Dualism and the Beholder's Eye: Inversional Symmetry in Chromatic Tonal Music

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3 Scopus citations


This article considers the theme of inversional symmetry as it manifests itself in Riemann's theoretical writings and in late-nineteenth-century chromatic music. It examines the mathematical properties of the concepts of symmetry underlying musical systems and explores how these symmetrical properties can be brought to bear in innovative ways on musical structures. Section 1 of the article provides a historical background by examining Rameau and his proposed laws of tonal harmony which are invariant under four basic operations: reordering, octave shift, note duplication, and chromatic disposition. It also discusses Weber's Roman numeral notation which develops and fulfills Rameau's ideas. Section 2 discusses Riemann's "dualism" as an attempt to incorporate inversion into the Rameau/Weber collection of symmetries. Section 3 examines whether the "second practice" of the nineteenthcentury chromaticism involves inversional symmetry. Section 4 provides a Riemannian understanding of dualism and Section 5 illustrates a contrapuntal approach by examining a Brahms intermezzo.

Original languageEnglish (US)
Title of host publicationThe Oxford Handbook of Neo-Riemannian Music Theories
PublisherOxford University Press
ISBN (Electronic)9780199940530
ISBN (Print)9780195321333
StatePublished - Dec 2 2011

All Science Journal Classification (ASJC) codes

  • General Arts and Humanities


  • Brahms
  • Chromatic music
  • Concepts of symmetry
  • Dualism
  • Inversional symmetry
  • Rameau
  • Tonal harmony
  • Weber


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