Formal Aspects of Cognitive Processes pp 126-141 | Cite as

# A mathematical model for perception applied to the perception of pitch

## Abstract

A mathematical model for perception which derives from a theory of efficient data representation in the central nervous system is described. A possibly infinite and continuous space, S (over which sensory stimuli range), is mapped into a finite space of discrete points, C (the indices on the classification of such stimuli). An ordering of pairs of points in S × S together with either the number of classifications required or a maximum tolerable error is given and assumed to derive from feedback (experience). The model chooses a "characteristic" finite subset, P, of the stimulus space, which defines a function and a range about each element of the subset such that the union of all such ranges is maximal and that the function provides a metric (on C) which preserves the given ordering. Restrictions on the choice of P derive from limitations in the information carrying capacity of the resulting classification system. A context-dependent "Gestalt" description of perception results in which extremely complex and varied phenomena can be perceived without proportionately large human memory. For each application specific distortions of perception in specified contexts are predicted. The system, in some aspects, resembles an hierarchical clustering scheme. It is hence use-ful for representing different patterns of satisfaction of several "features" in a pattern recognition scheme by a single set of integers with metric properties which reflect relevance to the task (i.e., an n-valued logic replace a two-valued logic).

## Keywords

Proper Scale Proper Modification Major Scale Tone Scale Musical Material## References

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