Emergency of geometry and physics in the historical process of the development of the theorical music in the Renascence

Abstract

This research aims at the emergence of geometry as the fundament for the treatment of structural problems in theoretical music in the Renaissance. Since Antiquity throughout the Middle Ages up to the Renaissance, western theoretical music developed from a cosmologic-arithmetic-speculative understanding based on the Pythagorean arithmetic, according to which the attention was focused mainly on a rational activity of speculation; to a mathematic-empirical comprehension founded on physical principles, which began to include the use of geometry as an instrument for the solution of its structural problems, a comprehension in which music was studied by means of its laws and effects on people and was seen as an experimental science. Such a change comprises mathematical structural modifications in musical concepts such as division of the tone, temperament, consonance, nature of the sound, as well as in theories of ratio on the fundaments of theoretical music; modifications related to the need of geometry and physics in approaching theoretical music. This proposal intends to analyses how such a tension between, at one hand, the practical needs, both from mathematics and from music, in the late Middle Ages and early Renaissance; and at the other hand, a strong arithmetic-speculative Pythagorean tradition contributed in the process in which physical principles began to fundament acoustic-musical phenomenon and in which geometry turned to be an instrument for the theorization and solution of structural problems in music. (AU)