We investigate the representation of n-tone rows as paths on an n-dimensional hypercube graph with vertices labeled in the power set of the aggregate. These paths run from the vertex labeled by the null set to the one la- beled by the full set, passing through vertices whose labels gradually accumu- late members of the aggregate. Row relations are then given as hypercube symmetries. Such a model is more sensitive to the musical process of chromatic completion than those that deal more exclusively with n-tone rows and their re- lations as permutations of an underlying set. Our results lead to a graph- theoretical representation of the duality inherent in the pitch-class/order-number isomorphism of serial theory.
['Robert W. Peck']
A Hypercube-Graph Model for n-Tone Rows and Relations