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In his most recent contribution to an important and well-framed series of papers on auditory grouping and the perception of polyphonic music, David Huron seeks further evidence for his working hypothesis that J.S. Bach controls the employment of perfect consonances by desynchronizing their onsets, thereby inhibiting the perceptual fusion of polyphonic voices. However the more novel contribution of the present study would seem to be its demonstration that Bach also regulates the employment of dissonant tones by consistently desynchronizing their onsets. This finding provides the first concrete evidence for Wright and Bregman’s otherwise untested hypothesis that the control and salience of dissonance in polyphonic music are closely related to principles of auditory stream segregation (Wright, 1986; Wright & Bregman, 1987).

The relative consonance/dissonance of 2-tone intervals is well understood both experimentally and theoretically and provides a strong foundation for explaining why diatonic scales or their subsets are used in most musical cultures. Frequent textbook assertions notwithstanding, however, the consonance of intervals fails to account for the basic facts of harmony (3 or more tone combinations). We have recently shown (Cook & Fujisawa, 2006) how consideration of 3-tone psychophysics can explain the fundamental regularities of diatonic harmony. Distinct from the dissonance of 2-tone intervals, 3-tone combinations introduce an effect described by Leonard Meyer (1956) as harmonic “tension”: when a third tone is located midway between an upper and a lower tone, the chord takes on an unresolved, unstable, tense character – a psychoacoustical property inherent to the diminished and augmented chords. If the effects of the upper partials are included in a formal model that includes both 2-tone and 3-tone effects, the perceived sonority of the triads (major>minor> diminished>augmented) is easily explained.

Cook & Fujisawa (2006) point out that, contrary to the predictions of psychoacoustic models, the diminished triad is more consonant and prevalent in western tonal music than the augmented. A possible simple explanation is that the diminished triad often functions as an incomplete dominant (major-minor) seventh chord, the most prevalent tetrad in mainstream tonal music.

The phenomena of consonance and dissonance are thought to involve both learned and innate components. Work by Greenwood (1961) and Plomp and Levelt (1965) established that an aspect of dissonance perception can be traced to unique physiological properties of the hearing organ. This aspect of dissonance is commonly referred to as sensory dissonance. Two computable models of sensory dissonance are described and discussed—those of Kameoka and Kuriyagawa (1969a; 1969b) and Hutchinson and Knopoff (1978). Software implementations of both models are provided, and their behaviors explored. Both models exhibit a number of conceptual and technical problems.

In line with musical “common sense” (but contrary to the century-old tradition of musical psychophysics), we show that harmony is an inherently three-tone phenomenon. Previous attempts at explaining the affective response to major/minor chords and resolved/unresolved chords on the basis of the summation of interval dissonance have been notably unsuccessful, but consideration of the relative size of the intervals contained in triads leads directly to solutions to these historical problems. At the heart of our model is Leonard Meyer’s idea from 1956 concerning “intervallic equidistance” – i.e., the perception of “tension” inherent to any three-tone combination that has two intervals of equivalent size (e.g., the augmented chord). By including the effects of the upper partials, a psychophysical explanation of the perceived sonority of the triads (major>minor>diminished>augmented) and the affective valence of major and minor chords is easily achieved. We conclude that the perceptual regularities of traditional diatonic harmony are neither due to the summation of interval effects nor simply arbitrary, learned cultural artifacts, but rather that harmony has a psychophysical basis dependent on three-tone combinations.

Mashinter’s (2006) mathematical model of sensory dissonance neglects the dependence of roughness on waveform, the role of masking, the distribution of roughness across critical bands, the possible positive contribution of fusion or toneness to euphony, and the familiarity and music-theoretical functions of a sonority. Of course not all these aspects can reasonably be included in a model, but they can affect the data with which its predictions are compared.

The commentary asserts the importance of conducting additional research on additive dissonance, and points to the need for terminological precision in discussions of sensory versus systemic (i.e. learned, context-dependent) dissonance.