[Smt-talk] Altered pitch, preserved contour

Dave Headlam dheadlam at esm.rochester.edu
Thu May 28 04:02:22 PDT 2009

Greetings Ian, Thomas, et al:

Of course, in forums for advanced study such as this one, one shouldn't
neglect to mention the contour charts that our quintessential pioneer
Schoenberg uses to illustrate tonal melodic contoural behaviors in
"Fundamentals of Musical Composition" pp. 113-115. The melodies are by Bach,
Mozart, Haydn, Beethoven.  See an online version at:


Then of course the obvious question is where do the earliest examples of
"contour" charts appear?


Dave Headlam

On 5/27/09 12:41 PM, "Ian Quinn" <ian.quinn at yale.edu> wrote:

> 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
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> rg


 Dave Headlam
 Professor of Music Theory
 Joint Professor of Electrical Engineering
 Eastman School of Music
 26 Gibbs St
 Rochester, NY 14604
 (585) 274-1568 office
 dheadlam at esm.rochester.edu

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