A Formal Theory of Generalized Tonal Functions

Abstract

Our point of departure is a common method of constructing a system of tonal functions and relationships given a tonic pitch-class T, a dominant interval d and a mediant interval m. The method is portrayed visually by Figure 1. In the figure we see a C major system constructed given the tonic pitch class T=C, the dominant interval d=fifth (modulo the octave), and the mediant interval m=major third (modulo the octave). From the tonic note C we construct notes a dominant and a mediant interval away, that is G=C+d and e=C+m. Together with the tonic note, these dominant and mediant notes constitute the tonic triad of the system. Next we construct a dominant triad, comprising the dominant note G together with the notes D=G+d and b=G+m which lie the intervals d and m respectively from that G. Similarly, we construct a subdominant triad comprising the tonic note C, the subdominant note F from which C lies the interval d away, and the submediant note a which lies the interval m from the subdominant note F. Since F is constructed to satisfy the relation F+d=C, we may symbolically write F=C-d; then a=F+m=C-d+m.