Although Music and Math may seem like two completely different things- music being associated with emotions and creativity while math is associated with being systemic and logical-they actually have many things in common.
The history behind its patterns
Think back to when you learned about the Pythagorean Theorem in school (A squared plus B squared equals C squared). It came from the Greek philosopher, Pythagoras, in the 5th century B.C.E. Pythagoras believed that numbers were the guideline to the universe, including music.
Pythagoras is credited with finding that a string half the length of another will produce a tone an octave higher when hit or plucked. Splitting a string into thirds raises the pitch by an octave and a fifth. Divide it into fourths to reach even higher – you get the idea.
He recognized a new sound that was distinct from the previous one. It wasn’t the same note an octave higher this time, but a separate sound that needed to be renamed. Because these divisions have 1/2 and 2/3 mathematical relationships (our brain prefers clearly-defined logical relationships), this sound harmonized nicely with the prior sound, providing a pleasing harmony to the ear.
This is known as the overtone series or harmonic series, and it is a physics element that affects waves and frequencies in ways we can see and hear as well as ones we can’t.
Exploring the intersection between music and math
Mathematics has existed for centuries, originating in ancient civilizations as it became employed by the Incas, Egyptians, and Babylonians, but was not studied for its own purpose until Greek Antiquity (600-300 BC). Mathematics is a vast topic that has been handled, employed, and studied in a multitude of ways and forms by various nations and civilizations for hundreds of years. It is a subject that is always changing, making it difficult to describe.
A western understanding of mathematics in the twenty-first century is that it is the abstract science of shape, space, change, number, structure, and amount. Mathematicians use rigorous deduction to discover new patterns and hypotheses. To solve problems, they employ abstract thinking, logic, and reasoning. Physicists, for example, explain the natural world using mathematical terminology.
Music, on the other hand, is defined as the art and science of mixing vocal or instrumental (or both) sounds to create a form of beauty and harmony. It is an inherent feature of human existence. Music, like mathematics, has been an intrinsic part of society throughout history. It is a creative means of expressing feelings and ideas and is frequently utilized to convey and depict oneself and one’s individuality. For instance, music has seen an abundance of genres being studied, performed, played, and listened to.
Mathematics and melody
Music theory, the study of how music functions and its qualities, is a fascinating subject that has been researched for millenium. It contains any remark, belief, or understanding of or about music.
Music theorists frequently examine musical language and notation. They look for patterns and structures in composers’ practices, across or within genres, and throughout historical periods.
Music as a language
When the basic general definitions of mathematics and music are compared, it is clear that they are two completely different sciences. Mathematics is a scientific discipline that is full of order, countability, and calculability. In contrast, music is regarded to be creative and expressive.
These two disciplines, albeit apparently disparate, are in fact related and have been for over two thousand years.
Music is, in fact, quite mathematical, and mathematics is incorporated in many fundamental principles in music theory. Music theorists employ mathematics, much like specialists in other fields, to create, express, and explain their ideas.
Mathematical concepts in Music Genres
The golden ratio is a notion seen in music as well. The golden section is found in musical timing and is frequently utilized to induce rhythmic variation or to establish a melodic line.
A song’s climax, for example, is frequently located at the golden ratio (about 61.8% of the way through a composition). This is frequently when dramatic shifts in key or chord structure occur. A 32-bar song, for example, would reach its peak at bar twenty.
The golden ratio is used deliberately in the Schillenger System of Musical Composition.
It is also visible in the opening movement of BĂ©la BartĂłk’s composition Music for Strings, Percussion, and Orchestra Celeste as it occurs in the fifty-fifth bar of an eighty-nine bar composition.
Many of Chopin’s compositions-particularly his Nocturnes and Études-are based on the golden ratio while his compositions became recognized for its musical expressiveness and technical challenge.
Whether Mozart employed the golden section in his compositions is a point of contention. Although Mozart was a musical genius, it is believed that no one knows how he composed his music. Did he draw inspiration from everyday happenings, or did he write musical measures from mathematical equations?
References
- Stewart, James. “Timeline 002: Pythagoras and the Connection between Music and Math.” Vermont Public, Vermont Public, 4 May 2015, www.vermontpublic.org/vpr-classical/2015-05-04/timeline-002-pythagoras-and-the-connection-between-music-and-math. Accessed 27 Jan. 2024.
- “Math in Music – Exploring the Connections | Simplifying Theory.” Simplifyingtheory.com, 2014, www.simplifyingtheory.com/math-in-music/. Accessed 27 Jan. 2024.
- An Exploration of the Relationship between Mathematics and Music. eprints.maths.manchester.ac.uk/1548/1/covered/MIMS_ep2010_103.pdf.
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