Abstract:
Theories of harmonic function usually fall into content and context-based theories. The former theorizes function in terms of similarity to prototypical triads, generally the tonic, dominant, and subdominant chords. The latter categorizes chords into functions based on their movement to and from other harmonies. While context-based theories provide insightful methods for tracking how chords behave, why chords behave this way cannot be fully explained without some reference to their scale-degree content. Previous content-based approaches have also left a gap, as they do not present a space for chromatic chords that includes precise placement for the degree of similarity to a prototype.
To fill this gap, I provide an expanded space of functional similarity for minor and major triads in tonal classical music. Single applications of P, L, and R generate the first level of similarity to a prototype, and compound operations, such as PL and PLP, produce the second and third levels of functional similarity. The theory presented possesses both theoretical and analytical advantages. In addition to refining the criteria by which harmonies belong in a given function class, the space also provides great power to deal with functional, but highly chromatic textures, excavating both functional coherency and expressive flexibility.