Among the qualities that distinguish dance from other types of human behavior and interaction are the creation and breaking of synchrony and symmetry. The combination of symmetry and synchrony can provide complex interactions. For example, two dancers might make very different movements, slowing each time the other sped up: a mirror symmetry of velocity. Examining patterns of synchrony and symmetry can provide insight into both the artistic nature of the dance, and the nature of the perceptions and responses of the dancers. However, such complex symmetries are often difficult to quantify.
This paper presents three methods - Generalized Local Linear Approximation, Timelagged Autocorrelation, and Windowed Cross-correlation - for the exploration of symmetry and synchrony in motion-capture data as is it applied to dance and illustrate these with examples from a study of free-form dance. Combined, these techniques provide powerful tools for the examination of the structure of symmetry and synchrony in dance.