Edward Large - Academia.edu (original) (raw)

Papers by Edward Large

Proceedings of the Annual Conference of the Cognitive Science Society, 2006

SCIENCE SINCE ANTIQUITY HAS ASKED WHETHER mathematical relationships among acoustic frequencies g... more 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 r¯ agas, 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. I S MUSICAL KNOWLEDGE MAINLY ACQUIRED through long-term exposure to the music of one's culture? Or do intrinsic properties of neural processing constrain music perception and cognition? What is the role of short-term exposure and rapid statistical learning? While all these likely play a role, it is unknown how these fundamental mechanisms combine to enable the rich cognitive and emotional experience of music. Here we use dynamical systems theory to transform recent findings about nonlinear auditory neural processing into predictions about the perception of musical relationships. We ask whether this theory can explain cross-cultural invariances in the perception of Hindu-stani classical music, a highly developed style different from the more well-studied Western tonal-harmonic music. The dynamical principles explain fundamental similarities between unfamiliar Western listeners and encultured Indian listeners. These combine with statistical learning and culture-specific knowledge to provide a new model of tonal organization. Consonance and dissonance are fundamental concepts in the science of music, with a long history of theory and experiment. The earliest observation, dating back at least to Pythagoras, is that small integer ratios, such as 2:1, 3:2, and 4:3, produce more pleasing or consonant musical intervals of the octave, fifth, and fourth—the ''perfect consonances''—because they are mathematically pure (Burns, 1999). Pythagoras designed a system for tuning musical instruments based on the perfect consonances (Table 1), and 500 years later Ptolemy proposed several small-integer-ratio tuning systems, known as just intonation (JI; Table 1), still current in musical practice. Three significant non-Western musical traditions—Indian, Chinese, and Arab-Persian—also use intervals that approximate small integer ratios (Burns, 1999). In the eighteenth century, Euler (1739) hypothesized that the mind directly perceives and aesthetically appreciates simple integer frequency ratios. Helmholtz (1885/1954) observed that purity of mathematical ratios could not explain perceived consonance in equal tempered tuning systems (ET; Table 1), in which small integer ratios are approximated by irrational numbers. Instead, he proposed that as the auditory system performs a linear analysis of complex sounds, proximal harmonics interfere with one another and produce a sensation of roughness, which he equated with dissonance. Small integer ratios yield more consonant musical intervals, he surmised, because they have more harmonics in common and thus fewer harmonics that interfere. When extrapolated to complex tones, the interaction of pure tone components predicts the perception of consonance well (Kameoka & Kuriyagawa, 1969).

Proceedings of the Annual Conference of the Cognitive Science Society, 2006

SCIENCE SINCE ANTIQUITY HAS ASKED WHETHER mathematical relationships among acoustic frequencies g... more 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 r¯ agas, 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. I S MUSICAL KNOWLEDGE MAINLY ACQUIRED through long-term exposure to the music of one's culture? Or do intrinsic properties of neural processing constrain music perception and cognition? What is the role of short-term exposure and rapid statistical learning? While all these likely play a role, it is unknown how these fundamental mechanisms combine to enable the rich cognitive and emotional experience of music. Here we use dynamical systems theory to transform recent findings about nonlinear auditory neural processing into predictions about the perception of musical relationships. We ask whether this theory can explain cross-cultural invariances in the perception of Hindu-stani classical music, a highly developed style different from the more well-studied Western tonal-harmonic music. The dynamical principles explain fundamental similarities between unfamiliar Western listeners and encultured Indian listeners. These combine with statistical learning and culture-specific knowledge to provide a new model of tonal organization. Consonance and dissonance are fundamental concepts in the science of music, with a long history of theory and experiment. The earliest observation, dating back at least to Pythagoras, is that small integer ratios, such as 2:1, 3:2, and 4:3, produce more pleasing or consonant musical intervals of the octave, fifth, and fourth—the ''perfect consonances''—because they are mathematically pure (Burns, 1999). Pythagoras designed a system for tuning musical instruments based on the perfect consonances (Table 1), and 500 years later Ptolemy proposed several small-integer-ratio tuning systems, known as just intonation (JI; Table 1), still current in musical practice. Three significant non-Western musical traditions—Indian, Chinese, and Arab-Persian—also use intervals that approximate small integer ratios (Burns, 1999). In the eighteenth century, Euler (1739) hypothesized that the mind directly perceives and aesthetically appreciates simple integer frequency ratios. Helmholtz (1885/1954) observed that purity of mathematical ratios could not explain perceived consonance in equal tempered tuning systems (ET; Table 1), in which small integer ratios are approximated by irrational numbers. Instead, he proposed that as the auditory system performs a linear analysis of complex sounds, proximal harmonics interfere with one another and produce a sensation of roughness, which he equated with dissonance. Small integer ratios yield more consonant musical intervals, he surmised, because they have more harmonics in common and thus fewer harmonics that interfere. When extrapolated to complex tones, the interaction of pure tone components predicts the perception of consonance well (Kameoka & Kuriyagawa, 1969).