It's one of those things that "experts" love to talk about ...but anyone who labels anything in art as a "rule" has me thinking "why?"....actually I must admit I wonder why about a lot of rules...BUT that is another issue!
As art quilt makers it's important that we know which guidelines are really useful in designing...and which are more the result of one person repeating what another said, and another repeating that. Like the old story of the famous grandmother's recipe for roast turkey which involved cutting a 2" slice off each end of the beast. The family swore for years this was the secret to her perfect roasts, finally somebody asked the old lady the reason for this rule..."oh", she said, "it was to fit in the oven, I only had a small oven!". And cooking isn't the only place where strange superstitions and practices have built up over the years...maybe we're all turning round and round before we peck at the feeder like Skinner's chickens!!! And I want to know why?
But first....what is this Ratio anyway?
Well, here's the standard definition:
The Golden Ratio the result of dividing a line into two parts (part a and part b) in such a way that:
the longer part (a) divided by the smaller part (b) is also equal to
the whole length divided by the longer part (b)
There's only one number ratio that will do that and it's approximately 1.618033989...
It is exactly equal to (1+√5)/2 - if you're the mathematical kind...which I'm not...alas!
but mathematicians really love these special numbers!!! And in mathematics the 1.618 number turns up everywhere e.g. in a pentagon - hence the "magic" of the five pointed star...but I digress.
There are many books and articles written about the importance of this ratio in art, in architecture, in painting, in photography (photographers cling onto their Rule of Thirds almost as tightly as to their cameras), in poetry, in music and in nature. The Greeks revered it. Kepler said that in geometry there are 2 treasures: pythagorus and the Golden Ratio.
So last week I went to a couple of lectures by the Famous Calculus Professor (FCP), now retired and keeping his mind active by examining any claims as to the magic of numbers!!
He showed us 9 different rectangles: which one was the most pleasing?
They were all different ratios: 1:0.75, 1:1, 1:1.25, 1:1.5, 1:1.6, 1:1.75, 1:2 etc
Take a look and see which one you think is the most attractive:
Opinion was somewhat divided but people did tend to prefer certain ones. Scroll down to the very end to see which one is the so called "golden" one.....
So is there something to this? Have artists, architects, musicians etc across the ages used these particular proportions to increase the beauty of their art form???
When the the GR experts show a picture of the Parthenon with the GR lines drawn around it. You can see, if you look carefully, that the position of those lines is largely arbitrary - done simply to create that ratio – do you include the steps or not??!!! It’s very random.
There is some evidence that Le Corbusier actually did use the number. But images of Mona Lisa with lines drawn on it are quite arbitrary too – often they don’t include the whole face! You could actually take any portrait and just randomly draw lines on it and sooner or later you'll come up with the right ratio.
People have spent a lifetime analyzing the number of words in verses e.e.g Vergil’s Aeniad….showing that they agree to the GR. But you can count up the words or the syllables in so many ways you can create something that approximates the GR if you pick your object carefully.
They thought people like Mozart used the GR and counted up the notes, or the phrases etc etc…but a careful analysis shows the same problems with music as with poetry. Imagine counting all those notes? and what about chords? d'you count them as 2, or 3 or 4??
Despite numerous claims that they did, one prestigious Latin professor even built his whole amazing career on revealing this in various writings - despite analyses of the art of Da Vinci and Micheangelo and Vergil and Dante and Mozart etc most of them DID NOT use this ratio. They simply used whatever felt right for their particular art form.
So is the whole thing about the Golden ratio a load of hooey then? well....having thoroughly debunked its use in art, the FCP (who is definitely not an LCD!) turned to nature and the Fibonacci series.
Now you all know the Fibonacci number sequence...a lot of quilt makers have used it in designing their quilts. This is the sequence where you simply add the two previous numbers in the row to create a third number: 0, 1, (then 0 +1 = 1) so 1 is the next number, but then 1+1 = 2, so the next number is two, and 1+2 = 3....
0,1,1,2,3,5,8,13,21,34 and on and on and on upto at least 17 thousand digits (somebody had a big computer and a lot of time on their hands!!)....
Now, consecutive Fibonacci numbers have a particular ratio to each other....and guess what? yes! it's 1.618...very approximate in the smaller number but by the time you get upto 233/144 it's spot on.
Then we looked at flower petals, and the spiral lattice you see on the bottom of pine cones and pineapples. Counting them up we realized that there were 13 clockwise spirals and 8 anti clockwise spirals. 13/8 = 1.625 - pretty close to THE ratio!!
But why? why does nature "choose" to use the Golden Ratio, the magic number beloved of mathematicians where artists (of whatever medium) actually haven't? The answer is efficiency. The best way to get the MOST little seeds into a sunflower head, or pine cone, is to create the lattice effect of two sets of spirals that are related in that particular ratio. And if you're going to survive, you want as many of your little babies out there as possible.
So...the ratio is Golden for survival, but...really not at all crucial for art! So don't worry if your ratios are a little off, your thirds not quite corresponding to the norm, Da Vinci didn't, the architects of the Parthenon didn't, Mozart didn't....just smile gently at the critic or the teacher who insists on concrete, permanent, eternal rules without question!!!
....and now for a nice cup of tea after all that hefty cogitation....if you have been, thanks for reading!
and the answer is: number three.