Commentary on Buechele, Cooke, & Berezovsky (2024): entropic models of scales and some extensions

I discuss Buechele, Cooke, and Berezovsky’s entropy-based model of scale structure and compare it with a different entropy-based model from Milne et al. (2017). I also present an augmented version of the 2017 model to provide an additional entropy-based explanation for preferred scale structures. Our models have similarities and differences in terms of their constructions and constraints, and their results differ somewhat in meaning. Despite this, they are broadly comparable in terms of the “optimal” scales found. This suggests that entropy-based approaches can explain the origins of historical and contemporary scales, whilst also indicating interesting alternative scales that align with psychoacoustic and cognitive affordances.