[Smt-talk] Altered pitch, preserved contour

[Ian Quinn]

Thomas and all,

What you refer to as a "diastematic matrix" has been exhaustively  
described in theoretical articles on contour by Robert Morris,  
Elizabeth West Marvin, Michael Friedmann, Larry Polansky, and myself  
in the late 80s and 90s, in addition to the work by Buteau that you  
mention.  I have also reported an experimental study ("The  
Combinatorial Model of Pitch Contour," Music Perception 16 [1999])  
that sheds some light on the perceptual significance of contour  
relations among nonsuccessive intervals as modeled by such a matrix.

cheers-

iq.


Thomas Noll wrote:

> A useful mathematical means to study contour might be diastematic  
> matrices or sub-structures thereof.
> A diastematic matrix of a melody with n tones is an nxn-matrix whose  
> entries at index (i,k) are +1, 0, -1 depending on the direction of  
> the interval between the ith and kth note of the melody.


-------------
Ian Quinn
-------------
Associate Professor (on leave, 2008-09)
Department of Music and Program in Cognitive Science
Editor, Journal of Music Theory
Yale University
-------------
2008-09 Residential Fellow
Center for Advanced Study in the Behavioral Sciences
Stanford University