A MATHEMATICAL MODEL FOR THE PERCEPTION OF TONES IN CONTEXT.
NEW YORK RESEARCH GROUP INC N Y
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A mathematical model is developed that suggests a method by which differentiation and classification of a large number of different stimuli, such as musical intervals, durations or timbres, can be accomplished with a small number of learned classifiers. The classifiers are orderings of stimuli and are extracted from the contexts in which the stimuli appear. It is postulated that people learn and remember orderings rather than fixed magnitudes. Bounds on the structure of the classifiers and the distortions of perception that characterize the use of each are deduced. A relationship is developed between the structure of each of the classifiers and its potential usefulness in transmitting information. A gestalt description of perception is proposed by which complex and varied phenomena can be perceived without proportionately large memory. Decoding of information carried by stimuli within such gestalt contexts is implicit in the model. Quantitative predictions suitable for experimental verification are given. Results of preliminary computations for Western and non-Western music account for previously unexplained discrepancies between theory and practice. Musical theories for Western music of different periods are shown to be special cases derivable from a proposed general theory. A set-theoretic notation for music a syntax and a semantics in which the symbols are intended to correspond to actual perceived gestalts is suggested for special purposes. Author
- Humanities and History
- Numerical Mathematics