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The Divine Proportion

Flat Lake Aspens by Keith Bond, 32 x 36
Flat Lake Aspens by Keith Bond, 32 x 36

  The Divine Proportion

By

Keith Bond

 I find it interesting how a single number has had such tremendous influence on me that it has opened my mind to a new way of thinking and a new way of seeing the world. I am not alone in this fascination with a number. Throughout history, many have discovered the mysteriousness of the number Phi. 

Recently, I have been reading a book about Phi entitled The Golden Ratio by Mario Livio. A while back, artist Skip Whitcomb turned me on to a study of Phi and encouraged me to consider using it to develop my compositions. Also known as the Golden Ratio, the Divine Proportion, the Golden Section, and the Golden Number, Phi is fascinating in both its unique mathematical properties and its manifestations in countless diverse places. It, along with closely related Fibonacci numbers, can be found in the patterns of a sunflower, the pedal arrangement of the rose, mollusk shells, and in the Milky Way. It is abundantly found in nature. With great aesthetic appeal, many artists, architects, musicians, and others throughout history have used it to their advantage. 

I won’t bore you with a discourse on Phi. If you want to learn about it, check out a few books on the subject. 

However, it has been so enlightening to me that I decided to share with you the growth I am seeing in my artwork. My compositions are becoming stronger and more dynamic as a result of using the ratios inherent with Phi. I now use the Golden Section to determine the placement of the major elements of the composition. I divide up my canvas based Phi. My center of interest in a painting is now placed on the Golden Section or at a derivative of it. I don’t want the work to look mechanical, but rather harmoniously pleasing to the eye. I want the compositions to look natural. 

I used to compose my paintings more intuitively.  I did what ‘felt’ right.  Looking back at older compositions, I find that many are coincidentally close to Phi. Some aren’t. I do realize that this won’t guarantee a stronger painting. It is however another tool I can put in my toolbox. 

So profound are the possibilities that it will likely take a lifetime of study to even partially incorporate them into my artwork. Most of what I have learned still needs to be sifted through. And there is more still to be learned. It is a wonderful road of discovery, experimentation, and artistic growth.

Sincerely,

Keith Bond

PS. As the most irrational of all irrational numbers, I am intrigued by the prevalence of Phi in the natural world. This number, which is farthest of any number from being expressible by a fraction, has qualities which make it far from random. There is order to it. It supports my firm belief that what may appear to our limited, finite minds as chaos is governed by a higher law which we don’t understand. 

 

13 Responses to The Divine Proportion

Carol McIntyre
via keithbond.com
HI Keith.
The painting is lovely! Can you show some drawings of the locations of PHI in this painting and others?

Thanks

Keith Bond
via keithbond.com
Carol,

I will put together an article or something which illustrates how I use Phi to develop a painting. In case you don't know, the number Phi is: 1.61803... I do round the calculations off a bit. I don't worry about being exact.

In the above painting, the lone aspen to the left of center falls along this vertical ratio division. The left edge of the tree at the base lines up with the Golden Ration and the right edge of the tree lines up with it towards the top of the painting and in the reflection at the bottom of the canvas.

The other verticals are derived from the ratio by subdividing several times.

Horizontally, the Golden Ratio intersects the aspen mentioned above at about a third of the way up the tree at precisely the black 'scar'. It's hard to see in this small image above. The horizontals along the bank of the lake are mostly subdivided based upon the ratio. The point where these horizontals end are mostly at vertically subdivided points.

Yes, it would be easier to explain with a visual. I will try to put something together in a week or two.

Keith

Keith Bond
via keithbond.com
I forgot one other important intersection. The most important! Midway between the base of this prominant aspen tree and the reflection of it is a Golden Section point. Although the intersection does not fall squarely on any specific element, when you look at the painting, the convergeance of the tree and its reflection on the narrow strip of land is the center of interest. The Golden Section lies directly in the center of this 'area'.

Carol McIntyre
via keithbond.com
Thanks Keith. When I studied this years ago (your blog is reminding me to look up the book I have), the artist/author said the dimensions of our paintings should be based on the Golden Mean, another words, not our standard sizes. Have run across this?

I look forward to your next article on this subject.
Carol

Keith Bond
via keithbond.com
Carol,

There is a certain pleasantness to the proportions of the Golden Mean (or Ratio or whatever you prefer to call it). Yes it does make a great composition. You are correct in that most of our standard sizes are not based upon this ratio. Some are, though.

But even if you use any sized canvas and divide it using the Golden Ratio, you can still come up with a great composition. There are also several other 'methods' which result in good compositions. The options are truly limitless. This is one of many tools and should be used as such.

It has become fascinating to me recently to explore its possibilities, but I do not suggest that it is the only way.

As a related concept, the Fibonacci numbers (1,1,2,3,5,8,13,21...) are closely related to Phi and therefore the Golden Mean (if you research the topic, you will find fascinating sources showing the relationship). With this in mind, a 1 to 1 ratio (or square canvas) can be pleasing. A 1 to 2 (such as 12 x 24) or 2 to 3 such as 24 x 36) or so on.

The Golden Mean is not as restrictive as many think. It is a starting point. It is about relationships, not exact coordinates.



Carol McIntyre
via keithbond.com
Did your research indicate how the Golden Ratio shows up in nature and in our hands? I think artists sometimes resist info like this because it feels like a "rule" whereas I think, like you, that is just another tool for us.

Thanks for bringing to the fore.

Inna Lazarev
via keithbond.com
Very lovely painting! Looks like spring with a crystal clear air. The reflection of the blue sky and birches in the water are done masterfully. There is almost spiritual dimension in this work!



Clint Watson
via keithbond.com
A couple of years ago I tried to register the domain "618.com", thinking I could create a website at "1.618.com" and make it a sort of "private" artist club that only those who "got" the reference could join. 618.com was already registered, alas it was not to be....

Dickson Brown
via keithbond.com
Hey Keith,

Just wanted to say hello, and comment on your painting 'Flat Lake Aspens'. I really like the way that you've captured the light.

All the best from the UK!

Dickson

Joe Soulagnet
via keithbond.com
I have enjoyed your artistic insights in Art Views and thought I would visit your website. I love this Flat Lake Aspens piece… the water is so well done. Which medium do you use? One thing I have noticed about lakes and ponds have been the small and thin portions of oil sheens on the waters. It troubled me so I asked a science teacher friend about it and he assured me that it is a natural occurrence due to the foliage and trees/roots that have natural oils contained in the plants. I knew this about conifers but not the deciduous plant species. Anyway, I thought it might be of interest to you because I’m sure you have seen this before yourself. I look forward to more of your insights and paintings!

Margi Lucena
via keithbond.com
Fascinating! I will definately be reading about Phi. It seems so natural, comfortable..this Golden Ratio. The examples you gave to Carol McIntyre are helpful. The composition is very pleasing. Makes sense!

Beautiful work, as always, Keith!

Margi Lucena
Socorro, NM

Janice Robinson-Delaney
via keithbond.com
That is the best haircut, ever!









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