In short, the formula illustrates a relationship between the parts and the whole of anything from buildings to faces, paintings, apple pie, and bunnies. Artists and thinkers such as Leonardo da Vinci and Salvador Dalí have known about this ratio and incorporated it into their most famous works. Whatever exhibits proportions close to the golden mean seems more beautiful, satisfying, and memorable to us. Music is no exception, and this article shows that composer Koji Kondo has incorporated the magical formula into several songs from The Legend of Zelda series.
It's an interesting theory and certainly a great excuse to use when your grandmother wants to know why you listen to the Minibosses so often. But the real question is: do we like a game's soundtrack because of the music itself, or because it accompanies a great game?
[Update: TheTanooki has posted a follow-up article explaining the golden ratio in more detail and answering a few reader questions.]