Mathematics and Music

Mathematics and Music have gone hand-in-hand since the early European Civilization. The deeper one looks for connections between mathematics and Music the more one will find.

The pure study and analysis of Mathematics began in 1600 BC; it was considered an art as it was studied just for the sake of amusement back then. The study of mathematics as a subject begins the Classical Period (600 - 300 BC), when the Pythagoreans originated the word Mathematics. The major role was played by Aristotle, Plato and Pythagoras in detailing the connection between Music and Mathematics. The education devised by them was called Quadrivium which was composed of subjects like - Arithmetic, Geometry, Music and Astronomy. This field of education was then visible in Greek literature; it was this time when theoretical Music grew as an individual subject and was no longer studied with math. But many individuals still studied both and discovered their philosophies through it.

In the beginning Mathematics was less theoretical and more applicative, it initially was a tool, an expression, an understanding or just simply a staple concept for people which was subconsciously in command. It was in the later centuries that Mathematics was constrained to just theories. The thought process linked in understanding Mathematics & Music requires similar contemplation and abstract thinking. There is a certain harmony in devising solutions and theorems, these solutions should flow naturally to one just as Music flows naturally to one’s heart.

The popular Greek Mathematician Pythagoras developed the Pythagorean Scale using the ratio of integers to find successive Music intervals. He used simple mathematics to find further intervals and how every note interacts with another. This was a crucial step in the era of Music and instrument creators regard these Pythagorean intervals as the purest of the bunch.

Music is not just notes but an intricate set of rhythms and melodies, where arithmetic and geometric sequences can be found if examined carefully. Leonardo Fibonacci’s timeless Fibonacci Sequence gave rise to what's known as the "Golden Ratio", which makes any piece of art aesthetically pleasing. Unsurprisingly, it is continuously used in Musical pieces, regardless of the intent of the composer. The climax of a song is usually the point where the golden ratio is often found, among the ratios of the intervals. After analyzing the works of prominent Musicians such as Mozart, Beethoven and Debussy, the Fibonacci Sequence can be found in their pieces, which is an exciting revelation.

French composer Jean Phillepe Rameau established a concrete connection between Music and mathematics. “Music is a science which must have determined rules. These rules must be drawn from a principle which should be evident, and this principle cannot be known without the help of mathematics.”, Rameau said. He further confesses that his ideas were detangled by the help of mathematics. He believed that the infinite sequence of positive integers is elegantly contained in nature as harmonic frequencies.

The definition of Mathematics as an art is subjective and can be best explained through one’s personal view and historical context. Mathematics was developed diversely throughout the globe and accepted for its authenticity and ambiguity. Mathematicians and Artists both are creators and love expressing their opinions and ideas. Both of them grow individually yet follow the same rules. Being different didn’t stop either of them and changed their perception of the world around them.

Mathematics and art are related in a variety of ways as Mathematics has itself been described as an art motivated by beauty. The connection between Poetry and Mathematics is immense as one of the primary characteristics shared by many forms of poetry and Mathematics is the use of formulas. Hence, this study argues that mathematics can be an artistic invention, and need not always be thought of in a scientific context.

The relationship between Mathematics and Music has been immense and incredibly interesting. Its history is of around 3000 years which includes a large number of mathematicians and Musicians. The most important thing to keep in mind is that mathematics is not simply a way of solving problems or proving concepts and Musical composition is not only a method of organising sounds. The beauty of both disciplines is how seamlessly they can work in tandem to enable us to explore and express our ideas.

A Literature Review by

Kishan Vagadia

Radhika Bhat

Vedant Malgaokar

Haya Jafri

Shailja Gajarmal

Cover Source- http://eprints.ma.man.ac.uk/1548/1/cov