This article centers on the phenomenon of tipping points—a case of extreme pulse elasticity—in music performance, and the dynamic interplay between tonal structure and musical timing. The article presents the idea and principles of tipping points. Examples illustrate three types of global and local tipping points: melodic, boundary, and cadential. Focusing on cadential tipping points, the article considers the role of tonality in a number of examples, thus bridging the subject of tipping points and prior work on the modeling of tonality. The spiral array model for tonality is described, including how the model traces the dynamics of tonal perception. A real-time implementation of the model is applied to cadential tipping point examples to visualize the effect of tipping points on tonal perception. The analyses show how tipping points influence tonal perception—clarifying, focusing, and exploiting harmonic function, in the case of cadential tipping points, to evoke tension and shape narrative structure.
Playing with the Edge