Post-Lewinnian Analysis: from Pitch Perception to Music Analysis

Abstract

Harmony is a fundamental concept in Western music theory, and its number-theoretical structure has been studied since ancient Mesopotamia. The relationship between music and mathematics has become stronger in recent years, leading to two questions: What is the reason for this connection? How can the mathematics of Western music theory be applied to other musical traditions? This article approaches these problems using the recently developed theory based on the group-theoretic description of pitch perception, where the perceptual structure of acoustic signals, represented by tetrahedral homology, is produced under the survival strategy exploiting acoustic signals. Here the constraints of a single source and temporal coincidence in the pitch perception are relaxed, and essential elements of music such as scales, chords, and chord progressions are discussed within a unified framework of Sound Integration. Musical analysis of seven pieces from different genres is used to test the idea. Through these considerations, it is shown that homology in group-theoretic structures helps to understand so-called 'ambiguous tonality'. The theory presented here provides a useful basis for understanding the mathematical structure of harmony in music perception.