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A Minimal Mathematical Model for Conducting Patterns

2026-04-11 21:47:36
Tom Verhoeff
arXiv_RO
   
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.

Abstract (translated)

URL

https://arxiv.org/abs/2604.10356

PDF

https://arxiv.org/pdf/2604.10356.pdf

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