The Golden Ratio in Art
|Bathers at Asnières
|The Fighting Temeraire
The placement of the golden ratio intersections varies according to the proportions of the canvas. In the first format below, the golden sections divide the square canvas almost in thirds. In the second format (a 1 x 2 ratio, for example a 12 x 24 canvas) the lines fall closer to the centre:
The Rule of Thirds
Most standard-sized canvases have a length:width ratio of between 1.2 and 1.4 to 1 (somewhat shorter than the “ideal” golden ratio of 1.618 : 1). A 12 x 16 canvas, for instance, is 1.33 : 1. On these formats, the golden sections (shown below in red) fall very close to the lines dividing the sides into thirds (shown in blue). This has led to a simplification of the golden ratio principle, known as the Rule of Thirds, which approximates the “sweet spot” by dividing each edge of the canvas into thirds.
Another interesting option for placing the centre of interest is the rabatment. The rabatment is the square that results when the short side of a rectangle is rotated onto its long side, as shown by the green line at the right. It’s not as well known as the Rule of Thirds and the Golden Mean, so I wanted to experiment with it a bit. In each of the examples below, I’ve marked the various methods as follows:
red = diagonals, with the “eyes of the rectangle” (halfway points) as dots
green = rabatment
purple = rule of thirds
blue = golden sections
This is the reference photo for a painting I did a couple of years ago. I cropped it to precisely a golden rectangle, so the length is 1.618 times the height. Not surprisingly, given the way the golden rectangle is constructed, the rabatment falls exactly on the golden section. The rule of thirds “sweet spots” are nearby (again, not surprisingly, since 0.667 is close to 0.618), and the eyes of the rectangle are just a bit further out, since they are based on quarters rather than thirds.
Van Gogh’s Sower with Setting Sun has a more standard length/width ratio of 1.26 (80.5 x 64 cm). In this case, the golden and rule of thirds “sweet spots are again close together and the “eyes” are a bit further out; this will always be the case since these methods are based on constant proportions. This time, though, the rabatment falls almost exactly on the eyes of the rectangle – again, not surprising, since they fall at the quarter marks of the canvas, and the height of the canvas is 0.79 times the length (very close to ¾). The figure of the sower falls on the rabatment. (He’s breaking another of the traditional composition “rules” by walking out of the picture, but rules are meant to be broken – or at least bent a bit!)
Finally, Thomson’s Jack Pine is an almost square format (127.9 × 139.8 cm), with a length/width ratio of only 1.09. In this case, the rabatment is way off by itself near the edge of the canvas, pretty well useless for composition planning. But look where the trunk of the tree falls, and the outer ends of those long branches!
Among modern artists, Alex Colville is perhaps the best known for his deliberate and extensive use of the Golden Mean and other geometric methods in planning the layout of his paintings. He’s not a landscape artist, so I’m not going to let myself get distracted by studying him right now. But he’s fascinating, so if you aren’t familiar with his work, I’d suggest looking him up.