Music is Math

Math has always been a fascinating subject to me. Not equations and formulas, but the fact that it shows up everywhere. It’s incredible that concepts that humans have invented, like addition, multiplication, and the like, can be combined to explain facts found in nature. We can use Math to find the reason behind the spiral of snail shells, the number of petals in flowers, and, yes, the harmony of music.

Sound, at a core level, is just wiggly air. It’s the subtle compression and decompression of air around you that your ear senses and then sends a signal to your brain to interpret it as sound. Sounds have pitches, or how high or low it is. We can measure Pitch in Hertz (Hz), or how many times the air wiggles per second.

Music, then, is a group of sounds that “sound good.” But how can we determine what “sounds good”? Is it just some inherent quality inside humans that makes us perceive the beauty in combinations of random noises? Where a philosopher might concur indubitably, a mathematician would say no. And while you should never listen to either too much, I’m going to side with the mathematician on this one. Turns out, two noises “sound good” to us when their pitches have perfect*, simple, mathematical ratios. For example, the ratio of 2:1 Hz between two sounds creates the octave, the most fundamental interval in music. On the other hand, a ratio of √2:1 would sound terrible to our ears.

If this little crash course in math behind the music has interested you, check out this booklist we have put together to get into more detail.

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*Technically, if we followed pure, perfect ratios of pitches to create all of our music, we would break fundamental modern music concepts because not every note would be equally spaced apart. If you’re interested, look into the difference between just intonation and 12-tone equal temperament.