New Directions in the Theory and Analysis of Musical Contour

The paper begins with a brief review of previous work on musical contour by Richard Bassein, Robert Cogan, Pozzi Escot, Michael Friedmann, Paul Laprade, Elizabeth Marvin, Robert Morris, Larry Polansky, and James Tenney. To this end, Schoenbergs' Piano Piece, Op. 19 No. 4 is analyzed. Its pc-set segmentations are associated with relations among sets of equivalent contours. The main part of the paper introduces the contour reduction algorithm, based on principles of perceptual organization from gestalt psychology. The algorithm allows one to associate nonadjacent contour pitches according to their degree of salience. Any contour can be reduced to one of a set of irreducible prime contours that defines its characteristic depth. The algorithm is applied to the six phrases of the Schoenberg piece and the result resonates well with the previous contour/pc-set analysis. The hierarchic nature of the algorithm also helps organize the many classes of equivalent contours. Morriss' definition of a contour as the association of any two sets leads to the construction of a taxonomy including all possible contours. Contours that include replication and simultaneities are defined by various categories in mathematical relation theory. The paper includes a discussion of the role of salience in musical structure. The contour reduction algorithm is compared to familiar reductive methodologies of tonal music and the perceptual gestalt theories of Tenney and Polansky.