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 how consideration of 3-tone psychophysics can explain the fundamental regularities

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... 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. WHILE noting the fact that there are yet unresolved issues in the psychophysics of harmony perception, Parncutt (2006a) did not address the main question that we raised concerning the possible role of 3-tone combinations . We have often cited his well-known work (Harmony: A psychoacoustical approach, 1989) because it is one of a small number of psychophysical models that was developed explicitly to explain the perception of diatonic harmony. Although many authors have implied as much, Parncutt and a few others (Terhardt, 1974; Tramo et al., 2001) have explicitly stated that the perception of chords is principally an issue of the perception of the summed effects of the 2-tone intervals (and their upper harmonics). This strongly reductionist approach has in fact had great success in explaining interval perception itself, but the inability to account for even the most basic facts about harmony (in the usual sense of combinations of three or more pitch classes) is a serious short-coming for any model that claims to provide the scientific basis for the perception of diatonic music. Experiments (with musicians and non-musicians from diverse cultures) and the statistics on the prevalence of triads in 18 th and 19 th Century classical music indicate that diminished chords are more consonant than augmented chords, but the Parncutt (1989) model incorrectly predicts that they should be more dissonant. This small discrepancy between theory and experiment is, however, only one flaw in a pattern of incorrect model predictions that we have shown to be characteristic of the interval-based models of harmony perception. More fatal than the incorrect prediction of the relative instability of diminished and augmented chords is the fact that Parncutt's model (Table 1 ) also predicts that the augmented chord is more consonant than 5 of the 6 major and minor triads, and that the 2 nd inversion of the minor triad is the most dissonant of all the triads! Such model predictions are, perceptually, nonsense. Since all of the harmony models that are based on interval dissonance make similarly poor predictions about triad perception, we have challenged the claim that even an approximate understanding of Western harmony can be obtained from the psychoacoustics of interval perception.