A detailed list and a periodic table of set classes

Abstract

In this paper, pitch-class sets are analyzed in terms of their intervallic structures and those related by transposition are called a set type. Then, non-inversionally-symmetrical set classes are split into two set types related by inversion. As a higher version of the interval-class vector, I introduce the trichord-type vector, whose elements are the number of times each trichord type is contained in a set type, as well as a trichord-class vector for set classes. By using the interval-class, trichord-class, and trichord-type vectors, a list of set classes and types is developed, including, apart from the usual information, the intervallic structures and the trichord-type vectors. The inclusion of this last characteristic is the most significant difference with respect to previously published lists of set classes. Finally, a compact periodic table containing all set classes is given, showing their main characteristics and relationships at a glance.