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

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%).

Nonspecific hebbian neural network model predicts musical scales discreteness and just intonation without using octave-equivalency mapping

“…This result and the comprehensive analysis with a very coarse resolution of 100 cents used in our previous study 11 show that the order of consonance of the emerged intervals is significantly affected by the selected number of harmonics and their magnitude distribution (the experience, exposure to various auditory contexts, the familiarity). The result that familiarity is a predictor of consonance agrees with recent experimental results by multiple authors—as in Eerola and Lahdelma 19 , reporting that the variance in consonance ratings comes 46.2% from familiarity (experience) and only 19.3% from roughness/harmonicity. This result suggests why our model does not perfectly predict Helmholtz’s consonance order of the least-consonant intervals: our selected corpus of input sounds (our model’s auditory “experience”) differs from the lifelong auditory exposures of the participants' in Helmholtz’s consonance studies.…”

“…Consequently, the consonance could be related to well-established long-term memory patterns ( familiarity ), which is why we are interested in the synaptic weights. In their recent (2021) impressively comprehensive study on Consonance/Dissonance (C/D), Eerola and Lahdelma 19 suggest that “Today, 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.” That combination of familiarity (represented by the high-magnitude synaptic weights) and harmonicity play core roles in our model. Our model does not explicitly consider the third concept highlighted by Eerola and Lahdelma—the roughness—demonstrating that it is not required for our simplistic bio-physical model to yield the obtained results.…”

Is Harmonicity a Misnomer for Cultural Familiarity in Consonance Preferences?

“…According to this concept the C/D of isolated pitch combinations depend on the scales in which they occur: pitch combinations occurring in a major scale are less dissonant than pitch combinations occurring only in a minor scale, which in turn are less dissonant than pitch combinations occurring in neither sort of scale. Eerola and Lahdelma (2021) took the parsimony of the tonal consonance/dissonance idea by Johnson-Laird et al (2012) a step further still by collapsing minor and other scales together to create a simple implementation called the Tonal Dissonance Model, which assesses whether a pitch combination can be constructed from a major scale (1) or not (0). Their choice was motivated by analyzing the contribution of the three principles of the original model by testing each principle as a binary coded variable in regression to predict consonance ratings together with roughness, familiarity, and spectral envelope predictors (see Eerola and Lahdelma, 2021).…”

“…Eerola and Lahdelma (2021) took the parsimony of the tonal consonance/dissonance idea by Johnson-Laird et al (2012) a step further still by collapsing minor and other scales together to create a simple implementation called the Tonal Dissonance Model, which assesses whether a pitch combination can be constructed from a major scale (1) or not (0). Their choice was motivated by analyzing the contribution of the three principles of the original model by testing each principle as a binary coded variable in regression to predict consonance ratings together with roughness, familiarity, and spectral envelope predictors (see Eerola and Lahdelma, 2021). Strikingly, Eerola and Lahdelma (2021) found this simple binary division model functions like a harmonicity model; it is remarkable how complex models calculating harmonicity of the partials do not perform better than a model that merely checks whether pitch combinations can be created from a diatonic major scale (i.e., whether the pitch combination can theoretically be part of a diatonic major key tonality).…”

“…Their choice was motivated by analyzing the contribution of the three principles of the original model by testing each principle as a binary coded variable in regression to predict consonance ratings together with roughness, familiarity, and spectral envelope predictors (see Eerola and Lahdelma, 2021). Strikingly, Eerola and Lahdelma (2021) found this simple binary division model functions like a harmonicity model; it is remarkable how complex models calculating harmonicity of the partials do not perform better than a model that merely checks whether pitch combinations can be created from a diatonic major scale (i.e., whether the pitch combination can theoretically be part of a diatonic major key tonality). It has been demonstrated that musicians tend to perceive specifically culturally familiar chords as more consonant compared to nonmusicians (McLachlan et al, 2013;Lahdelma and Eerola, 2016) as per the mere exposure effect (Zajonc, 2001)-this would readily explain the results of previous experiments with regard to the training-based differences in sensitivity to "harmonicity".…”