Simulations of self-organizing neuronlike networks are used to demonstrate how untrained listeners might be able to sort their perceptions of dozens of diverse musical features into stable, meaningful schemata. A presentation is first made of the salient characteristics of such networks, especially the adaptive- resonance-theory (ART) networks proposed by Stephen Grossberg. Then a discussion follows of how a computer simulation of a four-level ART network—a simulation dubbed L'ART pour l'art—independently categorized musical events in Mozart's six earliest compositions. The ability of the network to abstract significant voiceleading combinations from these pieces (and in fact to detect a possible error in the New Mozart Edition) suggests that this approach holds promise for the study of how ordinary listeners process music's multidimensional complexity. In addition, the categorizations produced by the network are suggestive of alternative conceptualizations of music's hierarchical structure.
A great deal of the motion perceived in music is apparent rather than real. On the piano, for example, no continuous movement in frequency occurs between two sequentially sounded tones. Though a listener may perceive a movement from the first tone to the second, each tone merely begins and ends at its stationary position on the frequency continuum. Recent advances in the modeling of apparent- motion effects in vision provide a starting point for the modeling of the strong apparent- motion effects in music. An adaptation of the Grossberg- Rudd model of apparent motion in vision, when given input representing the strengths of pitch sensations positioned along a one- dimensional frequency continuum, can simulate important musical phenomena of auditory stream segregation, van Noorden's melodic- fission/ temporal- coherence boundaries, various Gestalt effects, aspects of dynamic attending, and Narmour's predicted categorical distinction between musical intervals implying a continuation and those implying a reversal of direction.
Jean-Jacques Rousseau, eighteenth-century French author and philosopher, was first a musician. As a youth he had been unable to find a qualified music master and hence lacked the training required to excel in his chosen field. He did read carefully the harmony treatise of Jean-Philippe Rameau, but that study neither advanced his compositional abilities nor later shielded him from the scorn of Rameau himself. Had Rousseau found a master of the then fashionable Italian style of music, he would have studied exercises in partimenti and solfeggi. Solfeggi were studies for voice with bass accompaniment. Partimenti were instructional basses from which an apprentice was expected to recreate complete compositions at the keyboard. The prodigious mental powers developed through the study of partimenti, which greatly facilitated improvisation and composition, gave a competitive advantage to composers so trained. Though an old, nonverbal method of craft instruction, partimenti were nonetheless a cognitively optimal means of developing fluency in a complex, multivoice style of music. In memorizing exemplars of small contrapuntal schemata, fitting them to the matching locations in a partimento, and then realizing them in a current style, the apprentice was training himself to think in "free" counterpoint.
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