The Spiral Array and Computational Models for Tonal Induction and Segmentation (25/05/04)
This talk centers around a geometric representation for tonality called the Spiral Array (Chew, 2000). The model starts from a spiral configuration of the Harmonic Network (the Harmonic Network, also known to transformational music theorists as the tonnetz, has been described by Longuet-Higgins), and successively generates higher level tonal entities as convex combinations of their lower level components. Using the model, any segment of music can be mapped to its outermost pitch spiral and summarized as a spatial point, called the center of effect (c.e.), in the interior of the structire. This c.e. acts as a proxy for the tonal context, and problems of tonal induction and pitch spelling are transformed to computationally efficient nearest neighbour searches. The presentation will cover applications of the Spiral Array to problems of tonal induction, pitch spelling and tonal segmentation.