Measuring and Modeling Real-Time Responses to Music: The Dynamics of Tonality Induction

Abstract

We examined a variety of real-time responses evoked by a single piece of music, the organ Duetto BWV 805 by J S Bach. The primary data came from a concurrent probe-tone method in which the probe-tone is sounded continuously with the music. Listeners judged how well the probe tone fit with the music at each point in time. The process was repeated for all probe tones of the chromatic scale. A self-organizing map (SOM) [Kohonen 1997 Self-organizing Maps (Berlin: Springer)] was used to represent the developing and changing sense of key reflected in these judgments. The SOM was trained on the probe-tone profiles for 24 major and minor keys (Krumhansl and Kessler 1982 Psychological Review89 334–368). Projecting the concurrent probe-tone data onto the map showed changes both in the perceived keys and in their strengths. Two dynamic models of tonality induction were tested. Model 1 is based on pitch class distributions. Model 2 is based on the tone-transition distributions; it tested the idea that the order of tones might provide additional information about tonality. Both models contained dynamic components for characterizing pitch strength and creating pitch memory representations. Both models produced results closely matching those of the concurrent probe-tone data. Finally realtime judgments of tension were measured. Tension correlated with distance away from the predominant key in the direction of keys built on the dominant and supertonic tones, and also correlated with dissonance.