Tonal Cognition
Carol Lynne Krumhansl, Petri Toiviainen · Oxford University Press eBooks · 2003
This chapter 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 neighbours 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 keys as cues to keys becoming more or less clear and modulations occurring. 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. In general, experimental studies suggest that the sense of tonality undergoes dynamic and subtle changes when a listener hears music.