In the third and final book of his iconic piano etudes György Ligeti charts a new path relative to the rest of his musical output, representing a significant arrival in a composer’s oeuvre known for its stylistic transformations. This monograph is the first dedicated study of these capstone works, investigating them through a novel lens of statistical-graphical analysis that illuminates their compositional uniqueness as well as broader questions regarding the perception of stability in musical texture. With nearly 200 graphical illustrations and a detailed commentary, this examination reveals the unique manner in which Ligeti treads between tonality and atonality—a key idea in his late style—and the centrality of processes related to broader scale areas (or “macroharmony”) in articulating structures and narratives. The analytical techniques developed here are a powerful tool for investigating macroharmonic stability that can be applied to a wide range of repertoire beyond these works. This book is intended for graduate-level and professional music theorists, musicologists, performers and mathematicians.