Measuring the Invisible: A Process among Arithmetic, Geometry and Music

Resumen

Abstract: The parallel between music and mathematics abounded in sixteenth-century studies. Referring to the concept of proportions, it was then assumed that theorists considered audible and visible proportions to be analogous. However, when approaching the treatises and focusing on how those processes of mensuration took place, we realise that there were differences concerning the very notion of quantifying. In this paper, we would like to identify the roles played by arithmetic and geometry in the musical tradition through the notion of quantification, departing from the definition of the musical interval given by the most important theorist of the sixteenth century, Gioseffo Zarlino, and identifying the core of musical debates within the realm of mathematics.

Keywords: Mathematics; Music; Optics; Geometry; Arithmetic; Measuring