We often associate music with emotions - many see it as a source of shelter and a safe space. It gives us the unique ability to get in tune with ourselves and - as we commonly like to put it these days - ‘catch a good old vibe.’ Most of us, however, do not understand the technicalities of the music we listen to, of how it has a commonly overlooked, yet profound connection with mathematics.

We hear of rhythms, scales, intervals, patterns, harmonies, overtones, pitches and so on. There is a definite system and method to the production of a musical score. Every piece is divided into sections called measures, and each measure has an equal number of beats. This division of time allows the musician to produce rhythms. Each piece of music has a specific time signature that gives the rhythmic information about the piece. A time signature is like a fraction. Every note and rest in music has a numerical connection, as each of them carries a certain number of beats. Hence, it is imperative for musicians to understand the values of these fractions and notes in order to count their music correctly. Incidentally, counting is one of the most important aspects of creating music.

Clearly, the varied complexities of math are interwoven into all those songs that you play on loop on Spotify every day.

Studies have also found a correlation between math and music skills in students. Slow practise, constant attention to detail, and the discipline it takes to learn an instrument build the foundation for strong mathematical skills. The concepts required to understand topics like fractions, decimals, and percentages are relevant in understanding rhythm.

Perhaps the closest and most important connection between music and math is that they both make use of patterns. As humans, we innately seek out structures and patterns, and music tends to have repeating choruses and sections of songs. Research has even shown that certain pieces of music end up being more popular due to their mathematical structure. For example, Pachelbel’s Canon in D, which is commonly played during weddings, is said to be more popular with people because of its repetitive structure. This could also explain why most chart-topping music that is constantly belted out on the radio are those which are repetitive in their arrangement - it explains the reign of pop musicians in producing one hit after the other.

Everything in music can be studied from different mathematical perspectives. Many scientists and mathematicians have realised this through the course of their careers. In fact, it is claimed that Einstein used to sit down and play music when he was stuck on a mathematical problem!

So the next time you turn on your music, remember the complex system of numbers that are woven into those beats, the technical gift required to create them, and the structures, patterns and symmetry entangled within those poignant tunes.

Upasana Sasikumar