A Minimal Mathematical Model for Conducting Patterns

TL;DR

This paper introduces a minimal mathematical model for conducting patterns that separates geometric gestures from timing, enabling expressive control and implementation in interactive applications.

Contribution

The model uniquely combines geometric trajectories with a timing law, offering a compact and expressive representation of conducting gestures.

Findings

The model effectively separates gesture shape from timing control.

It can be tuned with a single parameter for different expressive styles.

Implemented as an interactive Wolfram Demonstration and web app.

Abstract

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.