Zelda music nails the golden ratio
by John Bardinelli 
{ Mar 3rd 2007 at 6:03PM }
Video game music has gradually evolved from background noise to the focus of professional composers and entire communities of remixers. Some tunes are far more recognizable than others, and a few have become so famous that professional orchestras perform them. But what makes one song better than another? The Tanooki thinks it's a little thing called the golden ratio.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.]
[Thanks, Christian]
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Reader Comments (Page 1 of 2)
Charron @ Mar 3rd 2007 6:10PM
"But the real question is: do we like a game's soundtrack because of the music itself, or because it accompanies a great game?"
Yes.
Matt @ Mar 3rd 2007 6:22PM
Sorry, this guy is on crack. His theory could be applied to music from any game series.
mepaco @ Mar 3rd 2007 6:47PM
All I can say is that the next Zelda needs some orchestral help. The synthesized music is feeling a little dated.
joshua lozano @ Mar 3rd 2007 6:50PM
The Febonnaci series of numbers and the golden ratio are often taught generally in advertising/graphic design classes today. A good read about numbers and relation to real world proportions is "The Book of Numbers".
The "Golden Ratio" has been used for quite some time and is often refered to as the ratio of beauty.
Maybe the Zelda composer heard the signifigance of the change or chord resolution and applied it at the right spot in the song or measure-- like many composers do.
A simple example of chord resolution in music theory can be explained with the major scale: *Do-Re-Mi-Fa-Sol-La-Ti...*Do
You start with *Do and resolve the scale by returning to *Do one octave higher. With out the resolution Do-Re-Mi-Fa-Sol-La-Ti would just sound weird and many composers leave that last note out on purpose to leave the listener with a feeling of a lack of resolve.
The Zelda game/series with such memorable musical pieces and moments in the game where resolve or a psychological accomplishment is met does indeed flourish with beauty and resolve.
Not all gaming music does this! No, the theory cannot be directly applied to all sings.
Otherwise, we would remember many of the tunes we heard from our games. I for instance know that the ghost and goblins song does the same thing... and happens to be a very memorable song to me. I don't recall God of Wars songs... instead I remember the bad ass boss fights!
Markham @ Mar 3rd 2007 6:55PM
The "Golden Ration" is anything but ramblings of a guy on crack. The Golden Ratio exhibits itself all over nature. Just lock at your body's physical proportions, for example.
scepia @ Mar 3rd 2007 6:58PM
"Sorry, this guy is on crack."
"The "Golden Ration" is anything but ramblings of a guy on crack."
Translation: "I don't get it, so he must smoke crack."
Twist @ Mar 3rd 2007 7:00PM
This is really stretching to make something like music fit into the golden ratio (which all my art & design professors called Golden Mean Proportions) which is a visual concept. It just happens that GMP can be represented mathematically as .618 on a flat line. To say that the best music has to have a strong point at .618 through the song or loop is beyond silly. Also I have heard many people say that strictly following GMP is something of an amateurish thing to do. GMP is sort of a beginners guideline: If you place visual emphasis here it will make your composition stronger. One of those rules that can be broken once you know what you are doing.
Zouden @ Mar 3rd 2007 7:09PM
Such a shame that the Zelda main theme song doesn't appear in Twilight Princess or Ocarina of Time.
Mikeo @ Mar 3rd 2007 7:12PM
Just another Zelda fanatic.
And they've come to show how desperate they are.
1.618 is a VISUAL indicator. And most of the time it goes against good composition. What's most annoying is that people have been scrambling to squeeze the ratio abysmally to any piece of visual art.
Well, this crossed the line further. Meh.
Omer van Kloeten @ Mar 3rd 2007 7:24PM
"But the real question is: do we like a game's soundtrack because of the music itself, or because it accompanies a great game?"
The only reason I have soundtracks is because I have been playing their games long enough to be accustomed to the music and therefore like it.
For me, it's the soundtracks to FF7, NFS Underground 1+2, wipEout and wipEout XL.
Hyouko @ Mar 3rd 2007 7:34PM
I will say that I got and listened to the music for Shadow of the Colossus long before I ever ponied up for the game, since I love its composer (Kow Ootani, does a lot of great work).
Triforceowner @ Mar 3rd 2007 7:31PM
Matt, I have not read the article, but I believe it is referring to the harmony humans search for in life: whether we are creating art or interpreting art. I could be wrong, though, but I do know that the Zelda themes do a great job of this harmony and balancing what we've heard to what we want to hear. Mozart did this... Dennis Alexander didn't.
Angelo @ Mar 3rd 2007 7:39PM
Personally, I find most Legend of Zelda music rather forgettable, aside from, maybe, the theme from the original NES title.
Kendrick @ Mar 3rd 2007 7:42PM
I can think of a few games I enjoyed playing that have great soundtracks, but weren't outstanding in any other way. Albert Odyssey on the Saturn was a conventional turn-based RPG made compelling by a score from a small orchestra. Commando is a slow, repetitive scrolling shooter in almost every port, but the Commodore 64 version had a driving theme song that made every action urgent and exciting. And the original Ys trilogy is far eclipsed by newer and better games, but there's nothing like that very first CD-quality overworld music to bring you back to the Turbografx version.
A great game will still be great even if the music isn't special. But excellent music goes a long way towards making a mediocre game tolerable, and even memorable.
Cheezeman3000 @ Mar 3rd 2007 7:45PM
Actually, the golden ratio can be seen in almost every aspect of music (and sound), from the frequencies to the instruments themselves.
This page gives some more in-depth details:
http://goldennumber.net/music.htm
Tejan Arora @ Mar 3rd 2007 7:59PM
the university of maryland band played the zelda song at the UMD mens basketball game during time out today.
Kitsune @ Mar 3rd 2007 9:25PM
It is flat out wrong to say that the use of the Golden Mean is for visual arts only. Fibonacci numbers show up constantly in the analysis of music. Bach, Mozart, Haydn, and Beethoven are just a few well known composers who's works use these ratios (1:1:2:3:5:8:13....)
As far as the subject at hand, I do believe that good music can make an already excellent game even more memorable. The gaming experience is more than just a visual one after all.
Joshua @ Mar 3rd 2007 8:50PM
Ha, I understand nothing about what he is saying. I've never taken a music class or truly played an instrument in my life. I just know Zelda songs are the best game songs, and the Skies of Arcadia soundtrack is really good, too...So is Shenmue's...
JAC @ Mar 3rd 2007 9:32PM
I don't know about this guy's theory, but Koji Kondo is the man, he has composed some of the most memorable and catchiest tunes in videogame history, mad props Koji, mad props.
Markster @ Mar 3rd 2007 10:29PM
"do we like a game's soundtrack because of the music itself, or because it accompanies a great game?"
The latter.
Shortly after playing games, I generally fall in love with the music in them. However, given some time, and some sober second thought, I generally realize that the music often sucks, and it's only the connection to the game that makes me like it.
(a specific example of this for me was Half-Life 2)
Burnt Meatloaf @ Mar 3rd 2007 10:30PM
Duh. The brain is naturally receptive to the golden ratio and many other patterns. We use it every day without even realizing it. Professional musicians are just more aware of why things sound good than most other people.
Remember, graphics doesn't matter, but music does.
Al @ Mar 3rd 2007 11:10PM
The only thing I know about the golden ratio is what Donald Duck taught me in "Donald in Mathmagic Land". Which is an awesome video.
fightinfilipino @ Mar 3rd 2007 11:30PM
"All I can say is that the next Zelda needs some orchestral help. The synthesized music is feeling a little dated."
come back when you've figured out a way to mix live, recorded music in the dynamic, fluid way Zelda uses its soundtrack to denote horse riding, enemy fighting, etc.
VanGuardian1 @ Mar 3rd 2007 11:58PM
Zelda : Twilight Princess - fav tracks
1) Twilight Princess Orchester (Don't want you no More) - If you consider this song the "theme" for Twilight Princess, then IMHO it is the best game theme song I've heard since Halo.
2) Midna's Desperate Hour
3) Twilight Princess Orchester (Medley)
4) Hyrule Castle Tower
These tracks, IMHO, are absolutely fantastic, and add a lot to the experience of the game while you're playing it.
Personally, the most disappointing soundtrack last year to me was Final Fantasy XII. :(
Matt @ Mar 3rd 2007 11:59PM
maybe if we think of increasingly more obscure things to point out about Nintendo then there stuff will seem cool.
keep up the hard work guys...
SynikaL @ Mar 4th 2007 12:05AM
I'd much rather experience the vibrant and much more lively tones of an orchestra over the psuedo-interactive MIDI crap. I think the franchise deserves better.
I don't know anything about music mixing, but I find it hard to believe that Nintendo can't record an orchestra and play with technologies to achieve similar effects. Somebody educate me on why I'm wrong.
-Kimosabae
Kannon @ Mar 4th 2007 12:12AM
In some ways the music may be more important then the image on the screen, in some ways no sound at all can tell an entire story, either way each element is truly important to making a great game great.
For those of you who wished Zelda had a more orchestral sound to it, listen to http://www.zreomusic.com/listen and you'll see exactly what its meant to sound like.
Tom @ Mar 4th 2007 12:12AM
If Zelda music has the Golden Ratio, then Sonic has purple music, and Final Fantasy music tastes like cherry coke. Also, the song from the first level of Mario Bros. 2 quite clearly smells like a mixture of triangles and the color green.
I'm not buying it. This article is completely irrelevant and any conclusions it reaches are based on the hallucinations of a superstitious numerologist.
Durinthal @ Mar 4th 2007 12:17AM
I generally enjoy video game music, and I've actually found several occasions where I've loved a particular game's music even though I've never played it. A few that come to mind are Chrono Trigger, Secret of Mana, and Xenogears (I've since played the first two).
deaftly @ Mar 4th 2007 12:25AM
video game music has sucked since everything went to 3d
GhaleonQ @ Mar 4th 2007 12:38AM
*is a huge music theory fan*
Yeah, I was intrigued when I found this.
Meatwad42 @ Mar 4th 2007 12:04PM
Wow, you guys really think this dude's full of it?
I have proof that they were using Golden Ratios when they designed the Zelda series...
Behold!
http://www.nlpu.com/Articles/artic24.htm
Scroll down to the second picture. This will blow your mind.
eialba @ Mar 4th 2007 1:16AM
The only people competent enough to assess the truth within the article are the writer's peers - namely, other music theorists. So put up or shut up.
KC @ Mar 4th 2007 1:14AM
I grew up on videogame music.
I believe thats why I like it so much. I didn't listen to any "real" music until high school. Prior to that, Megaman, StreetFighter, Sonic, Castlevania tunes all the way.
I STILL listen to that stuff though, along with my fav bands. New games that come out have music I totally dig too. The GuiltyGear series is now home to my favorite videogame music. It's not even because I like the game. The music simply ROCKS. Ys has fantasic music, but I dont like the game so much. Newer Megamans have some cool music, don';t like em like I liked the old ones.
Point being, the question "do we like a game's soundtrack because of the music itself, or because it accompanies a great game?", I like the music itself. If a game has music I like, it makes me like it more. Music in games is VERY important to me.
As for that Orchastrated vs. Midi for Zelda arguement.... The Midi stuff sounds great. Is it even Midi? It sounds very good, and Zelda TP has some great music in it. Nothing I'd rock out to in my car, but great for the game.
Matt @ Mar 4th 2007 1:56AM
I knew about the golden ratio while most of you were still wearing diapers. Just because he found examples from some Zelda songs doesn't mean you won't find examples in music from most video games. Look at enough songs and you will find what you are looking for. It's coincidence, nothing more.
Here's other examples of people on crack. http://www.brooksdesign-cg.com/Code/Html/bfp2.htm
Think a beautiful mind...when you look hard enough you will find what you are looking for everywhere...and at that point you are on crack.
jesus_bon_jovi @ Mar 4th 2007 3:41AM
Intelligent Qube!
Kendrick @ Mar 4th 2007 7:08AM
Tom, I don't think it's fair to describe the Golden Mean as superstition or numerology. Nobody ascribes any kind of mystical or religious significance to the number, it's just a proportion that occurs in nature that we like to see. It's quantifiable, it's measurable, it's been known to us since the height of the Greek civilization. The interesting part of this debate is whether or not the mean can be applied in a non-visual medium, like music.
Breserk @ Mar 4th 2007 9:13AM
By the way, for anybody interested, here's how the golden ratio is defined:
Let there be a straight line AB. Let C be a point on the continuation of AC so that AB>BC, AC>AB:
A-----B---C
Let AB/BC equal to AC/AB (the ratio of whole/big part equals to big part/small part).
This means:
AB/BC=AC/AB
AB/BC=AB+BC/AB
Let's assume BC equals 1 (since we're finding a ratio), and find AB (which we shall call x).
x=(x+1)/x
X^2=x+1
x^2-x-1=0
x=(1+squareroot(1+4))/2
x=(1+2.23606797749979)/2
x=1.6180339887498948482045868343656...
Breserk @ Mar 4th 2007 9:17AM
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
AbleJames @ Mar 4th 2007 9:34AM
Sorry, this guy is just totally unconvincing.
Listening to his samples and reading his explanations, it's clear you (or this guy) could choose an arbitrary song, find the golden mean point from either the start of the composition or the start of the loop, and then rationalize a music theory explanation.
I have a B.A. in music. It's not much, but it's enough to know that the music theory ideas this guy relies on as evidence of the golden mean manifesting itself at this or that point in the music are not especially uncommon, interesting, or convincing.
I mean, for example he says: "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."
Having grace notes, flavor chords or unexpected transitions happen all the time--all the time quite literally when you factor in that, like this guy, you may arbitrarily decide what the motives and expectations are at any moment to belie. You can deconstruct the motivation of any moment of any piece of music to arrive at such a conclusion.
Sorry, but I might as well go see Jim Carrey rant about the number 23--the connections are just as tenuous.
bm @ Mar 4th 2007 2:23PM
"All I can say is that the next Zelda needs some orchestral help. The synthesized music is feeling a little dated."
HAHAHAHA no.
Can you name any game with an orchestral soundtrack which has tunes that you remember? I can't. That kind of music usually focuses on using as many instruments per second as possible. It doesn't have anything such as "melody", and therefore fucking sucks.
Ap0c @ Mar 4th 2007 12:21PM
The golden ratio seems somewhat ubiquitous. Attributing the success of one piece of music, or the score to one game, to it seems pretty silly.
As for whether we love soundtracks simply because of the game we associate them with or for the music itself, i'd have to say that the two can be inseparable; would we have loved Chrono Trigger quite as much if it didn't have its great soundtrack? Would we have even given the soundtrack a chance if it wasn't rooted in something? I have a feeling that the answer to both is no.
Charles @ Mar 4th 2007 11:31AM
Perrrrrrfect! Sorry, any time I think of Intelligent Qube I want to say that. And all I had was the demo, which I played to death.
Anyway, on topic, I would say I like the game music I do because I like the game. Especially from Final Fantasy. Also, the Black Mages rock. I never tire of hearing battle themes from FF6 and FF7, played on guitar.
Nopar @ Mar 4th 2007 11:32AM
"But the real question is: do we like a game's soundtrack because of the music itself, or because it accompanies a great game"
It's probably a little of both. I love the God Hand soundtrack and I've never even seen the game in motion, let alone played it. I also love the Silent Hill 2 soundtrack, and I think the fact that SH2 is one of my all-time favorites enhances it a little bit.
Here's another question. Are there cases in which one could only like a game's soundtrack because of the game attatched to it? Come on, post-VII RPG fans. Confess.
Steve @ Mar 4th 2007 10:34PM
With this revival in retro gaming I've been playing lots of old games with the Wii's virtual console and emulator sites like vNES. It shocks how often it has occurred that I play some old game from my childhood and one of the themes is a ditty that I've hummed to myself for the past 20 years. Over that time I had forgotten where the tune came from, but it was in my head nonetheless. It doesn't matter if the game was great or lousy; as long as it was good and a game I played often years ago it might still be floating around in my head. I recently played "3D Worldrunner", a good unique but forgettable NES game from my past, and I couldn't believe how its main theme has been running around in my head for nearly 2 decades and I had no idea where it came from.
It's a good thing I'm not musically talented because I'd probably compose "brand-new" songs that are actually old NES songs!
Ragnarok @ Mar 4th 2007 12:05PM
Neskimos > minibosses IMO
OmegaX @ Mar 4th 2007 12:23PM
""Sorry, this guy is on crack."
"The "Golden Ration" is anything but ramblings of a guy on crack."
Translation: "I don't get it, so he must smoke crack.""
Wrong-o. Re-read the second thing you quoted, and learn some English. 'Anything but' means 'it is not'. The second guy you just implied the stupidity of, was actually saying that the first guy was wrong, and that the Golden Ratio is everywhere.
Triforceowner @ Mar 4th 2007 12:37PM
AbleJames, that's just it. People right music so that it sounds good. When they do this, one can find the "golden ratios" or whatever they are in the music. I'm pretty sure Kojo doesn't sit down and write his music thinking about a "golden ratio," but when his music sounds good, the "golden ratio" can fit it.
Aero @ Mar 4th 2007 1:36PM
I did about the Golden Ratio in Art class. It's a load of bull.
Nopar @ Mar 4th 2007 2:54PM
"Can you name any game with an orchestral soundtrack which has tunes that you remember?"
Shadow of the Colossus. Other than that, I completely agree with you. Orchestral soundtracks are over-done.