Modal Logic for Tonal Music

It is generally accepted that the origin of music and language is one and the same. Thus far, many syntactic theories of music have been proposed, however, all these efforts seem mainly to concern the generative syntax. Although such syntax enables us to construct hierarchical tree, the mere tree representation is not sufficient in representing mutual references in music. In this research, we propose the annotation of tree with modal logic, by which the reference from each pitch event to harmonic regions are clarified. In addition, while the conventional generative syntax constructs the tree in the top-down way, the modal interpretation gives the incremental construction according to the progression of music. Therefore, we can naturally interpret our theory as the expectation–realization model that is more familiar to our human recognition of music.