Index of /~echew/presentations/AMS2004

 Name                    Last modified      Size  Description
 Parent Directory                             -   
 1001-15-416.pdf         25-Oct-2004 09:03   46K  
 ec-AMS20041024.pdf      25-Oct-2004 09:00   14M  

In this directory is the PDF file for the presentation:

"Measuring Musical Dissimilarity: First and Second Order
Center of Effect (CE) Differences in the Spiral Array"
Elaine Chew (echew@usc.edu)

1001th Meeting of the American Mathematical Society's
Special Sessions on Mathematical Techniques in Musical Analysis
organized by Judith Baxter, Richard Cohn and Robert Peck
Northwestern University, Evanston, Illinois
October 23-24, 2004.

The presentation took place in the Technology Building
of Northwestern University, Lecture Room 2
10:30AM-11:20AM, October 24, 2004.

The conference website is at 
http://www.ams.org/amsmtgs/2113_program.html

The special sessions program site is at
http://www.ams.org/amsmtgs/2113_program_ss23.html

To view the PRESENTATION as a PDF document,
click on ec-AMS20041024.pdf

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"Measuring Musical Dissimilarity: First and Second Order
Center of Effect (CE) Differences in the Spiral Array"
Elaine Chew (echew@usc.edu)

ABSTRACT: The Spiral Array (Chew 2000) is an arrangement of tonal
objects as an array of spirals in three-dimensional space so that
inter-object distances match their perceived closeness. The outermost
helix is the spiral con guration of the "tonnetz" (see Cohn 1998), in
which pitches separated by a perfect fth are neighbors along the
spiral and those separated by a major third are vertical
neighbors. The helical structure allows interior points to be de ned
as convex combinations of pitch classes that summarize and approximate
musical context at various hierarchical levels.

The distance between these interior points, called centers of effect
(CEs), measures the difference between two tonal contexts. This rst
order di erence can be used to assign a value to contextual
dissimilarity between two musical selections.  When the selections are
neighboring segments of music, peaks in the rst order di erence time
series correspond to segmentation boundaries. This talk will present
the idea of the rst order CE di erence and extend it to a second order
di erence inside the Spiral Array space. As the name suggests, the
second order di erence will measure dissimilarity between the
directions of pitch context change within two musical
segments. (Received August 31, 2004)