In this dissertation I analyze the relations between mathematics, music theory, and experimental sciences from the scientific revolution through the Enlightenment. Music in the early modern period was seen as a mathematical science. More so than other branches of mathematics, music also had a direct connection to human sensory perception. I show that music, interpreted as a kind of “sensible mathematics,” played a crucial though largely underappreciated role in uniting mathematical and empirical European scientific traditions. I describe the upheavals that saw music theory become unmoored and drift away from what came to be known as modern science. During the Enlightenment it landed in the domain of fine arts and aesthetics, a separation we typically see as self-evident today. By elucidating the role of music in the scientific revolution and its aftermath, while emphasizing the shift from premodern musical science to modern physico-mathematical acoustics, I reveal the profound—even paradoxical—tensions between science and the practical arts.