Revision of Terhardt's Psychoacoustical Model of the Root(s) of a Musical Chord

Abstract

The predictions of Terhardt's octave-generalized model of the root of a musical chord occasionally disagree with music theory (notably, in the case of the minor triad). The model is improved by assigning appropriate weights to the intervals used in the model's "subharmonic matching" routine. These intervals, called "root-supports," include the P8 (unison), P5, M3, m7, M9 (M2), and m3. The new model calculates the salience of each pitch class (C, C#/Db..B) as an absolute value. The most likely candidate for the root of a chord corresponds to the most salient pitch class in all cases where the root is unambiguously defined in music theory. The model also calculates a "root ambiguity" value for each chord, a measure of its dissonance. Effects of voicing (inversion, spacing, and doubling) and context on the root are considered.