Dissertation Index

Author: Bor, Mustafa

Title: Contour Reduction Algorithms: A Theory of Pitch and Duration Hierarchies for Post-Tonal Music

Institution: University of British Columbia

Begun: October 2006

Completed: April 2009


This dissertation takes work on contour by Robert Morris as a point of departure and develops a set of contour reduction algorithms, called window algorithms. These involve the notion of a hypothetical window or frame of a specific width (i.e. number of events) through which the contour succession in a given melody is experienced temporally (much like the way a landscape is experienced visually through the side window of a moving automobile or train). Certain normative principles relevant to windows of various widths are devised and represented with the help of symbolic logic and flowcharts. Reiterative application of the window algorithms on a melody to prune pitches at a series of successive levels introduces notions of melodic contour hierarchy that are explored in various ways throughout the dissertation. The application of the algorithms is demonstrated on a variety of 20th century musical excerpts reflecting a wide range of melodic archetypes, thereby enabling observation of the behavior of the algorithms in different musical contexts. Phenomenological and cognitive implications of the algorithms are discussed from the perspective of a listener implementing the algorithm on the fly. An analysis focusing on the Hauptstimmen in the first movement of Schoenberg’s Third String Quartet explores how intervallic features of the reduced contours can form the basis for a tonal-formal reading of the movement. The possibility of extending the theory to the duration domain is also introduced; following a preliminary analysis involving instrumental gestures from the opening of Webern’s Variations for Orchestra, and a discussion of analytical, conceptual, and methodological inconsistencies arising from the application of the algorithms on duration contours, an alternative approach that attaches appropriate durations to (reduced) pitch contours is developed, examined, and advocated. The relationships and interactions between the pitch and duration contours in Berio’s Sequenza I are examined in the light of the proposed theory.

Keywords: pitch contour, melody, duration contour, hierarchy, reduction, algorithm, analysis, Schoenberg, Webern, Berio


Chapter 1. Introduction
Chapter 2. Theoretical Context: Selected Recent Theories of Contour in Music
Chapter 3. Window Algorithms and Contour Reduction Functions
Chapter 4. Applying the Algorithms: A Gallery of Examples
Chapter 5. The Listener’s Window: Reduction Algorithms, Memory, and the Listening Experience
Chapter 6. An Analytical Application: The Hauptstimmen in Schoenberg’s String Quartet No.3, Op. 30, I
Chapter 7. Duration Contours: A Cumulative Approach
Chapter 8. Analysis: Interacting Pitch and Duration Contours in Berio’s Sequenza I
Chapter 9. Conclusions and Future Directions


Mustafa Bor
Department of Music
University of Alberta
Edmonton, AB
Canada T6G 2C9
(780) 492-4286

Date Listed: 04/10/2009

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