In the article “Consonance preferences within an unconventional tuning system,” Friedman and colleagues (2021) examine consonance ratings of a large range of dyads and triads from the Bohlen-Pierce chromatic just (BPCJ) scale. The study is designed as a replication of a recent paper by Bowling, Purves, and Gill (2018) , which proposes that perception of consonance in dyads, triads, and tetrads can be predicted by their harmonic similarity to human vocalisations. In this commentary, we would like to correct some interpretations regarding Friedman et al.’s (2021) discussion of our paper ( Smit, Milne, Dean, & Weidemann, 2019 ), as well as express some concerns regarding the statistical methods used. We also propose a stronger emphasis on the use of, as named by Friedman et al., composite models as a range of recent evidence strongly suggests that no single acoustic measure can fully predict the complex experience of consonance.

In this paper, we introduce a small family of novel bottom-up (sensory) models of the Krumhansl and Kessler (1982) probe tone data. The models are based on the spectral pitch class similarities between all twelve pitch classes and the tonic degree and tonic triad. Cross-validation tests of a wide selection of models show ours to have amongst the highest fits to the data. We then extend one of our models to predict the tonics of a variety of different scales such as the harmonic minor, melodic minor, and harmonic major. The model produces sensible predictions for these scales. Furthermore, we also predict the tonics of a small selection of microtonal scales—scales that do not form part of any musical culture. These latter predictions may be tested when suitable empirical data have been collected.