Modelling tonal attraction: tonal hierarchies, interval cycles, and quantum probabilities.

How well does a given pitch fit into a tonal scale or tonal key, let it be a major or minor key? A similar question can be asked regarding chords and tonal regions. Structural and probabilistic approaches in computational music theory have tried to give systematic answers to the problem of tonal attraction. We will discuss two previous models of tonal attraction, one based on tonal hierarchies and the other based on interval cycles. To overcome the shortcomings of these models, both methodologically and empirically, I propose a new kind of models relying on insights of the new research field of quantum cognition. I will argue that the quantum approach integrates the insights from both group theory and quantum probability theory. In this way, it achieves a deeper understanding of the cognitive nature of tonal music, especially concerning the nature of musical expectations (Leonhard Meyer) and a better understanding of the affective meaning of music. [ABSTRACT FROM AUTHOR]