Western musical styles use a large variety of chords and vertical sonorities. Based on objective acoustical properties, chords can be situated on a dissonant-consonant continuum. While this might to some extent converge with the unpleasant-pleasant continuum, subjective liking might diverge for various chord forms from music across different styles. Our study aimed to investigate how well appraisals of the roughness and pleasantness dimensions of isolated chords taken from real-world music are predicted by Parncutt’s established model of sensory dissonance. Furthermore, we related these subjective ratings to style of origin and acoustical features of the chords as well as musical sophistication of the raters. Ratings were obtained for chords deemed representative of the harmonic language of three different musical styles (classical, jazz and avant-garde music), plus randomly generated chords. Results indicate that pleasantness and roughness ratings were, on average, mirror opposites; however, their relative distribution differed greatly across styles, reflecting different underlying aesthetic ideals. Parncutt’s model only weakly predicted ratings for all but Classical chords, suggesting that listeners’ appraisal of the dissonance and pleasantness of chords bears not only on stimulus-side but also on listener-side factors. Indeed, we found that levels of musical sophistication negatively predicted listeners’ tendency to rate the consonance and pleasantness of any one chord as coupled measures, suggesting that musical education and expertise may serve to individuate how these musical dimensions are apprehended.

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Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features; 3) tonal harmony conveys directedness in time; and 4) tonal harmony operates differently at the hierarchical levels of chords and keys. These results serve to characterize tonal harmony on empirical grounds and advance the methodological state-of-the-art in digital musicology.

Tonality is one of the most central theoretical concepts for the analysis of Western classical music. This study presents a novel approach for the study of its historical development, exploring in particular the concept of mode. Based on a large dataset of approximately 13,000 musical pieces in MIDI format, we present two models to infer both the number and characteristics of modes of different historical periods from first principles: a geometric model of modes as clusters of musical pieces in a non-Euclidean space, and a cognitively plausible Bayesian model of modes as Dirichlet distributions. We use the geometric model to determine the optimal number of modes for five historical epochs via unsupervised learning and apply the probabilistic model to infer the characteristics of the modes. Our results show that the inference of four modes is most plausible in the Renaissance, that two modes–corresponding to major and minor–are most appropriate in the Baroque and Classical eras, whereas no clear separation into distinct modes is found for the 19th century.