Mathematics and Music from a Historical/Epistemological Perspective: Conceptual Changes

Abstract

The passage from the late fifteenth century to the early sixteenth century witnessed the emergence of geometry as a tool for solving problems in theoretical music and, not independently, changes in the conception of ratios/number underlying theoretical music. In this passage, the musical theorist and mathematician Erasmus Horicius emerged as an important German humanist of this period involved with musical issues. He rescued Greek sources, enabling theorists of his time accessing important fruits of the revival of interest in ancient texts. He was the first, for example, in the Renaissance explicitly to apply Euclidean geometry to solve problems in theoretical music. Among the problems considered, Erasmus proposed a numerical equal division of the whole tone, which implies substantial changes in conceptions of ratios, in particular, towards promoting the emergence of the idea of real number in theoretical music contexts.