Norman Carey
Eastman School of Music
Regardless of its questionable acoustical foundations, the dualist perspective of the major/minor tonal system advanced by Oettingen and Riemann reflects an obvious truism, namely that the diatonic system is inversionally symmetric with respect to 2 of the major scale. Properties of inversional symmetry in a diatonic context are investigated within the methodology provided by David Lewin's Generalized Interval Systems. A system of six GIS structures serves as a model for common practice tonality. The model provides a platform from which to investigate the problem of tonal answers in the fugue. Various fugue treatises propose a number of apparently unrelated ad hoc procedures by which to initiate the young composer into the intricacies of the problem of fugal answers. The current study shows an underlying unity in these procedures, arising out of the dualist perspective as modeled by the GIS structures. This in turn leads to a method of constructing fugal subjects rich with inversional potential.
While the topic of fugal answers is inevitably complex, it is noteworthy that a combination of techniques new and old can, at least in broad strokes, capture many of the most important techmques, promising significant pedagogical application. Finally, the paper provides an entirely practical application for a much-maligned speculative theory.