Songs represented graphically

It’s Club Math from KCC with another math write-up. The last article we published examined the nature of math. Included in the article was an explanation of the omnipresent Golden Ratio and Fibonacci Sequence. We came to the conclusion that math, indeed, imitates nature. Now we discuss more math within nature, as long as music is considered natural.

I never knew that there was math within music; I couldn’t even begin to figure how there would be. After a rudimentary understanding some trigonometry, though, I was hinted at the possibility of music being mathematical. The graph of y=sin(x) and y=cos(x) (the basic sine and cosine trigonometric graphs) are cyclical waves – like light waves, x-rays and even sound waves. The only problem is that y=sin(x) would not be a discernible sound. The solution: y=sin(x) can be manipulated in a way that it can ditto a certain note; this was an advance towards knowing the math behind music.

So we now know that any note can be represented by a corresponding sine graph. Then how about entire songs? Whole songs couldn’t not be represented graphically until the advent of Fourier Analysis, given to us from the work of mathematician and physicist Joseph Fourier. What he concluded was that sounds that are beyond the fundamental building blocks can be made from these fundamental sounds; the process of reconstructing a more complex sound from the fundamental sounds is called Fourier synthesis.

This means that songs can be represented graphically — music is mathematical! In fact, most of the songs heard today through digital media, including mp3s and digital TVs , is communicated as a sum of the fundamental sounds. This is  evident proof of why math is beautiful. Surely anyone who listens to music can appreciate this — just another reason to truly love math.