Slicing it all ways: Mathematical models for tonal induction, approximation, and segmentation using the spiral array

INFORMS Journal on Computing

Volumn 18, Issue 3, 2006, Pages 305-320

  Chew, Elaine ^a  

^a Viterbi School of Engineering ^*  (United States)

Author keywords

Automated tonal analysis; Computational music cognition; Real time algorithms

Indexed keywords

EID: 33748557746     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1050.0134     Document Type: Article

References (22)

1. Cambouropoulos, E. 2003. Pitch spelling: A computational model. Music Perception 20 411-430.
2. Chew, E. 2000. Towards a mathematical model of tonality. Ph.D. thesis, Operations Research Center, Massachussetts Institute of Technology, Cambridge, MA.
3. Chew, E. 2001. Modeling tonality: Applications to music cognition. J. D. Moore, K. Stenning, eds. 23rd Annual Meeting of the Cognitive Science Society, Edinburgh, Scotland, UK. Lawrence Erlbaum Associate Publishers, Mahwah, NJ/London, UK, 206-211.
4. Chew, E. 2002. The spiral array: An algorithm for determining key boundaries. C. Anagnostopoulou, M. Ferrand, A. Smail, eds. Music and Artificial Intelligence. Proc. 2nd Internat. Conf. LNCS/LNAI 2445. Springer, Berlin, Germany, 18-31.
5. Chew, E., Y.-C. Chen. 2003a. Mapping MIDI to the spiral array: Disambiguating pitch spellings. H. K. Bhargava, N. Ye, eds. Computational Modeling and Problem Solving in the Networked World. Proc. 8th INFORMS Comput. Soc. Conf. Kluwer, Dordrecht, The Netherlands, 259-275.
6. Chew, E., Y.-C. Chen. 2003b. Determining context-defining windows: Pitch spelling using the spiral array. Proc. 4th Internat. Conf. Music Inform. Retrieval, Baltimore, MD.
7. Chew, E., Y.-C. Chen. 2005. Real-time pitch spelling using the spiral array. Comput. Music J. 29(2) 61-76.
8. Chew, E., A. R. J. François. 2003. MuSA.RT-Music on the spiral array real-time. ACM Multimedia Conf. 2003, Berkeley, CA. ACM Press, New York, 448-449.
9. Gomez, E. 2006. Tonal description of polyphonic audio for music content processing. INFORMS J. Comput. 18(2) 294-304.
10. Krumhansl, C. L. 1990. Cognitive Foundations of Musical Pitch. Oxford University Press, Oxford, UK.
11. Longuet-Higgins, H. C. 1962. Two letters To a musical friend. The Music Rev. 23 244-228, 271-280.
12. Longuet-Higgins, H. C. 1976. Perception of melodies. Nature 263 646-653.
13. Longuet-Higgins, H. C., M. J. Steedman. 1971. On interpreting Bach. Machine Intelligence 6 221-241.
14. MacDowell, E. 1896. To a wild rose. Woodland Sketches Op.51 No.1. EPS file typeset in SCORE by Craig Sapp. http://ccrmawww.stanford.edu/~craig/score.
15. Meredith, D. 2003. Pitch spelling algorithms. R. Kopiez, A. C. Lehmann, I. Wolther, C. Wolf, eds. Proc. 5th Triennial ESCOM Conf. Hanover University of Music and Drama, Hanover, Germany, 204-207.
16. Meredith, D. 2004. Comparing pitch spelling algorithms on a large corpus of tonal music. Proc. Comput. Music Modeling and Retrieval 2004, LNCS 3310. Verlag, Berlin, Germany, 173-192.
17. Pickens, J., J. P. Bello, G. Monti, M. Sandier, T. Crawford, M. Dovey, D. Byrd. 2003. Polyphonic score retrieval using polyphonic audio queries: A harmonic modeling approach. J. New Music Res. 32 223-236.
18. Schubert, F. 1828. Impromptus and Moments Musicaux. G. Henle Verlag, Munich, Germany.
19. Shmulevich, I., O. Yli-Harja. 2000. Localized key-finding: Algorithms and applications. Music Perception 17 531-544.
20. Temperley, D. 1999. What's key for key? The Krumhansl-Schmuckler key-finding algorithm reconsidered. Music Perception 17 65-100.
21. Temperley, D. 2001. The Cognition of Basic Musical Structures. MIT Press, Cambridge, MA.
22. Toiviainen, P., C. L. Krumhansl. 2003. Measuring and modeling real-time responses to music: The dynamics of tonality induction. Perception 32 741-766.