This study focuses on the melding of human agency, digital media, and algorithmic computer systems to create and explore potential taxonomies, modes of utilization, and genre trajectories for using generativity as a feature of sound-based artistic practices. With the automation of behaviours to produce or analyze sound using indeterminate or continuously evolving processes, artists and scholars can discover new identities for digital devices such as mobile phones, rediscover performance gestures of familiar musical instruments, and cultivate meaningful relationships with real and simulated spaces. In this dissertation, the inherently interdisciplinary nature of generativity in the sonic arts contributes to the way in which I draw on writings and related artworks from disciplines such as media studies, cultural studies, and computational visual art to reframe longstanding musicological theorizations of instrumentality, performance practice, and compositional style. In addition to discussing pieces that work as texts in a historiography of generative sonic art, exploring the relationship between system design and cultural positionalities of artists and/or technologists, and examining generativity as a heterogeneous concept that emerges in a variety of ways that can be practitioner or project specific, I also explore how the creation and use of such computer systems can act as a microcosm for broader issues of power that relate to the presence of algorithmic media in culture and the use or misuse of artificial intelligence technologies. As so much of the implementation and scholarship on generativity in the arts depends on the phenomenological perspective of creators, I have integrated some research-creation projects from my practice as an electroacoustic composer and technologist. Most of these works were not made for this dissertation but produced concurrently as part of my ongoing creative interest in generative music and sound art. They are discussed in order to provide an additional layer of context while I pursue my research questions.