[Smt-talk] Altered pitch, preserved contour

Richard Hermann harhar at unm.edu
Thu May 21 06:18:00 PDT 2009

Dear SMT-Listers,

	Steve's point citing Weyl is well taken, and thanks for reminding us.  
I would like to point out that not all of mathematics is concerned  
with symmetry. Inequalities, topology, statistics, probability, etc.  
can all give us useful results for our interpretative acts. Of course,  
other metaphors from other disciplines remain enticing and are  
potentially as beneficial. I also find Dmitir's point of interest.



Richard Hermann, Prof. of Music
University of New Mexico

On May 20, 2009, at 12:02 PM, Stephen Guy Soderberg wrote:

> Over-mathematizing can be a fatal error, Dmitri (or at least  
> unnecessarily limiting).  In my opinion, multiplication is simply a  
> subset of the (compositionally) much more interesting general idea  
> being discussed.  But since you bring up the math, I'm reminded of  
> some wise words from Hermann Weyl in his little book, Symmetry:
> "If nature were all lawfulness then every phenomenon would share the  
> full symmetry of the universal laws of nature....  The mere fact  
> that this is not so proves that _contingency_ is an essential  
> feature of the world."
> I would only add:  ... and what makes it at all worthwhile to be  
> alive.
> Cheers,
> Steve
> Stephen Soderberg
> Music Division
> Library of Congress
>>>> Dmitri Tymoczko <dmitri at Princeton.EDU> 5/20/2009 9:46 AM >>>
> You're actually talking about something a bit more specific than just
> "preserving contour" -- as music theorists use the term "contour,"
> this usually refers to just the ordinal ranking of notes in pitch
> space.  So (C4, C#4, B3) and (C4, B6, Db3) have the same contour,
> even though the ratio of their intervals is different.  This is
> because they both exhibit the sequence (middle, high, low).
> Interestingly, the relevant geometrical space is the (n-1)-
> dimensional sphere, which represents equivalence classes of n-note
> pitch sequences under positive pitch-space multiplication.
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