Hidden symmetries of classical tonality in schönberg's dodecaphonic compositions

Guerino Mazzola, Benedikt Stegemann

Research output: Contribution to journalArticlepeer-review


We exhibit symmetries on pitch classes that are intimately related to major/minor tonality, and then recover essential aspects of such tonality from these symmetries. This fact entails a relation to Schönberg's dodecaphonic series, where their two hexachords consisting of the first and second halves exhibit such symmetries. They are by no means isolated objects; it is shown that they can be thought of as simultaneous expressions of tonal and serial instances. These symmetries define a bridge between two apparently disconnected, and even antagonistic approaches to fundamental compositional designs. We discuss applications of this approach to Schönberg's Piano Concerto, op. 42.

Original languageEnglish (US)
Pages (from-to)37-51
Number of pages15
JournalJournal of Mathematics and Music
Issue number1
StatePublished - Mar 2008


  • Consonance
  • Counterpoint
  • Dichotomy
  • Dissonance
  • Dodecaphonism
  • Schönberg
  • Series
  • Symmetries
  • Tonality


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