Mathematics and Music

I think maths is beautiful. I've been saying this since I was in my teens and I don't think I'll stop until the day I stop being able to add one and one to make two. At the same time, I understand that a lot of people find maths very abstract and difficult to make sense of. (To me, maths is pretty much concrete, so I've had to actually put effort into understanding that other people don't see the world the same way.)

I also think music is beautiful. I try my hardest to keep an open mind; I frequently fail, but hey, my music taste is now pretty eclectic. Or maybe just random, if you're feeling uncharitable.

Over the summer, I had to write a vacation essay. Quite unsurprisingly, I chose to work on the physics of music. Slightly more surprisingly (at least to me), my friends all thought I was insane for working on something so boring.

I don't blame them; the basic physics of a simple harmonic oscillator is important, but it's not exactly the most exciting thing in the world. And if you find that off-putting, why dig deeper?

Well, I dug deeper because I thought that there must be something interesting down there - and I was right. The physics of music is a huge field, even crossing over with history and psychology at certain points. When I was doing my research, I came across so many things - far too many things to put in an essay - the way that hearing is affected by pressure, the mental maps we make of relations between notes and keys, the way we rely on imperfections in tuning and rhythm to make music what it is, the cold mathematics that meant no stack of perfect fifths could fit in an octave and gave birth to myriad temperaments, and the fractal geometry underlying all music and speech. And more. Music is actually incredibly complex when you think about it mathematically - yes, even those genres you love to bash for being too simple are reasonably complicated. From analysing the frequency of intervals, which can tell you about the character of a piece, to analysing the structure, to actually thinking about making instruments and designing concert halls and everything in between, the amount of physics, mathematics and psychology which goes into making even the simplest of pieces is just mind-boggling.

A lot of people have trouble with maths because of how abstract it is. I'm the opposite: the more abstract the maths, the happier I am. Even if the maths is nearly useless, I don't care as long as it has an internal beauty to it. And mathematical beauty is a concept which is really hard to explain to non-mathematicians - but I think I've found my analogue.

Think of your favourite piece of music ever. Really unpick it in your head - the structure, the instrumentation, the melodies, the harmonies, the chord progressions, the lyrics if there are anyway. Think about how amazingly it's constructed. Think about how achingly beautiful that is. Underneath that, underpinning it all, is mathematics - a simply stunning amount of mathematics, in dazzlingly rich detail. Musical beauty is mathematical beauty put into practice. And when the two intersect and intertwine, words are not enough to describe that beauty.