Abstract

Symmetry: Culture and Science
Volume 30, Number 2, pages 137-160 (2019)
https://doi.org/10.26830/symmetry_2019_2_137

SURPRISE SYMPHONIES – SYMMETRY AND SURPRISE IN PITCH STRUCTURES

David Andrew Banney *

* School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia.
E-mail: david.banney@newcastle.edu.au
Web: https://www.davidbanney.com

Abstract: Past research has identified useful parallels between the notion of symmetry breaking in the physical sciences and music. In that research harmonic structures and processes were considered in two general categories – symmetric, disorienting ones on one side, and asymmetric, informative ones on the other. Little attention has been paid to the role of symmetry breaking and information theory in understanding structures that lie in the middle of the spectrum, straddling the dichotomy of symmetry on one side and information on the other. This paper examines pitch phenomena that simultaneously exhibit characteristics associated with information, and characteristics that counter this by increasing rather than decreasing uncertainty. For example, in the setting of a diatonic melody, the appearance of a chromatic note is at once surprising (a characteristic of information) and a cause of more rather than less certainty. It is proposed that such events create a critical point akin to the situation in which a crystal is warmed to a temperature around its melting point, and that the resolution of the uncertainty created by such events is a symmetry breaking process. This phenomenon is seen at a local level in a number of works (Haydn, Bach, Scarlatti and Beethoven), before a discussion of the phenomenon in a global, historical context.