Feedback and feedforward models of musical key

Abstract

This study begins by drawing a distinction between two ways of framing the concept of musical key. Feedforward models understand key as arising from immediately apparent surface characteristics like the distribution of pitch classes or a melody's intervallic content. Feedback models, on the other hand, understand key as being determined in tandem with other domains. Here, key arises from the surface being organized into other more complicated musical groupings or schemata-harmonic progressions, cadences, prolongations, meter, etc.-that themselves are informed by the music's tonal center. While much music theory and theory pedagogy have acknowledged that feedback occurs in various approaches to tonality, formal modeling in the fields of music cognition and computation has focused primarily on feedforward systems. This article attempts to right this imbalance by presenting a corpus-based feedback computational model that can be tested against human behavior. My model will identify a passage's key by organizing a surface into its constituent harmonies. Here, harmonic organization and key will be integrated into a feedback system with the ideal key being that which produces the ideal harmonic analysis, and vice versa. To validate the resulting model, its behavior is compared to that of other published tonal models, to the behaviors of undergraduate music students, and to the intuitions of professional music theorists.