Abstract
Neural networks are used to study two issues pertaining to atonal music. In the first part of the paper, feed-forward neural networks, using a variant of the backpropagation learning algorithm, try to learn a variety of abstract theoretical constructs from pitch-class set theory. First, learning the properties of individual sets is studied. Then a network's ability to learn various relationships between sets is examined. Based on the behavior of the network during learning, conclusions are drawn with regard to perceptual issues relating to pcset theory. In the second part of the paper, an interactive activation and competition (IAC) network is used to parse a musical passage into analytical objects. The paper concludes with suggestions for further research.
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References
Bruner, C. (1984). The perception of contemporary pitch structures. Music Perception, 2, 25–39.
Castrén, M. (1994). RECREL: A similarity measure for set-classes, Studia Musica No.4. Unpublished doctoral dissertation, Sibelius Academy, Helsinki.
Dibben, N. (1994). The cognitive reality of hierarchical structure in tonal and atonal music. Music Perception, 12, 1–25.
Forte, A. (1964). A theory of set-complexes for music. Journal of Music Theory, 8, 136–83.
Forte, A. (1973). The structure of atonal music. New Haven, CT: Yale University Press.
Forte, A. (1985). Pitch-class set analysis today. Music Analysis, 4, 29–58.
Gibson, D. (1986). The aural perception of non-traditional chords in selected theoretical relationships: A computer generated experiment. Journal of Research in Music Education, 34, 5–23.
Gjerdingen, R. (1991). Using connectionist models to explore complex musical patterns. In P. Todd & D. Loy (Eds.), Music and connectionism. Cambridge, MA: The MIT Press.
Goldstone, R. (1996). Hanging together: A connectionist model of similarity (Vol. 185; Tech. Rep.). Bloomington: Indiana University.
Haimo, E. (1996). Atonality, analysis, and the intentional fallacy. Music Theory Spectrum, 18, 143–166.
Hasty, C. (1981). Segmentation and process in post-tonal music. Music Theory Spectrum, 3, 54–73.
Imberty, M. (1993). How do we perceive atonal music? Suggestions for a theoretical approach. Contemporary Music Review, 9, 325–337.
Isaacson, E. (1990). Similarity of interval-class content between pitch-class sets: The IcVSIM relation. Journal of Music Theory, 34, 1–28.
Isaacson, E. (1996). Issues in the study of similarity in atonal music. Music Theory Online, 2.
Krumhansl, C., Sandell, G., & Sargeant, D. (1987). Tone hierarchies and mirror forms in serial music. Music Perception, 5, 31–78.
Leman, M. (1992). Artificial neural networks in music research. In A. Marsden & A. Pople (Eds.), Computer representations and models in music. London: Academic Press.
Lerdahl, F. (1989). Atonal prolongational structure. Contemporary Music Review, 4, 65–87.
Lewin, D. (1959). Re: Intervallic relations between two collections of notes. Journal of Music Theory, 3, 298–301.
Lewin, D. (1960). Re: The intervallic content of a collection of notes and its complement: An application to Schoenberg's hexachordal pieces. Journal of Music Theory, 4, 98–101.
McClelland, J., & Rumelhart, D. (1988). Explorations in parallel distributed processing: A handbook of models, programs, and exercises. Cambridge, MA: The MIT Press.
Morris, R. (1995). Equivalence and similarity in pitch and their interaction with pcset theory. Journal of Music Theory, 39, 207–243.
Perle, G. (1990). Pitch-class set analysis: An evaluation. Journal of Musicology, 8, 151–72.
Riedmiller, M., & Braun, H. (1993). A direct adaptive method for faster back propagation learning: The RPROP algorithm. In Proceedings of the IEEE International Conference on Neural Networks 1993. San Francisco, CA.
Roeder, J. (1988). A declarative model of atonal analysis. Music Perception, 9, 21–34.
Rumelhart, D., Hinton, G., & Williams, R. (1986). Learning internal representations by error propagation. In D. Rumelhart & J. McClelland (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition (Vol. 1). Cambridge, MA: The MIT Press.
Schafer, S. (1991). Segmentation issues in the analysis of selected non-serial atonal works of Schoenberg, Berg, and Webern, 1908–1923. Unpublished doctoral dissertation, Indiana University.
Stammers, D. (1994). Set theory in the perception of atonal pitch relations. Unpublished doctoral dissertation, Darwin College, Cambridge, UK.
Taruskin, R. (1979). Review of the structure of atonal music. Current Musicology, 28, 114–129.
Todd, P., & Loy, D. (1991). Music and connectionism. Cambridge, MA: The MIT Press.
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Isaacson, E. (1997). Neural network models for the study of post-tonal music. In: Leman, M. (eds) Music, Gestalt, and Computing. JIC 1996. Lecture Notes in Computer Science, vol 1317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034118
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DOI: https://doi.org/10.1007/BFb0034118
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