@article{ABDOUNUR_2016, title={Emergence of geometry and conceptual changes in theory of ratios in theoretical music in the 16th century}, url={https://www.revistas.usp.br/khronos/article/view/134553}, DOI={10.11606/khronos.v0i3.134553}, abstractNote={The end of the 15th and the beginning of the 16th century witnessed intense structural changes in the conceptions underlying ratios and proportions as well as a significant extension in the spectrum of techniques used in theoretical music. In this context, changes in the conception of ratio brought about the strengthening of the arithmetization of theories of ratio and also the use of geometry as an instrument for solving structural problems in theoretical music. The sixteenth century represented thus a major revolution in the production of treatises on theoretical music and saw, in distinction to the Pythagorean tradition, the introduction of geometry as a tool not only to solve problems such as the division of the tone but also to solve theoretical problems related to the systematization of the temperament, symbolizing a substantial conceptual change in the mathematical foundations of theoretical music and eventually in the theory of ratios.}, number={3}, journal={Khronos}, author={ABDOUNUR, Oscar João}, year={2016}, month={jul.}, pages={81-92} }