The Golden Ocarina

The cognitive science guy in me has always been interested not only in learning how we can apply videogames to new learning contexts, but what games tell us about fundamental aspects of how we learn. That is, are there deep biological, social, and cultural ways of perceiving games that we need to take into account when designing them? What are our internal structures and how do they facilitate how we learn to play certain games? Lest you fear I’m going to get all academic in this post, don’t worry — this is really just a post about the music of Zelda.

A clever little analysis by Christian at The Tanooki has been making the rounds of gaming blogs in the past few days. He interpreted the music of various Zelda games by looking at how the “golden ratio,” or approximately .618 (a number that crops up in many places, from Fibonacci series to da Vinci’s famouse Vitruvian Man) might be useful in interpreting why many find that game’s music so appealing. Christian explains:

So what does this have to do with music? More specifically, what does this have to Zelda music? Well, the golden ratio is thought by many to represent a ratio of natural beauty. Buildings, human faces, and musical compositions that exhibit this ratio tend to be considered “beautiful,” regardless of whether or not the beholder realizes the presence of the Golden Ratio. In music, the golden section can be the measure that’s located at .618 the length of the song, and/or it can be the measure .618 the length of one section of the song, or the melody, or whatever. The fact that something significant lies at this point, dividing the musical piece or part of it into golden proportions seems to have a subconscious effect on the listener. The song seems to be a little closer to perfection, and the golden section is that “something” about the song that people aren’t sure why they love it. I’m pretty sure if you went through the top Billboard songs and checked, a good number of them would have some Golden Ratio significance.

Christian finds several examples of golden ratios in Zelda music, tracking significant moments in several songs to the “golden section” and thus concluding that perhaps one reason many of us love these games has to do with the occurrence of well-crafted music that makes use of the “golden section.” (Fair warning: There are some Twilight Princess spoilers snuck in there, so be careful!)

So, is there something here, or are analyses like these just finding what they’re looking for? Christian makes the argument that these structures in music occur; taking it for granted that he’s onto something, how might this reflect something fundamental about the way we perceive music? Or the attachment we get to certain games due to some kind of unconscious perception of golden ratios in the music? It seems obvious that, like with all other media, we don’t come to games without a set of preconceptions and expectations. Maybe Christian’s on to a way we structure that information?

I’m personally not convinced that this particular approach (unsystematically applying the golden ratio/golden section lens to whatever songs he felt like applying them to) has legs. It seems as though he cherry-picked both the songs he used as well as what he considered to be significant moments in each. I’d love to see a larger survey of game music, as well as a less subjective approach to determining what counts as an important part of a song. Regardless, it’s a fun way to think about the relationship between games, music, and our perceptions of beauty.

Edit: Whoooops, looks like a reader of Christian’s blog pointed out that the “golden ratio” is really 1.618 and not just .618 after all, which a quick Wikipedia check shows is correct. Was Christian just finding what he was looking for? Looks like we’ve answered that question.

Edit #2 Orrrrr not. As an intrepid comment-poster on Joystiq points out:

Oh, yeah, I forgot. Sometimes when people say “golden ratio” they mean the inversion of what I did, meaning, instead of AB/BC, they mean BC/AB, which is:
1/((1+squareroot(1+4))/2).

That amounts to:
0.61803398874989484820458683436588

So, okay, .618 is back in the game.