Music of golden proportions

March 7, 2007 1:51 PM

Zelda and the Golden Ratio.A fascinating examination of the music from Nintendo's Zelda games, and the recurring appearances of 0.618, the bisection point on a line at which the relationship of the shorter segment to the longer one is the same as that of the longer section to the whole line.
posted by jbickers (24 comments total)

Well! That certainly explains a lot.
posted by Baby_Balrog at 1:57 PM on March 7, 2007

Silly numerology.
posted by Khalad at 2:05 PM on March 7, 2007

A good read on &Phi: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. I do not recall it mentioning video games, however.
posted by boo_radley at 2:17 PM on March 7, 2007

UH, without meaning to bust his bubble, but his Golden Sections 18 seconds into his 29 second clips mean nothing if he cropped them himself.

Which he did.
posted by armoured-ant at 2:23 PM on March 7, 2007 [1 favorite has favorites]

UH, he cropped them that way, just for fun. The sections he was talking about occurred at the golden mean of the entire piece.
posted by knave at 2:30 PM on March 7, 2007

rule of 2/3rds?
posted by edgeways at 2:37 PM on March 7, 2007

Very nice piece, though it would be more interesting with speculation as to the reason that particular timing strikes us so.
posted by voltairemodern at 2:49 PM on March 7, 2007

Yet another reason why Zelda is the most awesome Nintendo game ever.
posted by inconsequentialist at 2:54 PM on March 7, 2007

A good read on &Phi: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. I do not recall it mentioning video games, however.

I just bought this online last week. I look forward to reading it.
posted by inconsequentialist at 2:55 PM on March 7, 2007

boo_radley: "A good read on &Phi: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. I do not recall it mentioning video games, however."

The book does spend a bit of time debunking common phi myths. For instance, it indicates that the idea that the Parthenon is shaped like the golden mean is wishful thinking. You need to make a lot of sketchy assumptions and estimates for it to be "accurate".

Hm, that sounds familiar.
posted by Plutor at 3:13 PM on March 7, 2007

I suspect the main reason you find the Climax where you find it has less to do with PHI/math than simple narrative structure:

exposition-rising action-climax-denoument

The Climax always occurs in the latter half. And you need some time at the end for Denouement/Resolution so, just by coincidence you'll often get it around 62% of the way through - this applies to Music, Literature and anything with a narrative structure.

Also, the guy actually said "Da Vinci’s Vitruvian Man." Ugh.
posted by vacapinta at 3:25 PM on March 7, 2007 [1 favorite has favorites]

Vacapinta, he makes up for that when he says 'bare with me, and we’ll get to the good stuff afterwards'.
posted by Dataphage at 3:39 PM on March 7, 2007

"What is a golden section? Well, it’s the point determined by the Golden Ratio, approximately 0.618."

This quote from the linked page is correct while the wording of your post is not. The Golden Ratio is irrational, in geometric terms incommensurable. It's approximately 0.618, just as it would be approximately expressed in any (rational) number base, any (rational) numeric representation.

Euclid's definition of this ratio is in terms of a proportion, where a line is divided such that the length of the line to the greater segment is as the greater is to the lesser. With the line symbolized as A, and G and L as the greater and lesser segments, respectively, we have this proportion:

A:G::G:L

Both the two ratios, A:G and G:L have the same relationship, and that relationship is the so-called Golden Ratio. In geometric, Euclidean terms, the length A cannot exactly measure length G, while the length G cannot exactly measure length L. They are incommensurable. This translates to the modern notion of an irrational number. That is, if you translate either of these two ratios (A:G or G:L) into a number (for example, by way of a fraction), you'll find that the number is irrational. The modern notion of irrational numbers (and, importantly and confusingly, the term irrational is a direct transliteration of the Greek term into English) is a distinct and great abstraction from the ancient geometric notion of incommensurability¹.

1. They shouldn't be thought to be, strictly speaking, synonymous. However, it's my opinion that a comprehension of incommensurability with its appeal to intuition (or counter-intuition?) is more helpful than not for young students of mathematics when contrasted to the simple taxonomic approach that most students get...at least in practice.
posted by Ethereal Bligh at 3:55 PM on March 7, 2007 [1 favorite has favorites]

Did you know that the Zelda soundtrack was actually designed as an alternate soundtrack for the Wizard of Oz?
posted by grouse at 5:39 PM on March 7, 2007 [1 favorite has favorites]

Why is it that whenever certain people measure an empirical ratio approximately between 2/3 and 3/5, they declare it must be the magical mysterious golden ratio, correct to infinite precision?
posted by metaplectic at 6:29 PM on March 7, 2007

The Climax always occurs in the latter half. And you need some time at the end for Denouement/Resolution so, just by coincidence you'll often get it around 62% of the way through - this applies to Music, Literature and anything with a narrative structure.

By this estimate, we'd expect the climax of a two-hour movie to come at the 75-minute mark, with another 45 minutes of wrap-up following.
posted by aaronetc at 7:38 PM on March 7, 2007

On a related note, Boards of Canada's "Geogaddi" album is also (intentionally) structured around the golden ratio... according to an interview I read with them somewhere (i think the same one where they copped to being brothers).
posted by dvdgee at 7:44 PM on March 7, 2007

The golden ratio appears in much of classical composition, as well. Many pieces have their climaxes at almost the exact point of the golden ratio.
results of cursory google search
posted by potch at 9:30 PM on March 7, 2007

Hold up. I'm way out of my depth here, but if the significance of the Golden Ratio to a piece of music is simply when the climax occurs as a fraction of its total length, irrespective of how much time actually elapses between its start and that climax, how does that make any sense for the listener?

Imagine you're listening to a track you've never heard before. It is 10 minutes long but you don't know that. You get to the climax at about 6.2 minutes. Were this Golden Ratio approach to music to have any effect, however, this should provide no satisfaction on first listening, because you don't know how long the song is. Were it 12 minutes long, that climax should have come later; 8 minutes, earlier.

So unless the point of this is that, post-climax, the listener expects the song to wind down by a certain point, and this is where the satisfaction comes in, or alternately, only when the song is listened to many times and appreciated as a whole, I don't get it.
posted by dreamsign at 12:48 AM on March 8, 2007

By this estimate, we'd expect the climax of a two-hour movie to come at the 75-minute mark, with another 45 minutes of wrap-up following.

Didn't you see Return of the King?
posted by Faint of Butt at 4:41 AM on March 8, 2007

grouse says: Did you know that the Zelda soundtrack was actually designed as an alternate soundtrack for the Wizard of Oz?

Silly rumour. Mute the movie instead and play the soundtrack alongside the video. It's trippy.
posted by purephase at 5:13 AM on March 8, 2007

I really like phi. I think it's a good place for things, psychologically. Edgeways said: "Rule of 2/3rds?" and I think he's kinda hitting it on the head. I think the rule of thirds is an easy trick but we actually prefer to have things a little off.

Imagine a box with a dot in the center - .5 across the way. Completely stable. Now move the dot a little one way or another: tension is introduced. We cannot help but give the dots personallity and that leads us to think of the box as an enclosure Dividing a rectangle into thirds is a good way to get this tension easily.
posted by Brainy at 6:09 AM on March 8, 2007

The analysis seems a little weak. I didn't spend too much time repeatedly listening to the musical examples, but in the first one, the author claims an unexpected chord occurs at the Golden Ratio. Sure, the chord is unexpected - but it sounds to me like it is immediately repeated. The doesn't explain how things like this affect the analysis. The other examples seem to be similar - pointing out that interesting musical things happen at the same point in the music. Yet, there are other interesting things that happen in the music at other points - things that might be more important in terms of form or harmonic progression. That's the problem with this type of analysis - the author decides that something is there, then (sure enough) finds it in every excerpt he looks at. {{overstating the point}}
posted by imposster at 7:14 AM on March 8, 2007

@ imposster:
There was often this refute during my courses of Contemporary Music Theory while analyzing certain pieces. Even down to interpretation of a chord in an important passage in a Debussy piece, though that's the preface of studying music theory: there's sometimes going to be varied interpretation unless you get a composer's explanation--which almost never exists.

If you can find a few reasons why a specific instance holds importance, then it can be valid. I think the Zelda analysis holds validity considering a few things:
-an N6 chord, ever since Beethoven used it as a climatic pedal in one of his symphonies, has become an iconic, important chord which appears in the first example
-instant change of timbre, dynamics, and instrumentation is as big a shift as you can get, which appears in the OoT example
-if the concept shows face a couple in a composer's repertoire (see Mozart, Bartok), it might be safe to say it's a valued technique of theirs and might translate to other pieces.

What might be a great follow-up analysis would be analyzing the melodies themselves, be it intervals or note length comparisons, and if they relate at all to the Golden Ratio. Stylistically Kondo seems to draw influence from 20th century techniques and artists, so this wouldn't surprise me due to their penchant for inserting patterns in any way possible.

I love discussing music theory... I miss my college days.
posted by blastrid at 3:06 PM on March 8, 2007