Mathematical systems theory

, Volume 11, Issue 1, pp 199–234 | Cite as

A model for pattern perception with musical applications part I: Pitch structures as order-preserving maps

  • David Rothenberg


The initial five papers of this series on pattern perception treat first, the perception of pitch in musical contexts and then, the perception of timbre and speech. Each sound is considered to be embedded in a “context” consisting of those sounds which surround it or coincide with it. The apprehension of a musical pattern depends upon the perceptibility of certain relations between, and properties of, its parts (e.g. “motifA is similar to motifB“ or “G is the tonic”). It is hypothesized that, because of the limitations of short term memory, the perception of specific relations and properties requires that certain “mental reference frames” be extracted from the various contexts. However, a reference frame which supports the perception of any specified relation may be extracted from only very few of all possible contexts. The choices of musical materials in both Western and non-Western music are shown to avoid precisely such difficulties. When they are not avoided, distortions of perception are predicted and methods for experimental verification are suggested. This theory is then applied to suggest new materials for the composition of both “microtonal” and “tonecolor” music. This is done in a manner which exposes the correspondence between each choice of musical materials and those musical properties and relations whose perception is (or is not) thereby supported.

This first paper discusses the relation between the ability to perceive relative sizes of musical intervals and the choice of reference frame from a given musical context.


Reference Frame Computational Mathematic Short Term Memory Relative Size Specific Relation 
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Copyright information

© Springer-Verlag New York Inc 1978

Authors and Affiliations

  • David Rothenberg
    • 1
  1. 1.Department of Computer and Information SciencesTemple UniversityPhiladelphiaUSA

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