# Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

## TL;DR

This paper introduces a novel application of category theory to analyze and compare musical gestures in orchestral performance, providing a mathematical framework for understanding relationships between musicians, conductors, and audiences.

## Contribution

It applies category theory to define and analyze gestural similarity in music, bridging mathematical structures with musical performance and perception.

## Key findings

- Defined the concept of gestural similarity using category theory
- Provided a framework for classifying musical gestures mathematically
- Suggested interdisciplinary applications to visual arts

## Abstract

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.