[Smt-talk] Classical Form and Recursion

[Fred Lerdahl]

Ildar Khannanov writes:

> You have mentioned that the studies oftonal  tension cover music from 
> Bach to Messiaen. I can argue that tension/relaxation can be applied 
> also to earlier and later periods. I have heard many times from my 
> colleauges that tension/relaxation model applies mostly to 19th 
> century music and it does not rise up to the level of Schenkerian 
> abstraction. Or, some say that there was no harmony in the 
> 18th-century music, let alone in the 17th and earlier centuries. What 
> do you think about my idea that tension/relaxation as a category 
> directly relates to harmony in a wider sense and as such it is 
> universal  and can be attributed to Greek music as well as Bach and 
> Messiaen?

Intuitions of tension and relaxation seem to be widespread if not 
universal, and they are by no means confined to music. In our tonal 
tension project, Krumhansl found mutually consistent responses using 
two contrasting experimental methods, indicating that these intuitions 
are robust.

So I agree that tension applies to all kinds of music. It would be 
valuable (if daunting) to investigate empirically how indigenous 
listeners in different musical idioms register intuitions of tension. 
Assuming consistent and robust responses, the modeling of tension 
across idioms would require theoretical modifications according to 
features of the idioms. For Machaut, for example, one would alter 
somewhat both the pitch space and the measures of surface dissonance. 
For Balinese gamelan, one would incorporate timbral features; these 
might outweigh the role of a comparatively simple Balinese pitch space. 
For West African drumming, a theory of rhythmic tension would have to 
be developed (such a theory is needed for standard tonal music, too).

I don't know much about ancient Greek music, but Costas Tsougras has 
developed an elegant model applicable to 20th-century popular Greek 
music in his "Modal Pitch Space" (Musicae Scientiae, 7.1, 57-86 
[2003]).

Fred Lerdahl
Columbia University
awl1 at columbia.edu