[Smt-talk] Classical Form and Recursion

Olli Väisälä ovaisala at siba.fi
Fri Apr 3 00:37:22 PDT 2009

Dear Ildar,

By all means interfere. Unfortunately, it seems that you have  
completely misunderstood my position in several issues.

> What makes you think that "closure" and its synonim "prolongation"  
> are the norms of music, and that they come directly out of musical  
> intuition?

I only meant that harmonic closure—starting from I and coming through  
V back to I—is an important phenomenon in classical tonal music. Do  
we disagree in this?

Closure is not synonymous with prolongation, but what I said is that  
closed tonic-to-tonic progressions may be treated prolongationally by  
assigning them the role of tonic in larger progressions.

> Cadence is an important device, but is it the goal and essence of  
> music?

Here, at least, we seem to agree.

> A product of real musical intuition is the sense of tension and  
> resolution. [...]. However, in your "prolongation" the role of the  
> chord which creates tension and requires resolution is reduced to  
> almost nothing. It looses its harmonic function, becomes a  
> "contrapuntal chord" or Nebenakkord.  The most important agency is  
> being reduced, the most important event--overlooked. By the way,  
> you cannot not notice it while listening to it, but it is possible  
> to "reduce" it in visual analysis.

I am afraid you have misunderstood what "reduction" means in  
prolongational analysis. If we say that a I–V4/3–I6 progression  
prolongs the tonic, it tells that the progression as a whole may  
represent the tonic in larger contexts but this  in no sense cancels  
or diminishes or overlooks the significance of V4/3 as an element of  
tension within this progression. Rather, prolongational analysis  
models one aspect of this tension, since prolongational weight tends  
to correlate with stability (= lack of tension).

(Lerdahl and Jackendoff expressly identify there concept of  
prolongation as a model of tension and release, but I think the issue  
is actually somewhat more complex and nuanced than what their  
treatises indicate.)

> A very common example, which is used to demonstrate the validty of  
> "prolongation," is the voice exchange progression. And you would  
> say that it has a "passing 6/4 chord in the middle." What is the  
> function of this middle chord:  "Passing."  How about passing  
> Dominant 6/4? Or the fact that it is the Dominant is unimportant?

Why would the dominant be unimportant? I certainly have not written  
anything to imply such a view.

Best wishes,
Olli Väisälä
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