This paper presents a generalization of the well-known neo-Riemannian group PLR to the classical five types of seventh chord (dominant, minor, half-diminished, major, diminished) considered as tetrachords with a marked root and proving that it is isomorphic to the abstract group $S_5 ltimes mathbb{Z}_{12}^4$. This group includes as subgroups the PLR group and several other groups already appeared in the literature.
On the Group of Transformations of Classical Types of Seventh Chords / CANNAS, SONIA; Samuele Antonini; Ludovico Pernazza. - STAMPA. - 10527:(2017), pp. 13-25. (Intervento presentato al convegno Mathematics and Computation in Music tenutosi a Mexico City, Mexico nel June 26-29, 2017) [10.1007/978-3-319-71827-9_2].
On the Group of Transformations of Classical Types of Seventh Chords
Samuele Antonini;
2017
Abstract
This paper presents a generalization of the well-known neo-Riemannian group PLR to the classical five types of seventh chord (dominant, minor, half-diminished, major, diminished) considered as tetrachords with a marked root and proving that it is isomorphic to the abstract group $S_5 ltimes mathbb{Z}_{12}^4$. This group includes as subgroups the PLR group and several other groups already appeared in the literature.
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