The Anatomy of Consonance/Dissonance: Evaluating Acoustic and Cultural Predictors Across Multiple Datasets with Chords

Tuomas Eerola,Imre Lahdelma

doi:10.1177/20592043211030471

Abstract

Acoustic and musical components of consonance and dissonance perception have been recently identified. This study expands the range of predictors of consonance and dissonance by three analytical operations. In Experiment 1, we identify the underlying structure of a number of central predictors of consonance and dissonance extracted from an extensive dataset of chords using a hierarchical cluster analysis. Four feature categories are identified largely confirming the existing three categories (roughness, harmonicity, familiarity), including spectral envelope as an additional category separate from these. In Experiment 2, we evaluate the current model of consonance/dissonance by Harrison and Pearce by an analysis of three previously published datasets. We use linear mixed models to optimize the choice of predictors and offer a revised model. We also propose and assess a number of new predictors representing familiarity. In Experiment 3, the model by Harrison and Pearce and our revised model are evaluated with nine datasets that provide empirical mean ratings of consonance and dissonance. The results show good prediction rates for the Harrison and Pearce model (62%) and a still significantly better rate for the revised model (73%). In the revised model, the harmonicity predictor of Harrison and Pearce’s model is replaced by Stolzenburg’s model, and a familiarity predictor coded through a simplified classification of chords replaces the original corpus-based model. The inclusion of spectral envelope as a new category is a minor addition to account for the consonance/dissonance ratings. With respect to the anatomy of consonance/dissonance, we analyze the collinearity of the predictors, which is addressed by principal component analysis of all predictors in Experiment 3. This captures the harmonicity and roughness predictors into one component; overall, the three components account for 66% of the consonance/dissonance ratings, where the dominant variance explained comes from familiarity (46.2%), followed by roughness/harmonicity (19.3%).

Highlights

The investigation of musical consonance and dissonance— that is, the relative agreeableness/stability versus disagreeableness/instability of simultaneous and successive pitch combinations—has a long and checkered history
The research field is starting to reach a consensus that the overall perception of C/D in simultaneous sonorities in the Western musical culture is arguably based on a combination of roughness, harmonicity, and familiarity
It is worth pointing out that the familiarity predictor carries the dominant unique contribution in the model whereas harmonicity plays a relatively small role, consistent with the analyses presented with the three datasets earlier

Summary

Introduction

The investigation of musical consonance and dissonance— that is, the relative agreeableness/stability versus disagreeableness/instability of simultaneous and successive pitch combinations—has a long and checkered history (see e.g., Tenney, 1988). The Pythagorean school in ancient Greece held that consonance/dissonance (hereafter referred to as C/D and implying exclusively simultaneous pitch combinations) can be explained through the simplicity of number ratios, and this view was upheld well into the 16th century In the 17th and 18th centuries, the origins of C/D were elaborated by scholars such as Marin Mersenne, Joseph Sauveur, and Jean-Philippe Rameau, who investigated the role of overtones and their relation to musical. In the 19th century, scholars such as Hermann von Helmholtz (1875) and Carl Stumpf (1898) brought the knowledge of physics, anatomy, perception, and empirical testing to characterize C/D as something that depends on frequencies of the fundamental and the partials of the sound and how these are interpreted within the musical tradition that the listener is familiar with. The research field is starting to reach a consensus that the overall perception of C/D in simultaneous sonorities in the Western musical culture is arguably based on a combination of roughness, harmonicity, and familiarity (see e.g., Harrison & Pearce, 2020; McLachlan et al, 2013; Parncutt & Hair, 2011)

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Conclusion