[Smt-talk] Classical Form and Recursion

[Olli Väisälä]

>
>> Owing to this property, music has, in my view, much stronger  
>> potential for extensive recursive (prolongational) structuring  
>> than has language.
>
> I'll just report that every psychologist, linguist, and  
> evolutionary biologist I've talked to about this issue has told me  
> that they find this suggestion implausible.

OK, Dmitri. If you base your arguments on consulting your linguist  
and biologist acquaintances—rather than on considering what actually  
takes place in music, or considering what might make music different  
from language in this respect—there may indeed not be sufficient  
methodological common ground for fruitful discussion.

(I doubt whether one can reliably derive the limits of human  
invention from evolution biology. Evolution seems to have endowed  
people with faculties that are used much beyond the purposes that  
originally pertained to their evolutional advantage.)

For those willing to consider my points, I outline the following  
three reasons why deeper recursive structures might have emerged in  
music than in language:

1. Perception of musical structure is much more strongly assisted by  
its relationship with factors such as meter, registral connection,  
consonance–dissonance relationship, and Gestalt principles that  
relate more or less directly with our primitive perceptual faculties.  
(I am not saying that functional consonance and dissonance, for  
example, is identical with perceptual consonance and dissonance, but  
a degree of correspondence between the two assists the adoption of  
the functional norm.)

2. The composition of musical structures that show the deepest  
hierarchy of recursion is not everyman's faculty as is language, but  
has emerged in the work of exceptionally gifted individuals who have  
devoted their principal ambitions to the creation of music.

3. In language, there is little motivation—even for the exceptionally  
gifted authors—to generalize syntactic principles to larger spans,  
i.e., to connect sentences through relationships that resemble those  
within the sentence. The larger coherence of linguistic discussion  
relies on other factors such as semantics, for which there is no  
access in music. In musical composition,  one has to resort to other  
kind of resources in order to create larger meaningful entities, and  
my claim is that one of such resources (but by no means the only one)  
is prolongation. If we think of a composer such as Bach, who  
doubtless had internalized principles of harmony and voice-leading to  
the extent that he applied them without conscious effort to surface  
progressions, it is, in my view, not at all implausible to think that  
similar principles also found their way to his creation of large- 
scale patterns (especially given point 1 above).

>
> My question was: what justifies the "reduction" of ABA to A.  Your  
> answer seems to be "there is a norm that harmonic progressions  
> begin and end with I."

No, that does not amount to my answer. "Reducing" ABA to A is a tool  
for indicating (1) that there is a well-defined sense in which we may  
perceive A as the governing element in this progression and (2) that  
A is the element that enters larger relationships of harmony and  
voice leading.

By referring to tonal closure, I identified one aspect of (1). Other  
aspects were illustrated by my reduction of the V–I–V to V in bar 2  
of my example progression. More generally, governing status in the  
sense relevant for present purposes depends on, first, archetypal  
patterns such as I–V–I harmonic motion and passing and neighboring  
voice-leading motions between the prolonged and prolonging elements,  
and, second, independent factors such as design, meter, and register.  
On these lines we may approach a stipulative definition of "governing  
status." Of course, modeling such status through the reduction tool  
would not be motivated if the elements enjoying such status did not  
enter larger connections (2), a hypothesis to which I have tried to  
present empirical evidence.

Olli Väisälä
ovaisala at siba.fi
Sibelius Academy