09/03/2020

Music and Mathematics is the theme of the 16th edition of OBMEP.

Foto: Reprodução G1

You may not understand music. But you don't need to be an expert to notice that an instrument can emit different types of sounds if the string is whole, divided in half or in three parts. And the answer to this lies in mathematics! This almost imperceptible magic between musical notes and numbers is the theme of the 16th edition of the Brazilian Mathematics Olympiad for Public Schools (OBMEP) , which today (20) reaches its last day of registration.

Throughout history, music has captured the interest and ears of many famous mathematicians. Galileo, Descartes, Huygens, and D'Alembert even wrote treatises on composition. Conversely, well-known musical scores have contributed to solving important mathematical problems, such as the vibrating string problem that led to the theory of Fourier series.

One person closely following this topic is IMPA postdoctoral researcher Vitor Guerra. Since 2015, the computer scientist has been using mathematics to analyze the complexity of musical networks in classical music. His research began during his doctoral studies, after he learned about the ChucK programming language, developed by Ge Wand, creator of the laptop orchestras at Princeton and Stanford universities in the United States.

For Vitor, musicians, mathematicians, and poets have something valuable in common. “We possess an inner ear that, in some conscious way, hears, follows, and counts properties such as frequency, quality, pitch, and duration of sounds and their combinations,” he assesses. “That’s what fascinates me about studying music and mathematics.”

The good relationship between them was also the subject of an episode of the Jornal Nacional series on mathematics . Featuring IMPA's director-general, Marcelo Viana, the four special reports broadcast by TV Globo in November 2017 showed how science is embedded in people's daily lives, often without them realizing it, as in music.

The series presented another definition for musical notes. Why not think of themas numbers in motion ? Viana explained the connection between sounds and fractions. “When you have a full string on an instrument, you have a note of a certain frequency. When you place your finger on it, the effect is that the string becomes half its length and the frequency doubles,” explained the director-general of IMPA to reporter Pedro Bassan.

The report also included the following challenge: if you don't like numbers, try spending a day without them . Those who think the result would be positive are mistaken. "Mathematics is a great friend," Viana stated.

OBMEP participants know this well. Experts in mathematics, they prepare for a competition that values reasoning, not formulas. The first phase of the exam is on May 26th. Until then, listening to music can be a good way to think about mathematics, even during leisure time.