AN EDUCATIONAL / HISTORICAL APPROACH IN MATHEMATICS AND MUSIC

In this study I shall consider educational aspects of the development of ratio and proportion, fo- cusing on the arithmetization undergone by these concepts in the light of the relations between mathematics and music. Since such relations, even if confined to the context of ratio and pro- portion, are fairly wide-reaching and also that the process of arithmetization is quite complex, we shall concentrate mainly on the instructional aspects of a structural peculiarity presented in such a fascinating dynamics. This peculiarity is the so-called compounding ratios , a curious fea- ture present in the structure of ratio since the Classical Period whose irregular transformation into the operator multiplication is quite representative of the importance of theoretical music in the arithmetization of ratios. As a consequence we shall also point out features of the differences between identity and proportion , which are capable of being didactically explored with a math- ematical-musical approach.