The concept of the linear progression is one of the most important principles in Schenker's theory of tonal structure. Yet, nowhere does Schenker present a single, comprehensive definition that accounts for both upper-voice and bass linear progressions occurring at all levels of structure. In this dissertation, a definition is proposed that interprets linear progressions as a connection between two voices of different structural rank. The structural inequality between the two voices distinguishes a linear progression from a line, whose boundary tones are of equal status. Based on this structural relationship, guidelines are proposed for determining when one of the boundary tones of a progression has been transferred to a new register, which in turn provides a mechanism for distinguishing between inverted progressions and those in their original form.
Schenker makes no provisions for the completion of upper-voice linear progressions in the bass, nor vice versa. A structural model is proposed in which the bass generates its own "inner voices" that are distinct from the inner voices of the upper parts, i.e., the alto and tenor. This results in the concept of separate "linear spaces" for the upper parts and for the bass, wherein each outer voice of the fundamental structure serves as the source of linear progressions in its own "linear space."
A set guidelines governing the formation and interaction of linear progressions on different levels of structure is proposed. Within each linear space, each level restricted to having a single moving linear progression at any given time. Schenker's two-part fundamental structure is compared with a model that allows for more than one structural upper voice. Schenker's concept of leading and following progressions is examined in light of the definition of linear progressions presented in this dissertation. Finally, the role of the fundamental structure is redefined as specific means by which the conditions necessary for the existence of linear progressions are established.