# A detailed list and a periodic table of set classes

A detailed list and a periodic table of set classes 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition" Taylor & Francis

# A detailed list and a periodic table of set classes

, Volume 15 (3): 21 – Sep 2, 2021

## A detailed list and a periodic table of set classes

, Volume 15 (3): 21 – Sep 2, 2021

### 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.

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# References (19)

Publisher
Taylor & Francis
ISSN
1745-9745
eISSN
1745-9737
DOI
10.1080/17459737.2020.1775902
Publisher site
See Article on Publisher Site

### 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.

### Journal

"Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition"Taylor & Francis

Published: Sep 2, 2021

Keywords: list of set classes; interval-class vector; trichord-class vector; trichord-type vector; periodic table