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 the acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this article, 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 the visual arts.

数学，更广泛地说是计算科学，介入音乐的几个方面。数学描述了作为物理形式工具的声音的声学特性，以及音乐本身的成分结构和策略方面的问题。数学也可以应用到整个制作音乐的，从分数来表现，组成结构连接到声音的声学现实。而且，手势的精确概念在理解音乐演奏方面起决定性作用。在本文中，我们应用类别理论的一些概念来比较乐团音乐家的手势，并研究乐团与指挥之间以及听众与指挥/乐团之间的关系。为此，我们将介绍手势相似性的概念。所使用的数学工具可以应用于手势分类，以及音乐和视觉艺术之间的跨学科比较。