This experiment was designed to address factors that make repetition of musical themes within a piece recognizable, and to explore the relationship between internal repetition and musical interest. Thirty-seven participants of varied levels of music training listened to Stravinsky’s Symphonies of Wind Instruments twice and responded to the music in real time. During the first listening, they continuously rated their level of interest and at the same time mentally identified the major themes. During the second listening, they indicated when they heard the major themes repeating. One theme was especially well recognized when repeated. It was relatively short, slow, began and ended with a predictable pattern, occurred relatively early in the piece, and was interspersed with other themes. Another theme stood out in the interest ratings, which was relatively long, fast, sometimes repeated immediately with a build-up of instrumentation and dynamics, and occurred later in the piece. In general, themes judged interesting were not those that were easily identified when repeated, suggesting these are independent aspects of this composition. No effect of music training was found. Extensive analyses of Stravinsky’s Symphonies consider how the themes are repeated and interwoven. The experimental results confirmed the musical attributes considered in these analyses.
Science since antiquity has asked whether mathematical relationships among acoustic frequencies govern musical relationships. Psychophysics rejected frequency ratio theories, focusing on sensory phenomena predicted by linear analysis of sound. Cognitive psychologists have since focused on long-term exposure to the music of one’s culture and short-term sensitivity to statistical regularities. Today evidence is rapidly mounting that oscillatory neurodynamics is an important source of nonlinear auditory responses. This leads us to reevaluate the significance of frequency relationships in the perception of music. Here, we present a dynamical systems analysis of mode-locked neural oscillation that predicts cross-cultural invariances in music perception and cognition. We show that this theoretical framework combines with short- and long-term learning to explain the perception of Hindustani rāgas, not only by encultured Indian listeners but also by Western listeners unfamiliar with the style. These findings demonstrate that intrinsic neurodynamics contribute significantly to the perception of musical structure.
This essay begins by reviewing issues in psychological measurement that motivated some of the research summarized in Cognitive Foundations of Musical Pitch (Krumhansl, 1990). These were challenges to geometrical models of similarity, asymmetrical measures of similarity, and contextual effects. It then considers the impact that statistical learning has had on research and theory about music cognition, suggesting this emphasis may have underestimated the importance of other psychological processes contributing to the experience of music. Finally, it discusses three problems with traditional analyses using unidimensional, sequential statistics. The first is that music is hierarchical, with important relationships between non-adjacent events. The second is that the dimensions of music, specifically, pitch and time, interact. The third is the assumption that probabilities remain constant throughout a composition. Rather, music contains artful deviations from normative probabilities contributing to the experience of tension and release.