Function is one of those words that everyone understands, yet everyone understands a little differently. Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. So many theorists - Daniel Harrison, Joel Lester, Eytan Agmon, Charles Smith, William Caplin, and Gregory Proctor, to name a few - have so many different nuanced understandings of function that it is nearly impossible for conversations on the subject to be completely understood by all parties. This is because function comprises at least four distinct aspects, which, when all called by the same name, function, create ambiguity, confusion, and contradiction.
Part I of the dissertation first illuminates this ambiguity in the term function by giving a historical basis for four different aspects of function, three of which are traced to Riemann, and one of which is traced all the way back to Rameau. A solution to the problem of ambiguity is then proposed: the elimination of the term function. In place of function, four new terms - behavior, kinship, province, and quality - are invoked, each uniquely corresponding to one of the four aspects of function identified. The meanings of these new terms are elucidated by such harmonic topics as secondary dominants and six-four paradigms. A notation system is developed for behavior, in particular, which is used in conjunction with two standard systems of harmonic analysis to form a Three-fold System of Analysis that yields deeper explanations of harmony characteristics.
Part II of the dissertation reveals how my theory of behavior leads to new explanations for chromatic harmonies. A definition of tonicization is proposed based on behavior paradigms. The models suggest that tonicization is a better explanation than is mixture for many chromatic notes and harmonies that are typically explained with mixture. Further, so-called linear or voice-leading chords (such as augmented-sixth chords, common-tone diminished seventh chords, chromatic mediants, etc.) are examined through the lens of the theory of behavior. Finally, I discuss ramifications of the theory of behavior for musics beyond the realm of classical diatonic tonality, including 19th-century chromatic tonality, jazz, and popular music.
Part III of the dissertation traces the history the four aspects of function from Rameau to Riemann. This account includes such figures as Rameau, Béthizy, Daube, Kirnberger, Koch, Vogler, Momigny, Weber, Fétis, Sechter, Hauptmann, Helmholtz, and Riemann.