Music makes me...

I’m not sure how many people realize how much physics there actually is in music. In fact, the art of music is a branch of physics all on its own, called musical acoustics. The mathematics applied to this artistic field actually present beautiful and intriguing sounds that one would never think of directly, but at the same time has already intuitively known.

Here’s an example of what I mean. If you play an instrument, you’re already familiar with the major scale: a series of whole notes that make a pleasing sound. In reality, every note in that scale is repeating sound wave, buffeting the medium around it at a certain frequency. This translates into a musical tone when it hits your eardrum. Yet did you ever consider that, by measuring these frequencies, all of these tones can be connected through the wonderful world of numbers?

YES! MATH!

Consider the note C, which has a frequency of 264 Hz (or in other words, waves per second). One can get the rest of the scale by multiplying that frequency by a certain fraction:

C	D	E	F	G	A	B	C
1	9/8	5/4	4/3	3/2	5/3	15/8	2

Looking closely, there are a lot of neat things about this:

• To get an octave, multiply the frequency by two
• Each fraction can be broken down by a certain denominator
• There is perfect symmetry between frequencies.

The mathematics probably wasn’t obvious, but look at the design of any instrument and you’ll notice that they’re made with this in mind. Hold down the string of a guitar at its exact middle, and you’ve halved the length, thereby multiplying the frequency by two, making an octave.  In pianos, you'll notice that the strings curve up a little like an upside-down parabola. That’s because, well, it does make a parabola, or rather an exponential graph with string lengths that closely follow the mathematical pattern above.

It's so pretty, in a totally mathematical sort of way. 

Of course, there are obviously more tones on a piano than just the eight notes above. Yet every single one of those tones has a frequency. All of the most pleasing patterns, like fifths, thirds, and sevenths, can all be mathematically connected to a base tone to create resonance; it’s beautiful, really. Given that music is just a series of waves, it’s a perfect model for any other wave function in the universe, even all the way down to quantum mechanics.

You think I’m exaggerating? Take a look at Schrödinger’s Equation, the basis for all Quantum Mechanics: 

It looks a bit complicated, no? Believe it or not, this whole thing is just a wave function. It can be simplified down into the same equation that dictates the motion of a spring:

…which gives the motion of a sound wave…

…which is what music is based upon. So, if you understand the motion of sound, you can understand pretty much any wave ever. Isn't that cool? And that’s why music is a wonderful thing.

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PS: if you want even more proof that physics and music are connected in some cool ways, check this video out. As the frequency gets higher, the resonance of the waves changes. It’s pretty amazing: