PAINTING SUPPORTS, WHETHER panels or stretched canvas, now come in standard sizes, by inches in the U.S. and by centimeters in Europe. The cross-Atlantic mismatch has made it difficult to universally navigate canvas and frame sizes, yet the preferred visual proportions roughly are the same.
This sameness—a kind of “golden” shape—may suggest that humans share a common preference for the proportions of a rectangle, a shape with long and short parallel sides.
We’ll leave the square painting out of this discussion, and look at the dominant trend in rectangles. General acclaim goes to the 3-to-4 proportion. That explains the ubiquity of the standard support sizes of 9x12, 12x16, 18x24, and 30x40. These are longish rectangles, usually best for landscapes but a bit tall for portraits or other vertical subjects.
The more squarish alternative is the 11x14 and 14x18, which are 3-to-4, then made a bit more squat. The most squarish rectangle is the 4-to-5 ratio, seen in the standard painting sizes of 8x10 and 16x20. We approach the almost-squared canvas in the standard 35x40 or 40x42 sizes (with proportions of 7-to-8 and 20-to-21).
Convention and the art supply market have put these sizes in stone, though painters can simply make any size support they like. Custom framers can simply match that. Yet hoovering in the background has always been the sneaking feeling that there is an ideal rectangle, a shape that is the most aesthetically pleasing. Something “golden,” perhaps.
This has been the idea behind the “golden ratio,” a mathematical idea seen since the time of Plato, revived in the Renaissance, promoted by the cubists and modernists, and now the serious domain of mathematicians, geometers, and naturalists.
The ratio can appear in a line and in a rectangle. In the latter, it is when the two different sides are in a ratio (1 to 1.6). Once you have that, it turns out that adding together the two sides (long and short) will also be in the 1-to-1.6 ratio to the longer of the sides.
Mathematically the ratio is 1-to-1.6180339887498948482 . . . Over centuries it has been found not only in mathematics (such as the Fibonacci Numbers) and geometry, but in nature as well, describing the curl of the nautilus shell or the growth pattern in some leaves. In short, the golden ratio has become perhaps the most ponder mathematical fact in Western history.
In visual art, the modern burst of interest came with the cubists, who evoked Leonardo da Vinci as a user of the golden ratio. One such group in Paris in 1912 called itself the “Golden Section,” perhaps more out of publicity than math, because almost none of their artworks used the 1.6 fraction.
The golden ratio is still taken seriously by some traditional painters who believe it was a formula for aesthetic excellence used by the Renaissance masters. There have also been speculative claims, reacted to by efforts to debunk them. The debunkers have shown that da Vinci's human figures don’t exactly fit a golden rectangle, that is, touching every side of the box and not going outside of it.
Advocates of the ratio in art, meanwhile, have come up with a number of paintings since the Renaissance that seem—with emphasis on seem—to show this kind of proportion, either in the support or objects in the painting. Zeroing in on objects can be rather speculative. Then there are hyper-advocates who argue that the proportions are in the Greek Parthenon and Great Pyramid. Still, while many longish triangles approach the golden ratio, to be “true,” they must finally meet the mathematical precision of 1-to-1.6.
As a counterpoint to ratio enthusiasts, one study of hundreds of prominent paintings across modern Western art have found that few if any intentionally match the golden formula. Instead, the average size is about 1-to-1.34—almost exactly the 3-to-4 proportion of today’s 9x12, 12x16, and 18x24 paintings.
To conclude, the ratio can be used easily enough if one chooses. Modern architects, cognizant of the exacting mathematics, simply measure it out. The Swiss architect Le Corbusier used the 1-to-1.6 proportion designing the floor plan and walls of some buildings. Knowing that this exactness is incorporated, the viewer is left to decide whether it makes such buildings more beautiful.
A painter can stretch a canvas at, say, an even 15x24 inches, and have a midsize painting in the golden ratio. But it’s a very uncommon size, for sure. Nor has the television industry gotten the message: The ratio of the standard widescreen TV is 1-to-1.78.
For everyday painters, all of this this can be fascinating art history, a reminder that two-dimensional visual art often has been seen as pointing to something transcendent. In practical terms, you can get a golden ratio painting panel by following this mystical recipe: buy a standard 16x20 canvas panel and cut it in half. You’ll have a golden 10x16, a very nice longish rectangle shape, perfect for a widescreen landscape or still life. Mystical it may be. Then, you’ll have to get custom framing.
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