[Smt-talk] Altered pitch, preserved contour
Stephen Guy Soderberg
ssod at loc.gov
Wed May 20 11:02:05 PDT 2009
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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