A Detailed List and a Periodic Table of Set Classes A Detailed List and a Periodic Table of Set Classes Luis Nuño Communications Department, Polytechnic University of Valencia, Valencia, Spain Dpto. Comunicaciones, UPV, Camino de Vera S/N, 46022 – Valencia, Spain
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[email protected] This is a preprint of an article whose final and definitive form has been published in the Journal of Mathematics and Music (JMM), Taylor & Francis. To cite this article: Luis Nuño (2020): A detailed list and a periodic table of set classes, Journal of Mathematics and Music, DOI: 10.1080/17459737.2020.1775902 To link to this article: https://doi.org/10.1080/17459737.2020.1775902 Published online: 17 Jul 2020 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.