Twelve-Tone All-Interval Series (AIS)

A Study on the Relationship Between Hexachordal Partitions Set-Classes and Their PCORD

Abstract

This study expands the application of the PCORD theory, or interval classes of set-classes, to the realm of twelve-tone music, focusing in the all-interval series (AIS). For that purpose, we revisited some classical analysis of AISs mentioned in the literature and studied the relations between the interval series, the set-classes of the hexachordal partitions, and their respective PCORD. We recognized three categories involving the same or different classes, respectively in the set-classes and in the PCORD classes, for the two hexachords of AIS series. We observed yet the existence of other cases of symmetry in AISs series besides those already reported in the literature. Finally, we concluded that the main application of this study may not be for the analysis of existing pieces, but for the composition of new works that employ twelve-tone material without using the traditional procedures of Schoenberg, but instead opt for a consistent use of parsimony principles as it is usual in Reich’s process form.