Generic Sequences and the Generic Tonnetz

Abstract

This article employs concepts from diatonic set theory, transformation theory, and neo-Riemannian theory in an investigation of sequences in generic (mod-7) pitch space. Sequences may be described using generic transposition operators, mod-7 analogs of the more familiar mod-12 chromatic transposition operators, and may be mapped in a generic Tonnetz analogous to the Tonnetz diagrams of neo-Riemannian theory. A complete classification of generic sequences with two-chord transposition blocks is derived from the paths described by the sequences in the Tonnetz. While it is tempting to regard generic space as “diatonic,” the examples demonstrate that generic structure governs many sequences that are not actually diatonic at all. The examples also show that the sequences found in the literature include many more types than are widely recognized and that generic sequence structure may apply in numerous other contexts besides patterns of chord roots.