A detailed list and a periodic table of set classes. Issue 3 (2nd September 2021)

• Record Type: Journal Article
• Authors: Nuño, Luis
• Is Part Of: Journal of mathematics and music. Volume 15:Issue 3(2021)
• Page Start: 267
• Page End: 287
• Publication Date: 2021-09-02
• Subjects: list of set classes -- interval-class vector -- trichord-class vector -- trichord-type vector -- periodic table; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2020.1775902
• Languages: English
• ISSNs: 1745-9737

Abstract

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.