[Smt-talk] Altered pitch, preserved contour
Dmitri Tymoczko
dmitri at Princeton.EDU
Wed May 20 06:46:29 PDT 2009
I would probably call this "augmentation in pitch space." Or
"interval stretching in pitch space." Or even "pitch-space
multiplication."
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).
We talk about this a bit in Section 8 of the supplementary material
sections in "Generalized Voice Leading Spaces."
http://music.princeton.edu/~dmitri/sciencearticle.html
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.
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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