What relation is there between Maths and Music?

Before explaining the relation between Maths and Music, it is important to know that sound is a wave and that the sound frequency is what defines the musical note. But what is a frequency? It is the repetition of something, having the time into account. Let’s think about a bicycle wheel that spins. f it takes the wheel a second to complete a turn, it means that the frequency of that wheel is “a turn per minute”, or “one hertz”. Hertz (HZ) is just a given name so as to represent the frequency unit.

Having in mind that sound is a wave (think about the string of the guitar that vibrates), if the sound wave completes 10 oscillations in a second, its frequency will be 10 HZ. For each frequency, there is a different sound. The musical note A, for instance, corresponds to a frequency of 440HZ. What about Maths? When does it make part of all this? Pythagoras noticed (through the vibration of a string) that when a frequency is divided by 2, the note remains the same. For instance, the musical note A divided by 2 – 440 HZ : 2 = 220 HZ – keeps on being the note A, but an octave lower. If the aim was to obtain an octave higher, it would be enough to multiply by 2.

But Pythagoras not only divided the oscillations by two but he also decided to try what the sound would be like if the ring vibration was divided into 3 equal parts. Then he noticed that a new different sound came out and it wasn’t the same note both if it was an octave lower or higher, but a different note, indeed. That was when the musical note G appeared. After having noticed that these notes were harmonic, he kept on proceeding from that note G on. So, he divided that piece of string in 3 parts and he found the note D. These sounds, in spite of being different, matched with the previous ones giving rise to a pleasant harmony, because the shown divisions have mathematical connections and our mind likes logical relations that are well defined. Thus, he kept on doing subdivisions and he mathematically matched the sounds, giving rise to scales that, later on, stimulated the creation of musical instruments that could reproduce those scales.

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