How maths is (quite literally) music to our ears

When it comes to music, most of us have strong feelings: there’s the stuff we love, and the stuff that immediately makes us smash the ‘skip’ button. Still, setting aside questions of taste, what exactly is it that makes a piece of music sound pleasing to the ear? And how might we exploit this knowledge if we hope to one day make music of our own?

The answer might surprise you: how music works and why certain notes sound better together has a lot to do with a subject that some musicians might consider outside their expertise. That’s right: if you want to really get music, you’re going to have to brush up on your maths. To get you started, here are 5 ways in which maths can improve your appreciation of the tunes you love.

Maths is the secret to metre

Rhythm is one of the fundamental building blocks of music. It organises notes of music in time by supplying a ‘pulse’ that animates a song,


A metre (or time signature) is one tool for defining rhythm, and it relies on maths to make its presence known. For example, a waltz has a ‘3/4’ metre, which tells us that every bar has 3 quarter-note beats.


What happens next is a matter of addition. For example, one bar of a waltz could contain 3 quarter-note beats or 2 quarter-note beats (or crotchets) and two eighth notes (or quavers). In other words, the metre tells composers which fractions they can add together to create a melody with a specific rhythm. Break those rules and a piece of music can quickly fall apart!

You can’t tune an instrument without proportions

The maths of tuning an instrument can get pretty tricky, but it starts with the type of twelve-tone scale we described above. To produce complex music, it’s important to replicate that scale on an instrument, be it a guitar, a piano, or a theremin. This means ensuring that the pitches produced by an instrument, such as when you strike a piano key or strum a guitar string, maintain a fixed relationship to each other. The strings on a conventionally tuned guitar, for example, are each ‘one fourth’ away from each other. Don’t mind the jargon: it’s another way of saying that, once again, the mathematical principle of the ratio is helping musicians express themselves in a consistent and musical way.

Harmony is a matter of thirds, fifths, sevenths, and octaves


Okay. If you’ve read that heading and you’re not a musician, you might be wondering what on earth it could possibly mean. Let’s make it easy: harmony describes the relationships between notes, and harmonisation refers to the process whereby certain notes sound pleasing together (such as the C, E, and G that make up a C Major chord).


It won’t come as a surprise that harmonisation is as mathematical as it is musical. Indeed, musicians talk about thirds, fifths, sevenths and so on because these terms describe ratios (there’s that term again) that occur between notes that have a sympathetic relationship with each other. There’s an elaborate science devoted to harmony, so look it up if you want to take a deep dive. For now, simply know that, without harmonic ratios, your favourite songs would sound far, far worse!

Music, like maths, is all about structures and patterns

In every area of maths, be it algebra or calculus, you’ll be learning how to use numbers to define patterns and structures. Indeed, the notes on a piece of sheet music are much like the mathematical symbols that we use to describe different sorts of relationships. But it goes further than that: as we’ve seen, ratios and fractions provide the building blocks of music.


Will a beautiful song still sound beautiful even if you don’t ace a maths test? Of course! But understanding the maths behind music will help you better appreciate the elegance of a winning melody and maybe, one day, even help you write one of your own.


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