This project aims to research on mathematical structural changes in musical thought in the early modern period. In this proposal, the development of theories of ratios in the context of such changes is investigated from the perspective of the interrelationships between practical and theoretical knowledge. From such a perspective, the role of practical knowledge in the transformations of structures of theories of ratios in the modern period and their repercussions on the concept of number can be deepened by investigating the conceptions in the light of which one dealt with structural mathematical problems in musical theory. In this context, the emergence of a tradition concerning the use of geometry in musical theory as well as conceptions of mathematical ratios as continuous quantities towards the identification of ratios with numbers in their modern sense have more broadly caused crucial changes in mathematical structures used by musical theorists mainly from the early modern period. Basically, two dual contexts of questions are at the center of the investigation, both related to the interrelationships between practical and theoretical knowledge. The first context encompasses the problem of why arithmetization of ratios and the intensification of changes in the structures of ratios and proportions could not take place over a long period of time, although such an idea goes back to at least the first century AD, whilst the second context of questions concerns the problem of how such a process leading to the emergence of the modern concept of number could occur in the beginning of the modern period. This project intends to investigate such mathematical structural changes in musical thought in the early modern period and is also an attempt to find explanations for the course of theories of ratios and proportions, as well as of mathematical thought, through an investigation of the epistemological dimension of the development of the concepts mentioned above.
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