A Minimal Mathematical Model for Conducting Patterns
This work provides a compact representation of conducting gestures for computer music and gesture analysis, but is incremental as it formalizes existing conducting patterns without empirical validation.
The authors propose a minimal mathematical model for conducting patterns that decouples geometry from timing, using cubic Hermite segments and a quintic timing law with one parameter to control expressiveness. The model is implemented in an interactive demonstration and a web app.
We present a minimal mathematical model for conducting patterns that separates geometric trajectory from temporal parametrization. The model is based on a cyclic sequence of preparation and ictus points connected by cubic Hermite segments with constrained horizontal tangents, combined with a quintic timing law controlling acceleration and deceleration. A single parameter governs the balance between uniform motion and expressive emphasis. The model provides a compact yet expressive representation of conducting gestures. It is implemented as the interactive Wolfram Demonstration "Conducting Patterns" and is used in the Crusis web app.