Proporción y música: el monocordio y la escala pitagórica traspuestos a la guitarra

Abstract

The present work intends to collect information regarding the articulation that exists between mathematics and music, since a relationship between these fields is observed that in many cases is forgotten. In addition, the purpose is to establish the use of proportion using two musical instruments: the monochord and the guitar. To achieve this, it is necessary to understand the influence that the proportion has had on these two instruments, to understand that it is possible to be observed from the lengths that the strings of the instruments conserve and depending on the distances in which they are pulsed, they can emit different sounds. which will present a proper relationship of proportionality. To observe this proportion in the sounds of the strings, it is desired to establish the history behind these instruments and how their construction has been permeated by the use of mathematics, since in ancient times music was observed as a necessary discipline in education. To further develop this idea of ​​the liberal arts, it is necessary to understand that in antiquity a set of knowledge called "quadrivium" was handled, which is understood as the four paths, that is, knowledge that grouped arithmetic, geometry, space and music, this gives greater strength to the intention of this text to look at a mathematical concept from music. To account for this, three chapters are presented divided into: theoretical framework, scales and guitar and conclusions, in order to collect the necessary information that allows to demonstrate the proportionality in the monochord and in turn, how this concept and instrument is linked with the guitar. The first chapter will present the background and conceptual references on monochord, Pythagorean scale, guitar, proportionality, among others. In the second chapter it will be presented in two sections, the first one has information regarding the scales 5 that are related to the two instruments to work and also to the Pythagorean scale, this being its starting point; The second section tells about the guitar and its history, how it is related to the monochord and the Pythagorean scale, allowing us to observe proportionality through the instrument. Finally, the respective conclusions will be presented on the relationships that can be established between the instruments, the scale and the concept of proportionality.