Building Generalized Neo-Riemannian Groups of Musical Transformations as Extensions

Alexandre Popoff

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Musicology and Musical Analysis Diverse Music Education Insights Music Technology and Sound Studies

Abstract

Since the seminal work of David Lewin [1], the field of music theory has seen huge developments with regards to transformational models and their use for musical analysis. In particular, the famous L, R and P operations acting on major and minor triads have been the basic building blocks for neo-

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References

1988Generalized Musical Intervals and Transformations 1996Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions 1997Neo-Riemannian Operations, Parsimonious Trichords, and Their "Tonnetz" Representations 1998Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective 1987Composition With Pitch-Classes 1998Some Aspects of Three-Dimensional "Tonnetze"2002Uniform Triadic Transformations 1998Moving beyond Neo-Riemannian Triads: Exploring a Transformational Model for Seventh Chords

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2015Old and New Isometries between Pc sets in the Planet-4D Model 2012Towards A Categorical Approach of Transformational Music Theory

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