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Non-Contextual JQZ Transformations

  • Franck JedrzejewskiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

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.

Keywords

Neo-Riemannian group PLR-group JQZ-group Generalized interval systems Lewin Parsimonious voice leading 

Notes

Acknowledgements

We thank anonymous reviewers for valuable remarks and Thomas Noll for comments that greatly improved the manuscript.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Atomic Energy CommissionUniversité Paris Lumières (CEA-CIPh)ParisFrance

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