The Golden Ratio is supposed to be aesthetically pleasing. Is it actually? Have any studies been done to compare how people react to different ratios when it comes to photographs, movies, paintings?
Are there equivalents in music, sculpture, architecture etc?
I personally think it’s oversold, and I see that a lot of other people are thinking so nowadays.
There was a study over a hundred years ago in which they presented people with rectangles of various proportions and asked them to select their “favorite”:. Supposedly the Golden Rectangle scored highest, with those of nearby proportions scoring higher than average. But the testing was somewhat ambiguous. I don’t think they equally sampled all possibilities.
Moreover, if the Golden Rectangle was the “best”, I’d expect to see it in a lot more places. But 8.5 X 11 paper, or legal paper, or European standard paper aren’t the Golden ratio. Neither are index cards, postcards, just about all currency, credit cards, driver’s licenses, tickets of all kinds, computer monitors, movie screens (original pre-wide-screen and any widescreen format), or television screens. If the Golden Ratio was our ideal, you’d think that more of these would have been made in that standard.
I came to this conclusion on my own, as I’ve said. But I was delighted to find that others share this idea:
This one is less definite, but still skeptical:
I’d guess that if you start with the premise that a rectangle of most any aspect ratio from square to quite “rectangular” (not sure what the correct term for it is, but you know what I mean) is particularly aesthetically pleasing, you could then go find examples from art, architecture, etc. to back up your claim.
One simple way I heard it described is that the golden mean “sweet spot” is at about 60% or 65%, Let me clarify:
[X]
[X________]
[X]
[___]
[X____]
[X____]
Putting the X in the middle is static, boring, you use it for portraits but for every other use you avoid placement in the center. Putting an X too close to the side, either on the right or on the left, that is too close to the border, it causes a slight amount of “tension” to the eye. Setting the X directly to the right or left, as in the example above, is close enough to the center to be engaging but not close enough to the edge to be distracting. I suck at Math but I hope you can see that if 50% is dead center then moving it over to the right or left takes you to 60 or 65%. That is also where the ratio for the Math works out.
I wish I had a link to verify this but I was an Art student and this how I heard it described in some random text book.
A slightly better indicator is music. If the Golden Mean is a mathematical ratio, and chords can be expressed as the distance between notes on a string, and chords which have either 2 or 3 notes that would line up in the golden ratio, well these chords are supposed to be more harmonious/pleasing/ etc. I think people have actually studied that and what not. The point being, it is kind of hard to say how many people like a painting by Van Gogh or Caravaggio, but it is pretty easy to look at the chord structure of the most popular songs from the Beatles or the Rolling Stones, or Jazz music, etc.
Poor example. 8.5 x 11 paper and the A4 equivalent are simply quartered sheets of broadsheet paper, the size of which evolved in the 17th Century (probably more because of the limitations of printing presses than any aesthetic concerns) and became more or less fixed in 1712 when the British began taxing newspapers.
I suspect it may be oversold too
I’d really like to see that experiment redone with better controls and standards
With 8.5 x 11 and monitors and such, I’ve heard there were technical/manufacturing issues. I’ve heard the opposite about dollar bills and credit cards, etc, that they do follow Phi (1.618) that’s the number of the Golden Mean, Phi is a lot easier to type and sounds a little less stupid. I am looking up Phi and Dollar Bill, Credit Card, Movie Ticket etc. I can tell from my “personal estimation” that a post card does not fit Phi, too short and fat. I’ve heard that 16:9 ratio for wide screen TV is set to Phi. Yes, 16 divided by 9 is 1.777 which is close to 1.618.
A very interesting topic but certainly worthy of critical review. So far google has confirmed Phi and Dollar Bill and Credit Card. I will keep looking and post the results. After that, probably before, I’ll look at your links…
I love the discussion on this board so much!!!
Not necessarily poor. People are free to change their ratios, especially today.
I realize that things long used tend to freeze that way because of the supporting infrastructure. But there’s been plenty of time (and, more recently, incentive) to change things. But no one’s marketed “Golden Ratio” paper, AFAIK>
More papers questioning the “idealness” of the Golden Ratio rectangle:
http://www.jstor.org/stable/1421471?seq=1#page_scan_tab_contents
Benjafield, John. “The’golden rectangle’: Some new data.” The American journal of psychology (1976): 737-743.
McManus, I. C. “The aesthetics of simple figures.” British Journal of Psychology 71.4 (1980): 505-524.
BTW is Phi pronounced like
Hi-Fi stereo (or)
Fee, like, Harvard has High Fee’s and Tuition
This guy goes on for almost 2 hours re Phi and The Golden Ratio. My link goes to the key section which has a quiz on the various claims about Phi and what is true and what is false. The first question addresses whether a rectangle with the Golden Ratio is the most aesthetically pleasing. He does an experiment with the class whereby several rectangles of various ratios of length and width are shown and the students pick the most pleasing… The Golden Rectangle does not win!
In Greek, it’s pronounced like “fee”, and similarly, pi is pronounced “pee”. But in English, calling pi and p by (what sounds like) the same name would cause confusion, so pi is usually “pie”, and by analogy, phi is usually “fie”.
Actually, pairs of tones sound best in a ratio that is a simple rational number, like 3/2 or 4/3. Phi is literally the hardest of all numbers to approximate as a simple rational, so the Golden Mean would make the worst possible chord, not the best.
Composition is filled with these rules of thumb. For example, basic ones like the rule of thirds and rabatment of the rectangle. I tend to think those are legit because I understood them intuitively before reading about them. Or maybe it was cultural brainwashing.
When I read about other techniques I feel like asking “cite?” at every suggestion like “people prefer looking at X type of lines” or “the human eye is drawn to Y.” Has anyone really done a psychological study on the rule of odds, for example?
Or ubiquitous orange and blue contrast. Color theory is filled with suggestions people supposedly like. Yet apparently tons and tons of people need to be taught this stuff, so how much of it is just dogma? So many times I’ll see someone say you shouldn’t put certain kinds of colors together because it’s ugly and I’m sitting here like an uncultured jackass thinking it looks fine.
I remember a long time ago reading that in horror movies right handed viewers are more frightened if something comes from the right side of the screen. I can’t find that nugget of information anywhere now, though.
??? How is it “harder” than, say, ( sqrt(7) + 1 ) /2 or ( sqrt(11) + 1 ) / 2?
Or pi or e?
It’s extremely easy to approximate phi as a simple rational, just as it is with pi and e. There are tons of ways to construct “continued fractions” to produce these targets as an asymptote.
And the continued fraction expansion for phi is further off at each step than the continued fraction for any other irrational.
Can you cite this, please? This is something I’ve never heard before.
I don’t know about it’s being the farthest off, term by term, but the Golden Ratio has the simplest continued fraction of any number – it’s 1+(1/(1+1/(1+1/(1+…))))). There are a lot of ways to show this, but the easiest is that 1/0.618033… = 1.618033…, so the first term is 1, but this leaves exactly what you started with, 0.618033…, so the next number in the continued fraction must be one as well, and so on into infinity.
One really great (actually provably the best) way to generate continued fraction approximations is to use the Stern-Brocot tree.
The Fibonacci numbers relate to that in interesting ways. (Scroll about halfway down or better yet do a text search for Fibonacci. Also check out the section near the end.)
This relates directly to the fact that consecutive Fibonacci numbers (whose ratio converge to Phi) are the worst case scenario for number of iterations in Euclid’s algorithm for GCD.
In other words, Fibonacci numbers are right on the “edge” in a certain way. How this might relate to aesthetics is another matter.
I’ve used the ratio 1:1.4[14] (1:√2) for a lot of things and it seems to be more well-received than 1:1.6-ish. (And it is the ratio of European paper sizes, by the way.) It’s always seemed like a more natural proportion to my eye.
Another way to look at it: If you start on a circle, and go, say, a quarter of the way around the circle, and then make a dot, and repeat, you’ll end up with dots at just four spots. Go any other rational fraction instead of a quarter of the way, and you’ll have dots at some finite number of spots (where that number is the lowest-terms denominator of your fraction). Go an irrational portion of the way around, and you’ll eventually end up with dots all over the place, but they’ll probably still clump, according to what rational numbers you’re close to: For instance, if your irrational number is pi, you’ll start off with 7 clumps, since you’re close to a multiple of 22/7, then eventually with 113 clumps, since you’re close to 355/113, and so on.
But if you go a proportion of phi around the circle, you’ll never clump at all. Each and every one of your dots is going to land in the biggest gap you have at that step.