Tonal cognition.
This article presents a self-organizing map (SOM) neural network model of tonality based on experimentally quantified tonal hierarchies. A toroidal representation of key distances is recovered in which keys are located near their neighbors on the circle of fifths, and both parallel and relative major/minor key pairs are proximal. The map is used to represent dynamic changes in the sense of key as cues to key become more or less clear and modulations occur. Two models, one using tone distributions and the other using tone transitions, are proposed for key-finding. The tone transition model takes both pitch and temporal distance between tones into account. Both models produce results highly comparable to those of musically trained listeners, who performed a probe tone task for ten nine-chord sequences. A distributed mapping of tonality is used to visualize activation patterns that change over time. The location and spread of this activation pattern is similar for experimental results and the key-finding model.
Krumhansl
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CL
Department of Psychology, Uris Hall, Cornell University, Ithaca, NY 14853, USA. clk4@cornell.edu
Toiviainen
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P
D003071:Cognition; D006801:Humans; D008962:Models, Theoretical; D009146:Music / Q000523:psychology*; D016571:Neural Networks, Computer; D010898:Pitch Perception; D013998:Time Perception