Abstract
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 language | English (US) |
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Pages (from-to) | 37-51 |
Number of pages | 15 |
Journal | Journal of Mathematics and Music |
Volume | 2 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2008 |
Keywords
- Consonance
- Counterpoint
- Dichotomy
- Dissonance
- Dodecaphonism
- Schönberg
- Series
- Symmetries
- Tonality