[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  

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."


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.


Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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