Interval-Class Succession Graphs in Edison Denisov's Sonata for Alto Saxophone and Piano

This article presents the interval-class succession graph (ICSG), an analytical tool intended for the comparison of twelve-tone row classes. The ICSG takes a very intuitive form: the interval classes that are found between adjacent pitch classes of a twelve-tone row form the labels of the graph's nodes, and arrows are drawn between each node to indicate which successions of interval classes are found in the row. I begin with a rationale for considering row classes in terms of their ordered interval-class content. After discussing a row's adjacency matrix and defining the ICSG, I turn my attention to special graph-theoretic relationships between different ICSGs. The paper concludes with some suggestions of ways in which the ICSG framework can be adapted to other musical contexts outside the realm of twelve-tone music. An appendix provides an introduction to relevant terminology from the world of mathematical graph theory.