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Determining Key Boundaries

In: Mathematical and Computational Modeling of Tonality

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  • Elaine Chew

    (Queen Mary University of London)

Abstract

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.

Suggested Citation

  • Elaine Chew, 2014. "Determining Key Boundaries," International Series in Operations Research & Management Science, in: Mathematical and Computational Modeling of Tonality, edition 127, chapter 0, pages 95-107, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-9475-1_6
    DOI: 10.1007/978-1-4614-9475-1_6
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