Structural transformations in theories of ratio and proportion in theoretical music in the 16th century

• Grant number: 13/20851-5
• Support Opportunities: Scholarships abroad - Research
• Start date: December 11, 2013
• End date: February 15, 2014
• Field of knowledge: Humanities - History - History of Science
• Principal Investigator: Oscar João Abdounur
• Grantee: Oscar João Abdounur
• Host Investigator: Juergen Renn
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Max Planck Society, Berlin, Germany

Abstract

The object of this research project is the theme "structural transformations in theories ratio and proportion in the historical development of music theory in the sixteenth century". Through the analysis of the structural conformation of theories of ratio and proportion with regard to the way in which such concepts were handled as well as the terminology and argumentation assigned to them in treatises of mathematics and theoretical music in the sixteenth century; we intend to evaluate, still in the context of the legitimacy of the Pythagorean-platonic tradition in resisting to such changes; signs of theories that advertise and/or promote the loan of attributes semantically distinct of analogous arithmetic structures; as well as the role of structural problems in music theory such as the division of the tone and temperament in enhancing transformations mentioned above.