The Emergence of the Idea of Irrationality In Renaissance Theoretical Music Contexts

Abstract

This paper intends to consider the interrelationships between mathematics and music in the context of changes in the conception of music during the Renaissance. Western music developed from relying on a cosmological-mathematical-speculative model, in which attention was focused on the rational activity of speculation, to a mathematical-empirical model, in which the main emphasis lay on the quality of the sound itself and on its laws and effects on people. Musical concepts such as temperament, division of the tone, changes in the foundations of theoretical music, mathematical-structural changes in theories of ratio and consequently the emergence of the idea of irrationals and number continuum in theoretical music contexts will be considered here in order to understand the substratum of such a change in the conception of western music.