Mathematics and Music: In Search of Harmony (part 10)


This paper aims to show the history of the discoveries of relationships and the importance of the interdisciplinarity of mathematical music.

We realize that it was 2500 years ago when the first manifestation of music's interaction with mathematics occurred. Later the relations between these areas go through moments of tension and rest as a 'music', dynamizing with the Temperament. Just as the ranges presented cannot produce the sounds mentioned and we may be able to construct new ranges capable of performing such an exercise, the constructed scales are unable to represent feelings or scenarios that may be expressed in other systems.

In this sense, the musical universe still has many possibilities in its expansion process with the construction of other scales, as well as broader languages, in which possibly different abilities can interact with music and mathematics, contributing not only to the example presented. of scales seasoned with an arbitrary number of notes, but through various other means that may or may exist.

The purpose of this research was to compare the reading of certain facts from the theoretical conceptions, allowing to unveil natures and collective flows not only about the subject in question, but the dynamics of scientific development.

An art form will never be objective and precise to the point of unanimity, but the symmetries and beauties observed in the laws governing the combination of mathematical structures used in the description of sounds, in general, which allow the sound spectrum of each musical instrument to be analyzed. are closely related to the area of ​​music known as Harmony. In this way, physics and mathematics are also able to show and describe, from an objective approach, the possibilities of infinite sound combinations created by a genius such as Johann Sebastian Bach, for example. The delicacy of the sound constructions of the great masters of music can be seen rather than heard in the analysis of the sounds of their works and in the perfect balance between the waveforms instinctively combined to form them. Listening to some of the "canonical works" of famous composers, we may consider them privileged to be able to express and / or create such beautiful emotions and "sound images", some perpetuated over centuries, that could be transmitted to others through art. from music. At the same time, as we study the history of science, we see that no less privileged are some of history's most important physicists and mathematicians. They were pleased to discover natural laws and phenomena, leaving us with powerful tools for understanding that same nature. It is the perfection of these tools and laws that allows us to look at Music from a different perspective, a different prism, uniting the wonderful worlds of Art and Science.

- ABDOUNUR, Oscar João. Mathematics and Music: The analogical thinking in the construction of meanings. São Paulo, 2002, 2nd Edition. Scripture Publisher.
- BOYER, Carl, Mathematics History, Sao Paulo, 1974, Ed. Edgard Blucher
- EVES, Howard, Introduction to the history of mathematics, Sao Paulo, 1986, Ed. Edgard Blucher

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