Mapping Midi to the Spiral Array: Disambiguating Pitch Spellings (original) (raw)

Abstract

The problem of assigning appropriate pitch spellings is one of the most fundamental problems in the analysis of digital music information. We present an algorithm for finding the optimal spelling based on the Spiral Array model, a geometric model embodying the relations in tonality. The algorithm does not require the key context to be determined. Instead, it uses a center of effect (c.e.), an interior point in the Spiral Array model, as a proxy for the key context. Plausible pitch spellings are measured against this c.e., and the optimal pitch is selected using the nearest neighbor criteria. Two examples are given from Beethoven’s Sonata Op. 109 to illustrate the algorithm. The algorithm is implemented and the results used in MuSA — a music visualization software using the Spiral Array. We present and analyze computational results from test runs on MIDI files of two movements from Beethoven’s Piano Sonatas Op.79 and Op. 109.

Partial funding provided by a Women In Science and Engineering grant and by the Integrated Media Systems Center, a National Science Foundation Engineering Research Center Cooperative Agreement No. EEC-9529152.

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References

• Cambouropoulos, E. (2001). “Automatic Pitch Spelling: From Numbers to Sharps and Flats,” in Proceedings of the VIII Brazilian Symposium on Computer Music. Fortaleza, Brazil.
  Google Scholar
• Chew, E. (2002). “The Spiral Array: An Algorithm for Determining Key Boundaries,” Special issue of the LNCS /LNAI on Music and Artifical Intelligence. Heidelberg, Germany: Springer.
  Google Scholar
• Chew, E. (2001). “Modeling Tonality: Applications to Music Cognition,” in Proceedings of the 23rd Annual Meeting of the Cognitive Science Society. Edinburgh, Scotland.
  Google Scholar
• Chew, E. (2000). “Towards a Mathematical Model of Tonality,” MIT PhD Dissertation. Cambridge, MA.
  Google Scholar
• Rowe, R. (2001). “Machine Musicianship,” Cambridge, MA: MIT Press.
  Google Scholar
• Steedman, M. (1994). “The Well-Tempered Computer,” Philosophical Transactions of the Royal Society. A:349. 115–131.
  Article Google Scholar
• Temperley, D. (2002). “The Cognition of Basic Musical Structures,” Cambridge, MA: MIT Press.
  Google Scholar

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Authors and Affiliations

1. Integrated Media Systems Center Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, 3715 McClintock Avenue, GER240 MC:0193, 90089-0193, Los Angeles, CA, USA
   E. Chew
2. Integrated Media Systems Center Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, USA
   Y.-C. Chen

Authors

1. E. Chew
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2. Y.-C. Chen
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Editors and Affiliations

1. The Pennsylvania State University, USA
   Hemant K. Bhargava
2. Arizona State University, USA
   Nong Ye

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© 2003 Springer Science+Business Media New York

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Chew, E., Chen, YC. (2003). Mapping Midi to the Spiral Array: Disambiguating Pitch Spellings. In: Bhargava, H.K., Ye, N. (eds) Computational Modeling and Problem Solving in the Networked World. Operations Research/Computer Science Interfaces Series, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1043-7\_13

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• DOI: https://doi.org/10.1007/978-1-4615-1043-7\_13
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• Print ISBN: 978-1-4613-5366-9
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