book, since after all Wegener was  
eventually vindicated with regard to continental drift ... but it  
does mean you've got your work cut out for you.  One paper might not  
have much of an effect.

Let me say that I think all of these questions are very, very deep,  
and very interesting  I've been struggling with them for years -- as  
you know, since I periodically pester you with private emails about  
the subject.  I don't think they can be answered by with general  
claims like "well, science always involves idealizations" or "well,  
only a philosopher would care whether there could be alternate  
explanations" -- we really have to get into the details.  And though  
I have my opinions, I acknowledge that I could well be wrong -- I  
don't by any means think any of these questions are conclusively  
settled.  I'd love to see more thinking and discussion about all of  
this -- in Spectrum, at SMT, on this list, or whatever.  The topic of  
recursive musical perception touches on so many subjects -- not just  
TPS, but Schenkerianism, and the relation between music and language.

DT

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://music.princeton.edu/~dmitri