Non-Contextual JQZ Transformations
Initiated by David Lewin, the contextual PLR-transformations are well known from neo-Riemannian theory. As it has been noted, these transformations are only used for major and minor triads. In this paper, we introduce non-contextual bijections called JQZ transformations that could be used for any kind of chord. These transformations are pointwise, and the JQZ group that they generate acts on any type of n-chord. The properties of these groups are very similar, and the JQZ-group could extend the PLR-group in many situations. Moreover, the hexatonic and octatonic subgroups of JQZ and PLR groups are subdual.
KeywordsNeo-Riemannian group PLR-group JQZ-group Generalized interval systems Lewin Parsimonious voice leading
We thank anonymous reviewers for valuable remarks and Thomas Noll for comments that greatly improved the manuscript.
- 7.Fiore, T., Satyendra, R.: Generalized contextual groups. Music Theory Online 11(3) (2005)Google Scholar
- 12.Hyer, B.: Tonal Intuitions in Tristan Und Isolde. PhD diss., Yale University (1989)Google Scholar
- 14.Jedrzejewski, F.: Permutation groups and chord tesselations. In: ICMC Proceedings, Barcelona (2005)Google Scholar
- 15.Lewin, D.: Generalized Musical Intervals and Transformations. Yale University Press, New Haven and London (1987)Google Scholar
- 16.Riemann, H.: Handbuch der Harmonielehre. Breitkopf & Härte, Leipzig (1887)Google Scholar