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So it turns out that if someone says that classical music is beautiful and heavenly, they aren't expressing their opinion...that person is stating a fact. I have to give a little background info before I explain.

A few years ago I heard about a phenomenon called "The Divine Proportion", also known as the Golden Section, the Golden Ratio, Phi, and a few others. For those who are new to this ratio, it is 1.61803399:1 and is everpresent in nature. This is the number of female bees to every male bee you will find in any hive in the world. The number of petals in relation to the number of leaves on a flower. It is the basis on which a person's beauty is measured - the closer one's face fits this ratio, the more attractive they are. The list goes on, but I want to get to the point.

Turns out, classical music is littered with this ratio. One of the most fascinating examples I discovered is in Mozart's first sonata. His first movement is 100 measures. The exposition is 38 measures. The recapitulation and development section contains 62 measures. In a 100-measure movement, you cannot attain a closer ratio to the Divine Proportion. Apparently other composers such as Beethoven and Dvorak also toyed with this ratio as well. This floored me upon discovery and I wanted to share it with those who were unaware of its presence. Personally, I can't wait to stop those who try to convince me of Green Day's superiority to Mozart or Beethoven in their tracks by busting out this little nugget of information.

http://www.americanscientist.org/template/AssetDetail/assetid/24551

Did you know that the golden ratio is actually taken out of Fibonacci's number-series thingy?

Wow, this is really cool, coz a few years back I did a little research on Fibonacci and his golden ratio - for a maths project, no less!

Damn, if I only knew it then...

This is really cool, thanx, pianoforte!

Cool, I still dont think its adaquate to call classical music superior though.

from the article:


A clear answer to Putz's question required looking at more than one sonata. So Putz examined 29 movements from Mozart's piano sonatas-the ones that consist of two distinct sections. Then he plotted the number of measures in the development and recapitulation versus the total number of measures in each movement, which is the right side of the golden--section equality as given earlier. The results reveal a stunningly straight line-so straight that its correlation coefficient equals 0.99, or nearly the 1.00 of a perfectly straight line. Moreover, the distribution of the ratios of the number of measures in the development and recapitulation to the total number of measures in each movement lies tightly packed and virtually on top of the golden ratio.

Although those results might seem like solid evidence that Mozart did use the golden ratio when he divided the sections of his piano sonatas, Putz knew that another comparison must be made. If Mozart used the golden section, then the other ratio from the golden--section equality--in this case, the ratio of the number of measures in an exposition to those in the recapitulation and development--should also equal the golden ratio. A plot of those measurements also produces a very straight line, but one with a lower correlation coefficient of 0.938, which Putz interpreted as "somewhat less goodness of fit." In addition, the distribution of the ratios of the number of measures in the expositions to those in the recapitulation and development peaks near the golden ratio of 0.618, but it also covers a considerable spread, ranging from 0.534 to 0.833.

The results from the two analyses seemingly conflict. The first analysis suggests that Mozart probably did use the golden section, but the variability in the ratios from the second analysis suggests that he did not use the golden section. That disagreement, however, did not surprise Putz, who wrote that the mathematics behind the golden section predict that "what we have observed in these data is true for all data...." That is, the ratio of the longer segment to the overall length is always closer to the golden ratio than is the ratio of the shorter segment to the longer one. As such, Putz concentrated on the distribution of the latter ratio as constrained by sonata form, and the spread in the distribution of ratios from that analysis suggests that Mozart did not apply the golden section to his piano sonatas.

In the end, we may never know if Mozart composed his sonatas, even in part, from equations. "We must remember," Putz writes, "that these sonatas are the work of a genius, and one who loved to play with numbers. Mozart may have known of the golden section and used it." Nevertheless, Putz thinks that the considerable variation in the data "suggests otherwise." In any case, Mozart did create divine divisions in his piano sonatas-making the interplay of sections shine like sunlight. Yet he apparently timed those divisions with his mind--not with math, or at least not with the golden section.

interesting. didn't know 'golden ratio' is applied to music, although it's widely applied in photography and cinemetography? can you apply it to music beside Mozart?

The ratio of consecutive Fibonacci numbers keeps getting closer to the Golden Ratio, or, in math-speak

lim (x->infinity) F_x/F_(x-1) = (1+\sqrt5)/2

I think it takes more than a piece's structure conforming to the proportions of the Golden Ratio to "prove" that classical music is superior to any other form of music.

Regards,

Haha, I was playing Good Riddance on the guitar when I read this.

I heard about this equation in Mozart and other composers a few months ago. It makes sense. It's odd though, because I'm sure other composers didn't know anything about this but they subconsciously followed it. It would be interesting to check my favorite pieces of all time and see how close they come to this ratio.

Agreed. Music is far more complex than even this "Golden Ratio" can be. And it's very opinionated as to what music genre/style is superior to another.

In every piece of music I've seen, even Green Day's, in every 100 bars, the first 32 bars maintains a ratio of 32 to 68 with the rest of those 100 bars.

There are lots of things you can prove mathematically. This isn't one of them.

I'm surprised noone has mentionned Bartok so far - he used the series, ratio and other natural mathematical elements far far more than any other composer in history... there's a great book on the subject but the name evades me at the moment.

I find so often that,
The rock music I used to listen to, Led Zeppelin, The beatles.

They dont have that same effect that classical does

Led zeppelin wrote songs
Chopin wrote beautiful Masterpieces.

The time, and effort that goes into classical burns any other type of music. Back when I played bass guitar I could learn probebly every Led Zeppelin song in a day. I could learn a Scriabin pieces in maybe a week or two.

Well, everyone's entitled to their own opinion. :p I'm sure there's those out there that believe that Roseanne is better-looking than Anna Kournikova. But the fact is, Anna's face fits the Golden Ratio much closer than Roseanne's. Looks are based purely on math. Someone may be exclusively attracted to obese women, for whatever reason (perhaps they enjoy the feel of love handles, for example). Same thing with music. There's people out there that believe rap is superior to classical music. Even though that nature dictates that classical music is beautiful, there are those out there may claim rap is superior because it gets them "amped up for da club" so they may "get their sip on". So I suppose it all depends on what you seek in music. You seek beauty, listen to Mozart. You seek bass, listen to Ludacris.

In hindsight, I should have entitled the thread "Proof that music is inherently more beautiful than any other genre".

I believe classical music to be superior to all other musics. I tend to think of other musics as savage musics with only a beat and a simple melody line. NOt complex enough for my taste. It's only MHO though.

In my opinion, Britney Spears is the greatest musician ever to walk the earth.

Britney Spear's baby is the next newborn mozart, just watch.

Your over-simplified rage at all things modern is, quite frankly, astounding. You know, I've never met a person who claimed "rap is superior to [insert genre here]." I only hear that from people I like to call "Classicists". People are, as you say, most certainly entitled to their own opinions, which, according to you, are inherently wrong if they disagree with whatever whimsical proof you can produce.

Once again I find myself in agreement with Bruce although I would go further and question whether the existence of a pattern has anything to do with musical quality in general.

I feel beauty and goodness in art are extremely complicated intuitive characteristics, far too deep and convoluted to be summarised in simple numerical and statistical properties of the music.

Once a mass of data reaches a certain heft it is possible to find all sorts of orders and patterns within it. This discovery, according to what I have read, goes back at least a century to the mathematician Frank Ramsay.

Also, there is the fact that much music considered good, particularly romantic music, does not depend on form for its effect but on the semantic, intuitive qualities in isolated segments - a particular turn of melody, a certain rhythm or a poignant harmony.

Classical music may well be superior to other idioms in the eyes of many, but I find it difficult to reason that this would be the case because of a very simple numerical property.

Perhaps, but Roseanne's body fits it better than Anna's.

LOL!! Very funny, but very excellent point.

There's nothing substantial in this thread supporting classical music's superiority based on the ratio. If there is in fact occurances of this ratio in classical music that DO indeed account for its appeal, then I would put any amount of money on the fact that other styles of appealing music would also turn up occurances of the ratio, including rock. (keep in mind, that sentence started with a really big IF)

And to assert that its better because it takes longer to learn just makes no sense at all. It would be REALLY hard to learn to play chopsticks at 10 times the tempo you normally hear it, does that mean that would be a superior musical experience?

1. I never equated rap with "all things modern". I love techno, rock, punk, and yes, even some rap. There goes that. And if you've never met a person that DOES claim rap's superiority, you need to get out more. I suggest you start with a few Philly alleyways.

2. Yes, people are entitled to their own opinions. However, we are discussing facts. Facts, by definition, are correct. Now, you can dispute that the sky is blue. But you can't disagree with its color. Know why? Cause it's a fact.

3. I didn't produce this proof. Nature did, and scientists discovered it. I just passed along the information.

From BDB:
Perhaps (Anna's face fits Phi better than Roseanne's), but Roseanne's body fits it better than Anna's.

Untrue, which brings me to another appearance of Phi. The ratio of your height to fingertip to fingertip (when arms are spread) plays a role in your attractiveness. How? The closer it is to the Divine Proportion.