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What is the difference in golden ratio air vents on Masterworks and Masters Premium?
The Golden Ratio has fascinated mathematicians since the time of the Pharaohs. It is a mathematical constant (1.61803) that is found repeatedly in nature and has been used by artisans for generations to create art and structure with pleasing proportions. Stradivarius applied the Golden Ratio to define the location of the "f-holes" and proportions of his masterwork violins.
Why do we like certain video game songs more than others? Maybe they’re catchy. Maybe they’re more varied than some of the looped sounds in other games. Or maybe there’s another factor no one’s aware of. More after the break!
I’m currently studying music theory under Dr. Zack Browning. One of the things he stresses is the existence of “golden sections” in contemporary music. What is a golden section? Well, it’s the point determined by the Golden Ratio, approximately 0.618. When you mark a line at this point, the shorter segment has the same relationship to the larger segment that the larger segment has to the whole line.
Another way to look at it is through the Fibonacci series of numbers. It’s the series of numbers where you add the two previous numbers to get the next one. The ratio between one number to the next just happens to be the so-called “Golden Ratio.” You can click the picture to the left to see how the ratio and Fibonacci series work. And for fans of classical art, Da Vinci’s Vitruvian Man has golden proportions all over.
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.
Initially, there were many game themes I wanted to check for a significant golden section. Unfortunately, the Mario songs I checked didn’t exhibit this, but low and behold, several Zelda themes do. It seems most of the pieces that do are written as actual pieces, and not as short melodies meant to be looped over and over, and Zelda games have a lot of those. While I can’t say it’s for sure, Koji Kondo probably doesn’t incorporate the Golden Ratio consciously into his music, but the fact that Zelda music holds more of a masterpiece status compared to Mario music or other video game music likely isn’t a coincidence. Let’s look at the music from The Legend of Zelda.
The Legend of Zelda – “Overworld”
I’m reluctant to start with this, because due to the lack of cinematic-like storytelling during the NES days, the significance of the Golden Ratio in the main Zelda theme is entirely musically based, and I’m pretty sure most of you don’t have a background in music theory. There’s not much else in the music or game that’s easier for you to relate to, so bare with me, and we’ll get to the good stuff afterwards.
The basic Zelda melody – no introductions, no later arrangements – is essentially 20 measures or, simply put, 20 sets of 4 beats each. I’m pretty sure you all know the melody, and could hum it to yourself to double check that length if you wanted. If you take 20 x .618, you end up with the Golden Section theoretically being just after the 12th measure ends (so basically at the 13th measure). If you want to be more precise, you can say that the entire melody spans the equivalent of 80 quarter notes, and the Golden Section should be at 80 x .618, or the 49th quarter note (which is at the beginning of the 13th measure).
So what happens at this point? Well, the melody is in the key of Bb Major, occasionally borrowing from parallel minor scales (e.g., Bb natural minor, harmonic minor). However, at the moment in question, the theme goes into what seems like a major chord built on the flat second scale degree, or a bII chord. Depending on how you interpret the three voices, you could argue that it may be a Neapolitan 6th chord, or N6. While the rest of the theme stays in Bb, placing a bII chord smack in the middle of the theme makes it stick out like a black sheep. What does it do? It adds tension to the theme. Whether you understand music progressions or not, the fact that it’s not a naturally occuring chord in the Bb scale means that your ears hear tension in the chord, and want it to resolve back into the key of Bb. Koji Kondo places this anamoly of a chord right at the Golden Section, making it that much more intriguing.
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