Supplementary Information for Consonance-emerging Hebbian Learning neural network model predicts discreteness of musical scales and the Natural Just Intonation scale

The following phenomena and features are apparent in music and auditory perception in general: the discreteness of the tones in musical scales [1], the prevalence of the tonal frequency span of one semitone (100 cents) in musical scales across cultures [1], the list of tonal intervals ordered by consonance [2], and the musical performers’ preference of the Natural Just-Intonation scale [3] (A). However, researchers still have no agreement about the causes and the emergence of said phenomena (A). Here we show that the consonance-pattern emerging neural network model introduced in our previous study [4], predicts and yields all the said phenomena (A) with a precision of 1/100^th of a semitone (1 cent). This precision is beyond the resolution of human hearing [5], [6], [7]. Since the Hebbian learning paradigm and harmonicity are the main features of our model, we propose that they are sufficient conditions for any system to yield the said phenomena (A). Therefore, they have a crucial role in processing pitch, consonance, and music perception in general. As a consequence, we additionally propose that the mentioned phenomena (A) are a balanced result of the joint workings of the Hebbian paradigm (nurture and cultural exposure) and harmonicity (auditory physics and biology).