Wow. My article looking at golden proportions in Zelda music stirred up some interesting and intelligent discussions across the internet yesterday. Unfortunately, it also brought about some criticism and debate. Reading all the many sites and comments made in response to the article, I felt it was necessary to follow up the article with a little bit more explanation as to the theory and my application of it. I’ll be summing up some of the criticisms I’ve seen and responding to those criticisms. I’m hoping to clear up some confusion as well as address the criticisms I’ve come across, but if anyone has any further questions or comments, please feel free to leave a post on our forums for me to respond to.
0.618 vs. 1.618
My article used 0.618 to find golden sections in music. One big argument against my article was that the Golden Ratio is 1.618, thus nullifying my article. In fact, if you take each number in the Fibonacci Series and multiply it by the 1.618, you’ll get approximately the next number in the series. So what’s up with my article?
Well, a ratio is one number’s value in respect to another. The Golden Ratio is determined by comparing longer and shorter segments of a line. However, if you compare them in a different order, you get the inverse of 1.618 as the ratio. The inverse of 1.618 is approximately 0.618, which still represents the same ratio between the two segments of the line – just in a different order. Also, instead of labelling the entire length of the song as 1.618 and dividing to find the moment in a song where the division should occur (1.000), making the length of the song 1.000 and multiplying by the inverse is a little easier to comprehend, and you still get the same point in the song. For this reason, using 0.618 was still a valid method of finding golden sections in music.
Golden Proportions is a Visual Concept
When golden proportions were first noticed, they were noticed in geometry because they were naturally occurring. They weren’t designed to occur in visual scenarios, they just naturally do. As such, is it any surprise that golden proportions could possibly appear in music? I can’t necessarily prove or disprove a phenomenon or theory, but hopefully that analogy will help you realize that something doesn’t have to be a visual work in order to exhibit golden section proportions.
Preserving original proportions / The 29-second clips
I’m well aware that by trimming the original musical works, I’ve ruined the very proportions of the Zelda music examples that I spent so long to explain. For example, the Ocarina of Time credits music spans 7:07, placing the golden section right at 4:24 when the “Chamber of Sages” motif comes in. If I could I’d place the entire seven-minute recording up there for you to listen to, preserving the original proportions of the composition, and allowing you to hear the golden section as it was meant to be heard. However, I can’t do that for legal reasons.
What I was allowed to do instead was post audio clips of less than 30-seconds each per work. I knew that this would ruin the original proportions of the song, but I didn’t want to leave those reading the article with nothing to listen to. I justified my decision to go with clips by assuming that those reading the article would either have previously heard the entirety of the Zelda songs I mentioned, or would do so after reading the article. By providing the clips, I would at least be able to let you hear exactly which sections I’m talking about so that you could hear them in the full recordings later.
The songs were clipped not at the beginning of each song, as some people assumed, but rather around the golden section of the whole piece. To be creative, I decided to trim the music so that the moment in question would appear at the golden section of the 29-second clip; that is, at 18 seconds in. It was NOT placed at 18 seconds just to pick any random “big moment” and stick it at the 18-second of the clip to claim it as being at the golden section, as many have criticized me for doing. Those are indeed the golden sections of the whole pieces.
Using Golden Proportions is basic and amateurish to do
Golden section proportions are generally not used as a music composition guideline as much as they are in visual art. If golden section proportions are found in music, it’s more than likely not by design, but instead by coincidence. Mozart, Beethoven, Debussy, Phil Collins, and Eminem didn’t know about golden section proportions, but it’s in their music. If golden proportions really do have ties to perfection and beauty, perhaps these artists composed their music to what their ears thought were good, and it should be no surprise that their music lines up with these proportions.
That’s not to say golden sections can’t be by design. The first non-pop musical work we looked at in my music theory class this semester was Bela Bartok’s Music for Strings, Percussion, and Celeste. The piece has the Fibonacci Series written all over it, moreso than any composition before it. Bartok used golden section proportions intentionally, and it resulted in some of the most famous art music of the early/mid-Twentieth Century.
You could take any song and fudge the numbers to find what you want
I can’t find anything at the golden section in my favorite song
Christian just picked songs he liked and said the golden section is in them
The golden ratio doesn’t appear in every song. If it did, I wouldn’t really have to point it out. In fact, when I started planning out my article about a month ago, I was hoping to find a wide assortment of Nintendo music exhibiting the golden ratio to include in the article. Being a Nintendo news site and with the Super Mario Bros. theme probably being the most memorable of Nintendo themes, I was hoping I could open my article with that. However, even the iconic Mario theme doesn’t exhibit the golden ratio (at least not horizontally, which is the only aspect I was looking for). When I came across it in the Zelda theme, I checked other tracks from Zelda games. Princess Zelda’s Theme, one of the favorites from the series, doesn’t exhibit golden section proportions. It was not, by any means, in most of the examples I looked at.
There was also no number-fudging. Depending on circumstances, I found the golden section based on the number of eighth notes, the playing time, or both in each song used. While the reasons for saying the golden section was important in the six examples provided, I felt that these were significant examples for the article. There were other examples I could have used with something at the golden section, but they were very weak in comparison to the examples used. For example, the Lost Woods theme does have a high point at 0.618 the length of the melody, but it’s merely the top of a scalar passage and only the second highest point in the whole piece. In contrast, in the credits from A Link to the Past, the entire portion of the song before the golden section is percussion-free. Right at the golden section, the snare drum enters. I believe that is much more significant.
Golden Sections aren’t the only thing that make a song good
You’re right. Golden proportions are a natural phenomenon, but they don’t exist in every piece of music, nor do they exist in all the best pieces of music. Natural symmetry (0.618) isn’t the only type of symmetry either. Static symmetry is probably most common in video game music, as well as in pop music and early Baroque or Classical music. Static symmetry divides music into equal halves, or halves into halves, etc. Even then, neither natural symmetry nor static symmetry is necessary to make a good composition.
Golden section proportions in music is a part of music theory. It being a significant part of music isn’t always fact, it’s speculation – which is why my examples have various amounts of impact at their respective golden sections. In addition, just because a song has something at the golden section, that doesn’t mean it’s the reason people like the song. It’s just another layer of analysis. Yes, most of you like your game music because it accompanied a great game. I’m just providing another concept from my music theory classes for you to think about.
But theory is theory.