A detailed list and a periodic table of set classes
[EN] 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...
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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.
I am grateful to the Editor Jason Yust and the anonymous reviewers for their valuable comments on the manuscript, which contributed to improve its quality.
Nuño Fernández, L. (2021). A detailed list and a periodic table of set classes. Journal of Mathematics and Music. 15(3):267-287. https://doi.org/10.1080/17459737.2020.1775902 |
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