The Hitchhiker's Guide to the All-Interval 12-Tone Rows

TL;DR

This paper explores the generation and classification of all-interval 12-tone series using complex network theory, providing a new re-ordering scheme that links these series through chains of relations for composers and theorists.

Contribution

It introduces a novel complex network approach to analyze all-interval 12-tone series and offers a comprehensive re-ordering scheme connecting all AISs.

Findings

Developed a network-based classification of AIS

Established a re-ordering scheme linking all AISs

Enhanced understanding of AIS relationships

Abstract

This article revisits the generation, classification and categorization of all-intervals 12-tone series (AIS). Inspired by the seminal work of Morris and Starr in 1974 (Morris and Starr, The Structure of All-Interval Series 1974), it expands their analysis using complex network theory and provides composers and theorists with the re-ordering scheme that links all AISs together by chains of relations.