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A load of old ROT — an exploration of the Rule of Thirds

Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who being naughty in my sight, shall snuff it

— Monty Python

I'm sure everybody who works in the visual arts — whether it's drawing, illustration, photography, oil painting, or whatever — will have heard of the Rule of Thirds (ROT). It's a well-established compositional guideline, which suggests that one or more elements of the main subject of the picture should be placed at the points of intersection of lines that divide the frame into thirds. The photograph below is an example.


Here the subject's eye, and the tip of the magic wand she is holding, lie (more or less) at two of the intersection points of the lines that divide the frame into thirds. Arguably the chimney of the house in the background lies on one of the other intersection points, but that was just a coincidence.

You'll notice that the subject is much larger in the frame than the point of intersection which is, well, a point. There have never been any compelling arguments to line up any particular feature of the subject with the intersection points, nor to line anything up exactly. So the question must naturally arise: is there anything particularly relevant about the division into three here, or is it simply a matter of placing the subject somewhere off-center?

Origin of the ROT

The term "Rule of Thirds" appears to originate from a book Remarks on Rural Scenary (1797) by one John Thomas Smith, an English engraver and painter.
"Two distinct, equal lights, should never appear in the same picture : One should be principal, and the rest sub-ordinate, both in dimension and degree: Unequal parts and gradations lead the attention easily from part to part, while parts of equal appearance hold it awkwardly suspended, as if unable to determine which of those parts is to be considered as the subordinate. [...] Analogous to this "Rule of thirds", (if I may be allowed so to call it) I have presumed to think that, in connecting or in breaking the various lines of a picture, it would likewise be a good rule to do it, in general, by a similar scheme of proportion; for example, in a design of landscape, to determine the sky at about two-thirds; or else at about one-third, so that the material objects might occupy the other two : Again, two thirds of one element, (as of water) to one third of another element (as of land); and then both together to make but one third of the picture, of which the two other thirds should go for the sky and aerial perspectives. This rule would likewise apply in breaking a length of wall, or any other too great continuation of line that it may be found necessary to break by crossing or hiding it with some other object : In short, in applying this invention, generally speaking, or to any other case, whether of light, shade, form, or color, I have found the ratio of about two thirds to one third, or of one to two, a much better and and more harmonizing proportion, than the precise formal half, the two-far-extending four-fifths—and, in short, than any other proportion whatever."
Notice that Smith does not begin by considering proporption, but the balance of light and shade. His argument is that if two features in an image are of equal prominence this will confuse the viewer, whose attention will be drawn back-and-forth between them. Presumably the same reasoning applies to composition, but Smith gives no particular reason for chosing thirds, beyond the fact that four-fifths would be too unbalanced. No reason is given, so far as I can see, for excluding the use of a quarter however, which lies between a third and a fifth in size.

So, ultimately, it would appear that the so-called Rule of Thirds stems from one artist's assertion that two-thirds to one-third is a more agreeable proportion than some other: not particularly scientific. I think that we might reasonably rewrite Smith's guidance like this without changing its meaning very much:

"Try to vary your image in terms of proportion, colour, and light, but not too evenly, and not too unevenly."
But thirds is what he asked for and, since 1797, the ROT has been elevated almost to an undisputed principle of art. My camera has ROT guidelines in its viewfinder, and many photo-editing applications (for example, Adobe Lightoom) display ROT lines whilst cropping images. Nobody seems to give a whole lot of thought to whether the ROT has any empirical basis.

Of course, I don't know many visual artists who comply slavishly with the ROT — although I've certainly heard tales of some who do. Very often, those who seek to elevate the importance of the ROT do so by comparing it to the Golden Ratio, to which we now turn.

The Golden Ratio

The Golden Ratio (GR, or Golden Mean, or Divine Proportion, etc) is a way of dividing a line into two such that the resulting division has — or is claimed to have — a particular aesthetic appeal. The value of the GR is determined by considering a rectangle being cut in half along its long edge. If the two rectangles that result from the cut have the same proportions as the original rectabngle, then the cut was at a distance along the long edge defined by the GR.

Anybody familiar with British paper sizes will have seen the GR in use: the common A1, A2... sizes all have their heights and widths in proportion to the GR. However, I suspect that this is less a matter of aesthetics and more one of pragmatism: all the other paper sizes can be cut from an A1 sheet with no wastage, something that is not true for other proportions. In addition, an A3 sheet can always be photo-reduced to A4 with no change in the aspect ratio, and the same is true for all the other sizes.

Mathematically, the GR is the number φ which solves this equation:

1/φ = φ-1
and is approximately equal to 1.618.

The GR does appear clearly from time to time in the natural world, such as in the proportions of certain sea shells or, remarkably, some spiral galaxies. However, claims that this ratio is widespready in nature need to be considered with a degree of scepticism: there are many, many measurements that might be made of any natural object, and it is very easy to find whatever propertions we go looking for. The GR is mathematically related to the Fibonacci series, which is something that also appears in nature from time to time. The Fibonacci series is what we get when start with the number sequence "1, 1" and extend it by adding the previous two numbers together. So the first few terms are 1, 1, 2, 3, 5, 8, 13... 13/8 (1.625) is pretty close to the GR (1.618) and as the terms increase in size, the ratio of two successive terms gets closer and closer to the GR. This is not a coincidence, of course.

The Fibonacci sequence is a striking feature of certain natural structures, such as the distribution of petals on the leaves of some flowers. However, like the GR itself, it is hardly ubiquitous, and there are enough measurements in nature that it can be found if we seek it hard enough in enough places.

Similarly, while the mathematics of the GR were known in antiquity, there aren't a whole lot of historical buildings that are proportioned according to it. The Parthenon in Athens is an example that is often cited — the GR appears several times when comparing the lengths of certain features. However, the Parthenon is prominently symmetrical (that is, it's primary division is into two) and the GR was used, if it was used, for less prominent measurements.

If the GR does lead to an aesthetically-pleasing rectangular shape, it's worth asking why traditional sizes of photographic paper or painter's canvas are rarely in this ratio. In practice, these items are usual manufactured to have sides in a ratio 3:2 or 4:3 — a standard 35mm negative has a 3:2 aspect ratio. Computer and television screens are increasingly made with a 16:9 ratio or even wider — cinematography has usually favoured wide aspect ratios. This is a bit of a digression, however, because we aren't really considering the aspect ratio of an image here, but the placement of objects within it, and there's no particular reason to think that the same considerations should apply.

The Golden Ratio and the ROT

I've lost count of the number of times I've heard that the ROT is derived from, or based on, the Golden Ratio. Even if it were, we are still left with attempting to justify the GR in terms of natural aesthetics which, as I've explained, might not be as straightforward as is often claimed.

The reality is that the GR and the ROT are not related to one another in any non-contrived way. They give very similar proportions, but that is merely a coincidence.

The diagram below shows a rectangle divided both according to the ROT and to the GR (shown as φ in the diagram). The vertical red stripe shows the area of difference between the two approaches.


We just can't write down some simple mathematical formula that will turn φ into the number 1/3 or 2/3 — that connection simply isn't there.

What could legitimately be claimed, I think, is that the ROT is a simplification of the GR. It's much easier to say "divide the width and height into three equal parts" than to say "divide the width and height into two unequal parts such that the ratio of their lengths is given by the solution of this equation..." If there were some aesthetic significance to the GR, then simplifying it this way might be a sensible, pragmatic thing to do.

However, looking at the examples that various photographers and photography tutors use to illustrate their use of the Golden Ratio, it's pretty clear that it's applied pretty loosely when it is applied (the same is true of the ROT, in my experience.) If the GR genuinely were aesthetically compelling, I would think that artists would tend to gravitate towards following it quite closely but, in practice, this does not seem to be the case.

Thirds in art

Whatever we might say about the GR, the number three, or ratios involving the number three, do crop up in the arts, and do so very commonly.

For example, the ratio of musical pitches that we call a fifth in the Western world is a frequency ratio 3:2. A fourth is 4:3 (sort of; see this article for a much more detailed discussion of the significance of integer ratios in musical scales.) A large-scale musical composition has traditionally comprised three movements; often individual movements will have three sections of which the first and third are similar (or even identical) while the second is in contrast to them.

Many plays are divided into three acts. In Britain, half-hour radio and television shows were traditionally divided in to three, ten-minute 'acts,' although the need for advertising breaks has somewhat eroded that practice.

In ancient Greek literature and mythology entities tended to be grouped into threes: three Fates, three Furies, three Graces, etc. Macbeth had three witches. Threes turn up also in Christian, Jewish, and Buddhist mysticism, and probably in other traditions as well.

A common way of presenting paintings, particularly of religious subjects, was as a triptych — three connected panels, usually with the central panel larger or differently shaped to the outer panels. The same layout sometimes features in religious architecture: the facade of Notre Dame Cathedral resembles a triptych.

It isn't hard to find other threes in architecture, both ancient and modern. There's a whole bunch of three-arch buildings in Washington, DC, for example. In fact groups of three in architecture are so ubiquitous that it's scarely worth trying to list examples.

Despite all these threes in the arts, there remain plenty of twos and fours. Three is a common number of movements in a symphony, but four-movement pieces are far from rare. There are many pieces of music written for trios of instruments, but the number of string quartets alone probably outnumbers them all put together. Most buildings have a four-sided plan, and usually a four-sided elevation. The pyramids at Giza have four faces, not three (five if you count the base.)

And, of course, three is the number to which we count before throwing a hand grenade. Modern software engineering favours a three-tier approach to system architecture. There are three sizes of coffee cup at Starbucks. And so on.

Perhaps the reality is that three is nothing more than a convenient small number?

Summary

Rules, we are often told, are made to be broken. The so called 'Rule' of Thirds is broken so frequently that it is safe to say explicitly: There is no Rule of Thirds. Any claimed connection to the Golden Ratio — itself a concept of dubious aesthetic significance — is bogus.

The reality is that, in the visual arts, we humans tend to prefer our focus of interest to be somewhat away from the centre, but usually not right on the edge. And that's really all there is to it.

Copyright © 1994-2015 Kevin Boone. Updated Feb 10 2015