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.

BackgroundGaze abnormality is a diagnostic criterion for autism spectrum disorder (ASD). However, few easy-to-use clinical tools exist to evaluate the unique eye-gaze patterns of ASD. Recently, we developed Gazefinder, an all-in-one eye-tracking system for early detection of ASD in toddlers. Because abnormal gaze patterns have been documented in various ASD age groups, we predicted that Gazefinder might also detect gaze abnormality in adolescents and adults. In this study, we tested whether Gazefinder could identify unique gaze patterns in adolescents and adults with ASD.MethodsWe measured the percentage of eye fixation time allocated to particular objects depicted in movies (i.e., eyes and mouth in human face movies, upright and inverted biological motion in movies that presented these stimuli simultaneously, and people and geometry in movies that presented these stimuli simultaneously) by male adolescents and adults with ASD (N = 26) and age-matched males with typical development (TD; N = 35). We compared these percentages between the two groups (ASD and TD) and with scores on the social responsiveness scale (SRS). Further, we conducted discriminant analyses to determine if fixation times allocated to particular objects could be used to discriminate between individuals with and without ASD.ResultsCompared with the TD group, the ASD group showed significantly less fixation time at locations of salient social information (i.e., eyes in the movie of human faces without lip movement and people in the movie of people and geometry), while there were no significant groupwise differences in the responses to movies of human faces with lip movement or biological motion. In a within-group correlation analysis, a few of the fixation-time items correlated with SRS, although most of them did not. No items significantly correlated with SRS in both ASD and TD groups. The percentage fixation times to eyes and people, which exhibited large effect sizes for the group difference, could differentiate ASD and TD with a sensitivity of 81.0 % and a specificity of 80.0 %.ConclusionsThese findings suggest that Gazefinder is potentially a valuable and easy-to-use tool for objectively measuring unique gaze patterns and discriminating between ASD and TD in male adolescents and adults.Electronic supplementary materialThe online version of this article (doi:10.1186/s13229-016-0083-y) contains supplementary material, which is available to authorized users.