Illustration by Louise Flanagan

We like to keep art and science separate in our minds. Art is expressive and free, whilst science is bound by rules and rigidity. But music lies on the cusp of these descriptions. Music itself is always governed by the laws of mathematics, and interacts with neural communication to affect our thoughts and emotions, and some would argue, our very nature of being.

Anyone who has played a music instrument can affirm the importance of timing in playing music. Timing of music refers to the beat – how the beat is split within sections of the music, do you count the music in twos, threes, fours and so on. When playing, listening or dancing to music it can be instinctive to count to the beat. Even though we don’t think it, the timing of music is all about the math.

Different rhythms require the beat to be split into different units of measurements, into halves, quarters, a half plus a quarter. Every single rhythm you hear is a combination of different fractions combined together. For some rhythms, the beat isn’t split at all, but combined with the next to give notes of longer value, one beat plus one beat equals two beats.

Timing can be sped up or slowed down, so one beat for one song can be longer than in another song. Longer beats are associated with slower songs, whilst shorter beats with faster songs.

Less obvious perhaps is the maths behind the melody. Melody is a sequence of musical notes. Mathematics dictates what sequence of notes sound best. Mathematics also dictates what notes sound best when played together. Notes are arranged on a scale and the distance between the notes on the scale determines whether or not they sound good together. Every note resonates through the air at a different frequency, when two notes are played at the same time, it is the difference in frequency between them that determines whether or not they sound good to the ear.

The difference in frequency also dictates what note sounds best when played directly after another note. We all know what sounds good; it’s an inherent ability, and is why the sound of someone sitting on piano sounds truly awful to the ear.

In music we talk of the “ear”. Phrases like “you’ve got such a good ear for music” get bandied about all the time. When it comes to music, the ear doesn’t actually have too much of a big role to play. The ear is where sound waves come in, and resonate at different frequencies and is sent away to the processing centres of the brain where what we’re hearing is worked out and then relayed to our conscious as music.

Like many things in our lives, it’s the brain that does a lot of  the work when music is concerned. How do we figure out if we like a piece of music? Why do some songs make us feel blue whilst others make us want to get up and dance as if no-one is watching? Why do certain songs bring back specific memories? It all comes back to the brain.

Dopamine is a chemical in the brain associated with a great number of tasks: love, chemical addiction, feelings of pleasure, and so it’s not terribly surprising that this chemical has been identified to be released when people listen to music. Even more specifically, the chemical has been found to be released in the reward pathway of the brain, the area associated with pleasure. This same area responds to food, sex and drugs, so… sex, drugs and rock ‘n’ roll.

Music is based on mathematical patterns. Songs where the musical patterns are predictable are often deemed boring and don’t make it to the big time. But songs where this pattern gets broken, and does not go as expected have been shown to elicit greater dopamine release when the pattern returns and thus are associated with greater reward. The music is hailed as great and pleasurable and the musician sky rockets to success.

It is the anticipating, the waiting for the return of the pattern that gives the most pleasure but how the pleasure of listening to music links to our emotions is not wholly understood. The reward pathway connects to other brain regions which control our emotions, and the surge of dopamine released after the anticipating may be responsible for strong emotional reactions to different musical works.

The reward pathway is also linked to the memory formation pathways of the brain. Activating the reward pathway by listening to music whilst memories are being formed explains why listening to a certain song brings back memories of a rainy day, just because it was raining when you were avidly listening to that song.  

Evolutionarily the reasons behind music being so pleasurable aren’t totally clear. Sex and food have fairly obvious reasons for being important to survival of the species. But what possible reasons could there be behind such a physiological reaction to music?

No solid reasons have yet been agreed upon for humans, but let’s take a look at birds. Take a walk near a wooded area and you will be greeted with the songs of many different birds, singing for all kinds of different reasons.

Birds can identify each other based on their calls, and is often used for this purpose by birds who nest in colonies to locate their own chicks. A bird’s ability to sing is affected by its health. If the bird has been infected it will be unable to sing so well. In this way birdsong can be used to determine sexual fitness and aid mating, as well as to defend territory. By singing, a strong healthy bird can indicate its strength and fitness, warding off potential invaders.

Figuring out the myriad of reasons behind music remains beyond our grasp for the time being. Music is a complex blend of mathematics and mind. It is something so personal that can affect us right to the core of our very being. One day, we shall have a scientific explanation for just how it does so, but for now, we can blame it all on the mathemagics of the music.