Slicing It All Ways: Mathematical Models for Tonal Induction, Approximation,

and Segmentation Using the Spiral Array

(Abstract)

This talk will present the spiral array model and its associated algorithms for tonal induction, approximation, and segmentation.  Tonality is the system of relations among pitches that forms the framework through which we hear tonal music.  The spiral array is a geometric model for tonality that clusters perceptually similar tonal entities.  The model summarizes music information as interior points inside an array of spirals.  Distances in the spiral array space are used to quantify tonal similarity.  I shall trace the evolution of computational algorithms for key finding, pitch spelling, and segmentation, using the spiral array model, giving numerous musical examples.  The talk will include examples of applications of tonal recognition, and a brief introduction to recent developments in the growing field of music, mathematics, and computation.