Formalized Harmony

Abstract

Different theories have been proposed to explain the perception of a root in a pitch set, with Terhardt’s (1984) virtual pitch theory being the one generally considered most plausible, despite none of them having been confirmed empirically. Understanding the perceived root phenomenon is an essential component in explaining the origin of the major and minor triads as the most fundamental chords in twelve-tone equal temperament or 5-limit just intonation, as well as in proposing new chords for new tunings. This music perception study, in which 42 participants rated chords in 10 different tunings, empirically establishes harmonic dualism, negative harmony, and Barlow’s harmonicity as the key factors for the perception of the harmonic root and the origin of the major and minor triads, and proposes a model as a basis for a tuning-agnostic—trans-spatial—music theory.