Cross-cultural data shows musical scales evolved to maximise imperfect fifths John M. McBride1,* and Tsvi Tlusty1,2,* 1Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, South Korea 2Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea *
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[email protected] June 2, 2020 Musical scales are used throughout the world, but harmonicity follows from the idea that exposure to harmonic the question of how they evolved remains open. Some sounds in animal vocalisations may have conditioned humans suggest that scales based on the harmonic series are to respond positively to them [9, 10]. Musical features related inherently pleasant, while others propose that scales to harmonicity – harmonic intervals [11–13], octave equivalence are chosen that are easy to communicate. How- [14, 15], a link between consonance and harmonicity [16–18] – ever, testing these theories has been hindered by the are indeed widespread, although their universality is disputed sparseness of empirical evidence. Here, we assimilate [19, 20]. One study attempted to explain the origin of scales data from diverse ethnomusicological sources into a as maximization of harmonicity [8], however the universality cross-cultural database of scales. We generate pop- of their findings is limited by the scope of cultures considered ulations of scales based on multiple theories and as- [21]. sess their similarity to empirical distributions from the The vocal mistuning theory states that scales, and intervals, database. Most scales tend to include intervals which were chosen not due to harmonicity, but because they were are close in size to perfect fifths (“imperfect fifths”), easy to communicate [22, 23].