A matemática na música: divisibilidade do compasso

Abstract

This work presents a study on the relation between music and mathematics, highlighting the great mathematicians involved and their contributions to the evolution of the theoretical musical study. Also, a theoretical response was sought to a questioning of the author on the impossibility of filling a compass 4 4 without using repeated figures or point of increase,which mathematically means to study Sn = 1 + ½ +¼ + ⅛ + ... + 1 2n e lim n!1 Sn. Subsequently it was observed the existence of a Zeno paradox, on the arrow reaching the target, and rewritten in musical timings to be answered in a way analogous to the problem of filling a compass 4 4 . In addition, the work studied the Pythagorean scale and simplifications presented by Gioseffo Zarlino, as well as Marin Mersenne’s smooth tuning system. Afterwards, the length of a rope and its subdivisions in each scale was compared and the characteristics of each one were observed. The frequencies of the musical notes on the tempered scale and the audible capacity of the human ear were analyzed. The results were presented in a program developed in VBA language to assist in the construction and study of a monocord. Also presented was a proposal for a high school class involving music and mathematics. It was concluded that the relationship between music and mathematics generated great results and revealed that there is still much to be explored of the beauty and accuracy that both provide together.