Right Reading

concept to publication

Vitruvian Man (detail), by Leonardo da Vinci.

On Aspect Ratios

La condition humaine, 1933, by René Magritte. Oil on canvas, National Gallery of Art, Gift of the Collectors Committee1987.55.1.

La condition humaine, 1933, by René Magritte. Oil on canvas, National Gallery of Art, Gift of the Collectors Committee1987.55.1. The aspect ratio of the work on Magritte’s easel is about 1:1.2.

Most photographic and print publication work involves operating within rectangular frames. The relationship of width to height is the aspect ratio, expressed as, for example, 1:1 for a square, 1:1.5 for a 6 x 9 book, or 1:2  for a sheet that is twice as wide as it is tall. Conventionally, the width is stated first: that 6 x 9 book is in portrait format, whereas a 9 x 6 book would be landscape, bound on the short side, and most inconvenient to read.

A special case is the golden section or golden ratio, a rectangle with the proportion 1:1.618 (between 3/5ths and 5/8ths). In this rectangle the smaller dimension is to the larger as the larger is to the sum. In other words, 1 is to 1.618 as 1.618 is to 2.618. And as 2.618 is to 4.236, and so on. This relationship, which can be extended indefinitely, was known since classical times, and it underlies the Fibonacci Series and the modular architecture of Le Corbusier, among other expressions. Gustav Theodor Fechner, a German scientist, studied people’s responses to rectangular shapes in 1876 and concluded that the golden section is the most pleasing, though his methodology and results have been questioned. But other aspect ratios also have historic and aesthetic associations.

Photographic Associations

I am not aware of any cameras that produce images  in the relationship 1:1.618. The most common photographic formats, from squarest to widest, are these:

Differences among standard photographic aspect ratios.

Differences among standard photographic aspect ratios.

1:1

The square format, for photographers, is associated with relatively high-end cameras such as Hasselblads, though it was also used in some cheaper cameras. My first camera as a child was a cheap Kodak that shot in a square format. Square is an aspect that tends to say “photography,” since few traditional paintings used a square format. Square photos often crop their subject more aggressively than was common in fine art. The square format can also have a contemporary association, since many profile photos and logos on the web fit within square frames.

5:4 (4:5 = 1:1.25)

This format was used by large sheet-film cameras, formerly mainly in the size 8 x 10 in. but now also 4 x 5 in. It’s a great aspect that I wish was more readily available.

4:3 (3:4 = 1:1.33)

This is the native format of the micro four-thirds camera that I shoot with. It is also used in non-widescreen TV and computer monitors.

3:2 (2:3 = 1:1.5)

This is the format of 35 mm cameras (actually 24 x 36mm), once looked down upon by many professionals but now, ironically, seen as a professional aspect ratio because of its use in DSLR photo sensors. It is easier to use in landscape than in portrait mode. (Photographer Oleg Novikov, as we shall see, hates this format.) A great deal of twentieth-century photograph work was in this format.

16:9 (9:16 = 1:1.78)

Offered as an option in many digital cameras, this aspect ratio is used in newer televisions and films. Its wide aspect gives a sweeping quality in landscape mode, but it is difficult to use in portrait mode.

I have tended to use the 4:3 ratio in my photography because I have wanted to take advantage of the full sensor in the camera. Recently, though, I have shot jpeg + raw, which allows me to shoot in other ratios (such as square) as jpegs, while retaining the full sensor image in the raw version.

Gruss an Äachen rose. Some images look good in square format. For more on photography in square format, see <a href=” https://photography.tutsplus.com/articles/a-guide-to-producing-beautiful-square-format-images--photo-6615”>this post by Andrew Gibson</a>.

Gruss an Äachen rose. Some images look good in square format. For more on photography in square format, see this post by Andrew Gibson.

Photo Printing

There is a vexing disconnect between common camera aspect ratios and common photo print sizes. This is because paper size in the US is determined by convenient divisions of standard sheets (in other parts of the world you will likely be offered different standard trim sizes). If you are doing your own printing or have good control over the process, and you want to print a full image, you can accommodate different paper sizes by leaving variable white space margins or trimming the sheet. But cheaper photo print processors often simply crop the image for fit. Clearly this is something the photographer would like to control, as I will discuss further in a bit.

As an example of low-cost photo printing, the following sizes are offered by my local CostCo Photo Center. I have arranged them by aspect ratio (of which there are five, two of which are offered in only one size). Remember that the most common camera aspect ratios are 1:1, 1:1.25, 1:1.33, 1:1.5, and 1:1.78. Of these, only 1:1, 1:1.25, and 1:1.5 are represented in the common photo print sizes. That means if you are shooting with the common aspect ratios 4/3rds or 9/16s there is no paper size that will not require cropping or adding white space. In addition, the paper sizes 11 x 14 and 5 x 7 correspond to no common camera size.

  • 1:1
    5×5
    8×8
    12×12
  • 1:1.25
    8×10
    16×20
  • 1:1.27
    11×14
  •  1:1.4
    5×7
  • 1:1.5
    4×6
    8×12
    12×18
    20×30

Aspect Ratios in Book Publishing

A similar aspect ratio disconnect between favored graphic design proportions and common paper sizes exists in book publishing. This is an area in which I have decades of experience, and I have always been strongly influenced by the work done by Robert Bringhurst in his Elements of Typographic Style. Bringhurst has closely studied historical book production, particularly that of the Renaissance. He has identified several page shapes that “derive from” geometric forms. According to Bringhurst, pages derived from the pentagon tend to have an organic quality (“pentagonal symmetry is rare in inanimate forms … [but] basic to many living things”). Other pages are derived from the hexagon (“hexagonal structures are present in both the organic and the inorganic world”) and the octagon. The standard US letter size is within one percent of a page based on the octagon. “Are proportions derived from the hexagon and pentagon livelier and more pleasing than those derived from the octagon?” Bringhurst asks. “Forms based on the hexagon and pentagon are, at any rate, more frequent in the structure of flowering plants and elsewhere in the living world.”

To understand how page sizes are derived from geometric shapes, you will need to consult Elements of Typographic Style, as the explanation is beyond the scope of this post. According to Bringhurst,

Scribes and typographers, like architects, have been shaping visual spaces for thousands of years. Certain proportions keep recurring in their work because they please the eye and the mind, just as certain sizes keep recurring because they are comfortable to the hand. Many of these proportions are inherent in simple geometric figures — equilateral triangle, square, regular pentagon, hexagon, and octagon. And these proportions not only seem to please human beings in many different centuries and countries; they are also prominent in nature far beyond the human realm. They occur in the structure of molecules, mineral crystals, soap bubbles, flowers, as well as books and temples, manuscripts and mosques.

Below is a chart of common page aspect ratios presented by Bringhurst (his book, by the way, is based on a shape derived from the hexagon). Note that few of the common camera and photographic print aspect ratios are among the most distinguished in traditional book design. (In practice, this has often meant trimming down standard page sizes, resulting in waste and increased expense).

Shaping the page, a chart from Robert Bringhurst's <a href="http://amzn.to/2qzNx7E">Elements of Typographic Style</a>

Shaping the page, a chart from Robert Bringhurst’s Elements of Typographic Style. Click for a larger version.

Here are three examples of print aspect ratios from my work:

1616: 7.25 x 10 in. Aspect ratio: 1:1.38, a shape based on the short pentagram.

1616: 7.25 x 10 in. Aspect ratio: 1:1.38, a shape based on the short pentagram.

 

River of Ink: 6 x 9.25 in. Aspect ratio: 1:1.54, a shape based on the pentagon.

River of Ink: 6 x 9.25 in. Aspect ratio: 1:1.54, a shape based on the pentagon.

Bali: Art, Ritual, Performance, by Natasha Reichle, 10 x 12 in. Aspect ratio: 1:1.2, a shape that is close to the half octagon. Many museum catalogues are 9 x 12 in., so this is larger and squarer.

Bali: Art, Ritual, Performance, by Natasha Reichle, 10 x 12 in. Aspect ratio: 1:1.2, a shape that is close to the half octagon. Many museum catalogues are 9 x 12 in., so this is larger and squarer.

 

Aspect Ratios in Fine Art

As I mentioned above, photographer Oleg Novikov abhors the 35 mm 2:3 ratio. “There is something fundamentally wrong and unbalanced about the 2×3 aspect ratio,” he writes. “It is neither here nor there for portraits, it is neither here nor there for landscapes; indeed, I cannot think of any type of photography that would naturally call for this image aspect ratio.” Yet countless photographers have shot this format and done good work in it.

Novikov says he looked for examples of 2:3 in the Museo Nacional del Prado. “I could not find any. Not a single one. Now, think about this: the painters were not restricted by image aspect ratios in any way whatsoever; how come, then, that none of them ever used this particular aspect ratio?”

In the book world, 2/3 (1:1.5) is a common size. It is close to the pentagon page (as used in my River of Ink, see above). Indeed, the 6 x 9 in. trim size might be the most common of all among trade books (other contenders are 5 x 7 and 5.5 x 7.5). Here’s an example of a 6 x 9 book pulled more or less at random off my bookshelf:

Reading Jazz, by David Meltzer. San Francisco: Mercury House, 1993. Cover design: Sharon Smith. Cover art & type: Ward Schumaker.

Reading Jazz, by David Meltzer. San Francisco: Mercury House, 1993. Cover design: Sharon Smith. Cover art & type: Ward Schumaker.

Is Novikov correct that the 2:3 proportion does not appear in fine art? Michael Trott, Chief Scientist at Wolfram Research, performed an intensive mathematical investigation of this question, using several large databases, “totaling well over a million paintings and spanning the last millennium in time.”

It appears that Trott’s data is overwhelmingly drawn from Western painting. Among non-Western art, the use of scrolls as a medium in East Asian painting, for example, makes the issue of aspect ratios problematic.

In the following chart, Trott presents his results according to date of composition.

"Time Dependence by Grouping," from <a href="http://blog.wolfram.com/2015/11/18/aspect-ratios-in-art-what-is-better-than-being-golden-being-plastic-rooted-or-just-rational-investigating-aspect-ratios-of-old-vs-modern-paintings/">a study by Michael Trott of Wolfram Research</a>.

“Time Dependence by Grouping,” from a study by Michael Trott of Wolfram Research.

It can be seen that roughly 1:1.3, and its inverse, 0.77:1 (depending on whether the orientation is landscape or portrait) are among the most common aspect ratios throughout history. Trott says that “the median of the aspect ratios of all paintings decreased over the last 500 years and is slightly higher than 1.3. …The mean also decreased and seems to stabilize slightly above 1.35.” This conforms roughly to the shapes Bringhurst calls the tall half octagon and short pentagon. It is, surprisingly, close to the standard US letter size.

Looking at the following chart of the aspect ratios of some famous painters, again from Trott’s study, it appears that Novikov is correct that the 2:3 aspect is not a popular one. One exception, however, is the contemporary commercial artist Thomas Kinkade, who favors this aspect. (He was probably not represented in the Museo Nacional del Prado.) Perhaps Kinkade was influenced by 35 mm photography?

"Histograms for Famous Painters," from <a href="http://blog.wolfram.com/2015/11/18/aspect-ratios-in-art-what-is-better-than-being-golden-being-plastic-rooted-or-just-rational-investigating-aspect-ratios-of-old-vs-modern-paintings/">a study by Michael Trott of Wolfram Research</a>.

“Histograms for Famous Painters,” from a study by Michael Trott of Wolfram Research.

Trott’s study is a fascinating deep dive into mathematical analysis of aspect ratios in fine art. I have only touched on it here. Among his conclusions that seem relevant to this discussion are these:

  • “The aspect ratio distributions of many collections shows for both tall and wide paintings at least two clearly visible global maxima: one around 1.3 and one around 1.27 (and the reciprocal values for wide paintings).”
  • “Starting in the eighteenth century, aspect ratios that are rational numbers with small denominators become more and more popular; this trend is still ongoing—the timing coincides with the French standardization of canvas sizes.”
  • “Nineteenth- and twentieth-century paintings show pronounced maxima in their aspect ratio distributions at the aspect ratios 6/5, 5/4, 9/7, 4/3, and 3/2.”
  • “The golden ratio is not an aspect ratio that occurs prominently in paintings.”
  • “The distribution of paintings is unique and quite distinct from the distribution of rectangular objects from the modern world (such as labels, stamps, logos, and so on).”

Trott references a study by Jessica Winne et al in the journal Behavioural Brain Research that appears to show that humans and other mammals respond most favorably to aspect ratios around 1:1.2. This is close to the size Bringhurst calls the half octagon. The closest photographic standard is the large-format 5:6, though this format is no longer particularly common. The next closest is the 4/3rds. Among standard photo print sizes, the closest are 8 x 10, 11 x 14, and 16 x 20.

Conclusions

For the practicing photographer, printer, or painter, I think the main take-away from all of this is simply to be sensitive to the impact of aspect ratio on the subject of the work. Certainly no one ratio is always best, and few of us would be excited about visiting a museum where all of the works had identical proportions.

For the photographer, it is helpful to be aware of the disconnect between standard camera aspects and print sizes. If a photo is intended for print, there are likely to be cropping or margin issues that must be accounted for. When I crop a photo for low-cost printing, the technique that I use is to calculate the print aspect ratio based on the size of the original file. (I’m told there is an easy way to do this in Lightroom, but I work in an aging version of Photoshop.) For example, my micro four-thirds file sizes are usually 3024 x 4032 pixels. If I want to print such an image at 5 x 7, for example — a size that is wider and less square — I divide the width, 4032, by 7, which gives 576. Multiplying that by 5 gives 2880. This will be the new height as a 5 x 7.

My next step is to create a new document in Photoshop that is 2880 x 4032 pixels. I fill the entire document with a color that is different from the photo image. I select the entire new document and paste it as a new layer in the original photo document. Next, I adjust the transparency of the new layer so that it remains visible while allowing me to see through to the underlying image. Now I can move the semi-transparent layer around to select a desirable crop. Then, in the new layer, I select all of the fill color. This selection will be precisely 2880 x 4032 pixels. I use that selection to crop the image, and then I delete the new layer. I now have a version of the photo that is exactly in the proportion 5 x 7, so I do not have to leave any cropping up to the photo processor.

Recommended Online Resources

 

 

 

 

Previous

Links for May 25

2 Comments

  1. This is a really wonderful overview – I haven’t seen anything so good since Bringhurst. One extension that might be wondered about: how do screens come into this? There’s of course the long history of aspect ratios of film and television. I remember the shift when Apple went from a 4:3 ratio to a 16:9 ratio on their screens, which seemed to get picked up by almost everyone – computer screens (and televisions) are mostly 16:9 now. A 4:3 screen almost looks squashed to me now, which I expect is true for most people? (The iPad would be the exception.)

    I do wonder a little about how perceptually accurate ratios are in the real world – while the cover of 6” x 9” book certainly appears to be 2 : 3, a spread of an open perfect-bound 6” x 9” book is going to appear different – the gutter swallows some of the width of the page.

  2. Thanks, Dan. I think it’s possible the mind subliminally adjusts for the portion of the page lost to the gutter. A book is, after all, a three-dimensional object, and the reader’s hands can feel the extra bit. And the pages when the book is opened are subtly curved, leading to awareness of the concealed portion.

Leave a Reply

Some rights reserved 2017 Right Reading. This work is licensed under a Creative Commons (attribution, noncommercial, no derivs: 3.0) License (US), although some of the work this blog incorporates may be separately licensed. Text and images by Thomas Christensen unless otherwise noted. For print permissions or other inquiries please request via rightreading.com/contact.htm.