There are many ways in which Music is connected with Mathematics. In fact, it is incredible to only take a glimpse of that connection. One of the first people to investigate this relation was Pythagoras, around 530 BC. What he discovered is that the lengths of vibrating strings for notes which harmonized musically were in simple numerical ratios. We will explain this later in this article. Let’s begin with the bigger picture and dive into the details later.
What are the mathematical features of music? Four fundamental elements of music are melody, harmony, rhythm, and timbre(sound quality), and each of these elements can be analyzed from a mathematical viewpoint.
Melody is composed of collections of notes, known as keys, each of which can have its constituent notes assembled in ascending or descending order. Such a stepwise assembly is known as a scale, a simple and common example is the scale of C major.
If two or more notes blend together aurally they are said to be in harmony. The numerical ratios for harmony which Pythagoras discovered, can be revealed by simple mathematical analysis of frequencies of notes in the scale.
But what are the music frequencies and their central role in music? Let’s suppose we have some music strings. If these strings are made of the same material, have the same length, and the same thickness, then they will produce the same notes. This means that the strings will vibrate with the same frequency since every note is represented by a particular frequency ( usually measured in Hertz). Hertz represents how many times a sound wave vibrates in one second. So, a note measured at 440 Hz completes 440 vibrations per second. Slow vibrations, or lower values, result in deeper pitches, while faster vibrations (higher values) sound higher.
In terms of harmony again, the ratio for C’ and C is 512:256 (Hz), which is 2:1. Ratios for notes which harmonize together are 384:256 (3:2) for G and C, and 320:256 (5:4) for E and C.
What about rhythm? Well, here the relation between music and maths is even bolder since we enter the kingdom of time. The sequence of the various time values of the notes in each music piece is called rhythm. As a result, we can find the rhythm of each song if we execute only the time rules and exclude the different notes (which compose the melody).
This was a brief introduction to this ancient, yet ongoing, love story and we will dive into more details in our future posts. Feel free to leave a message and ask for specific topics that you want to learn more about.
Until then, let’s see what will change!
Change is the only Constant