Is there any relationship between Mathematics and Music? Come to think of it, examining it carefully, it looks like it has nothing to do with it! But actually there is! Math and music have a lot in common!
You've heard of Pythagoras, Archytas, Aristoxenes and Eratosthenes? All of them were great mathematicians, developers of mathematical theories that are so important that they are still used today. But something you probably don't know is that they were also music theorists, responsible for great advances in the study of music. Although musical scales were created in different ways in different places around the world, these men became known as the ones responsible for creating them. For this creation, they used mathematical concepts and ideas, such as the golden reason.
You may have heard of musical scales as we know them and use them today:
C, Re, Mi, Fa, Sol, A, Si, C
This sequence was once known as Pythagorean range, in honor of Pythagoras.
Depending on how a guitar string vibrates, we have a different musical note. Each of them can be represented through a fraction. Let's see below:
Of: 1
1
Re: 8
9
Mi: 6
81
Fan: 3
4
Sun: 2
3
There: 16
27
Yes: 128
243
Of: 1
2
Youyou can see that the numbers in the numerators are all powers of two, and the numbers in the denominators are powers of three (with the exception of the Fa, that the order is contrary). Let's see:
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
26 = 64
27 = 128
30 = 1
31 = 3
32 = 9
33 = 27
34 = 81
35 = 243
The Pythagoreans used the numbers two and three because they believed they were special numbers, because through them any number could be generated. Therefore, they should be present in Mathematics and Music.
It is worth remembering that the sequence we describe as the fractions that represent each musical note has undergone several changes since the time of the musical theorists we commented on. But even today fractions are used to represent musical notes.
By Amanda Gonçalves
Graduated in Mathematics
