The contemporary divisions of knowledge are familiar to most of us: mathematics belongs with the sciences, music with the creative arts, and philosophy with the humanities. These divisions, in general, seem natural and obvious to us and, despite a growing interest in 'interdisciplinary studies', the work done in these various fields generally hews to the lines that divide them. To point out that these boundaries are historically contingent or that they were erected relatively recently in history is not exactly a novel point. However, while most would acknowledge this, it can be difficult to shed our preconceptions about where these divisions in our body of knowledge lie. As a result, it is all too often the case that we bring these preconceptions with us into our study of intellectual history, especially in the form of assumptions about which topics belong to which fields and the ways in which these topics can interact. The aim of this dissertation is to give an account of a particular issue, the problem of musical consonance, that historically does not fit neatly into the disciplinary divisions with which we are now familiar. In particular, I will discuss 17th century approaches to this issue with the aim of showing that this problem, and the solutions proposed to it, had a wide-ranging influence on a number of areas in philosophy and science
