A model for pattern perception with musical applications part II: The information content of pitch structures

Abstract

This is the second paper of a series which begins by treating the perception of pitch relations in musical contexts and the perception of timbre and speech. The first paper discusses in some detail those properties of musical scales required in order for them to function as “reference frames” which provide for the “measurement” of intervals such that ([1], p. 270),Every melodic phrase, every chord, which can be executed at any pitch, can be also executed at any other pitch in such a way that we immediately perceive the characteristic marks of their similarity. Here we continue this discussion by developing quantitative measures of the degree to which different scales possess the above properties. Then that property of musical scales which permits a listener to code the pitches of which it is constituted into “degrees” is examined and a corresponding quantitative measure developed. Musical scales are shown to be optimal choices with respect to both the former and latter measures, and a theory limiting those scales which are musically useful to a small fraction of possible sets of pitches is proposed. Existing scales which have been examined fall within the theory, which links the techniques of composition which may be used (i.e., those which produce perceptible relations between musical segments) to the above properties of the scale structures. This paper is not self-contained—reading of the previous paper in this series is required.