Determining Key Boundaries

  • Elaine ChewEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 204)


Computer models for determining key boundaries are important tools for computer analysis of music, computational modeling of music cognition, content-based categorization and retrieval of music information and automatic generating of expressive performance. This chapter describes a Boundary Search Algorithm (BSA) for determining points of modulation in a piece of music using a geometric model for tonality called the Spiral Array. For a given number of key changes, the computational complexity of the algorithm is polynomial in the number of pitch events. We present and discuss computational results for two selections from J.S. Bach’s A Little Notebook for Anna Magdalena. Comparisons between the choices of an expert listener and the algorithm indicates that in human cognition, a dynamic interplay exists between memory and present knowledge, thus maximizing the opportunity for the information to coalesce into meaningful patterns.


Phrase Structure Major Section Event Onset Pitch Class Pitch Collection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I thank Jeanne Bamberger for her guidance and cogent advice that made this research possible; and Martin Brody for his insightful comments on interpreting the results in an early version of this document.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Centre for Digital MusicQueen Mary University of LondonLondonUK

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