[Smt-talk] Classical Form and Recursion

[Dmitri Tymoczko]

Hi Panos,

> One important distinction must be made: recursive vs non- recursive  
> is a property of the grammar (i.e. the model), not of the corpus.   
> Any finite corpus can be modeled with a non-recursive grammar, even  
> if it contains strings like
>
> ABCDCBA
>
> This is because, if the corpus is finite, you'll never have to deal  
> with infinite depth of recursion.  Of course, if recursive  
> structures keep occurring with high frequency and at deep levels of  
> embedding, it will be rather forced and unnatural to insist on a  
> non-recursive model.  The real question therefore becomes one of  
> the model's economy, explanatory power, ability to relate to other  
> disciplines (e.g. cognition) etc.
>
> To summarize, in my mind recursive vs non-recursive is a question  
> of model selection, not a question of what the music is intrinsically.

You're right, I was speaking too loosely.  Typically, in both music  
and linguistics, we have an open-ended corpus in mind.  We might be  
interested in sequences such as:

{ABA, ABCBA, ABCDCBA, "and so on"}
{I-V-I, I-ii-V-I, I-vi-IV-ii-V-vi-IV-I, "and so on"}

It's the "and so on" that causes problems.

Furthermore, since we believe these sequences to be caused by human  
beings following some sort of rules, we're really asking questions  
about the causal structure of the universe, rather than about  
sequences themselves.

That said, the points I was making can be translated into this more  
precise language.  We may have sequences that can be modeled very  
nicely with a nonrecursive grammar, such as

AB, ABAB, ABABAB, "and so on"

Which we still perceive and organize recursively.

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





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