As visual displays, paintings have the potential to be three things at once: a representation that mimics natural perception in a physical environment; a pleasing geometrical or abstract arrangement of line, texture, symbol and color; and an artful arrangement of forms within the edges of a flat surface.
So there are three design systems operating in an image at the same time: (1) the proportions among physical objects in relation to a projective geometry that simulates the appearance of a three dimensional space, taught as linear perspective; (2) the arrangement of shapes, tones and colors in relation to each other that creates an attractive visual pattern, usually taught as principles of composition and design; and (3) the distribution of all image elements within the format proportions, the space defined by the image boundaries.
Across a long pictorial tradition, the picture plane was thought of as a window opening onto a three dimensional picture space. Linear perspective dictated the size and shape of objects in this space, but left to the painter the problem of presenting them to view, much as a director arranges the actors and props on a stage. These problems of "staging and set design" were governed by principles of composition, primarily to make the grouping of elements in the painting legible, pleasing and meaningful.
This emphasis on perspective and composition demoted the format edges to peripheral vision and, until the early 20th century, paintings were almost always framed (often ostentatiously in ornate and gilded materials) in order to separate the image limits from the image itself by making the image limits appear to be imposed by a foreign object the frame. These conventions transformed the format into an illusory, arbitrary restriction, as if removing the frame would reveal an expansive, unedited view of the picture space.
In contrast, the 20th century esthetics of nonrepresentational and pop painting often made explicit expressive use of the size and shape of the image itself. Everything imagined to create the image is available to view on its surface; the limits of the painting were integral to its overall legibility and impact, and there was no implied representation outside the format. These paintings are typically displayed unframed or, in paintings by Paul Gauguin, John Marin, Howard Hodgkin and many others, image elements were actually painted onto the frame, or framing elements were painted into the canvas, so that frame and image united as a single object.
To govern these new styles, painters did a peculiar thing: they attempted to justify in abstract or "scientific" terms the compositional principles developed in the representational (perspective) tradition. This process of abstraction took off in the 19th century, for example in the writings of John Ruskin or Auguste Laugel, and it flowered into a largely subjective system of "design principles" that is still taught to art students today. These dogmas disregard format based rules of design, although format principles seem clearly implied by contemporary painting assumptions.
As a corrective to this oversight I have tried to understand how the different format dimensions create lines of proportional stress or emphasis on the picture plane. In this page, I describe an explicit proportional system based on half folds or squares of the format dimensions, and suggest some design principles based on them.
These format proportions apply to rectangular formats with proportions between 1:1 and 2:1 (height:width or width:height). This includes the majority of artworks etchings, prints, paintings, frescos since the Renaissance, and all popular watercolor paper formats. I believe other formats circular, oval, elongated landscape or standing figure formats can be controlled with similar proportional schemes by enclosing the format within a rectangle or square, though I don't pursue those possibilities here.
In my experience these format proportions produce balanced and satisfying images that can be architectural in their stability and poise; compositions judged with them are often very good, and never "bad". They provide a reliable frame of reference simple, explicit, objective within which the perspective and formal composition of a painting can be critiqued. They are apparently an intuitive solution to compositional problems, as paintings that rely on the format proportions can be found in any survey of Western paintings from the 15th to 20th centuries. In many cases an artwork does not conform to the proportions exactly, but achieves dynamism by approaching them nearly.
Analyzing a painting in terms of the format proportions puts both representation and "composition" on an equal footing, and is surprisingly useful to uncover basic design decisions. In fact, editing an "unruly" painting to improve its format proportions often clarifies the effects that are created by disregarding the proportional divisions.
Note added in 2005: Several years after this page was written, a reader alerted me to Charles Bouleau's Frameworks: The Secret Geometry of Painters (1963), which analyzes paintings in terms of "the armature of the rectangle" and describes a method of rabattement des petits côtés that I present as the square divisions and quarter folds of the rectangle. However, I was disappointed to find that across more than 100 painting examples Bouleau merely inserts whatever ad hoc "framework" seems convincing to him in each case, without any historical testimony or xray evidence to confirm the constructions were actually used by the painters. Despite Bouleau's priority, this page is my independent and far more systematic contribution to the problem of design within rectangular formats.
the key format proportions
The key format proportions are based on symmetrical folds across the picture space and squares constructed from these fold dimensions. The folds divide the format into fundamental units, while the squares are (as it were) the harmonics that emerge from the fundamentals.
In rectangular paintings with an aspect ratio (the ratio of height : width) between 2:1 (a "portrait" rectangle) and 1:2 (a "landscape" rectangle), the obvious format proportions are the dominant half folds of the height or width, which divide the picture plane into quarters and locate the format center; and the weaker quarter folds that divide the sheet into sixteenths. (These "folds" are imaginary; you don't actually crease the paper.)
As shown above, these folds create the horizontal midline (M, blue in the figure), which divides the picture into two equal horizontal bands, and the vertical centerline (C, red in the figure), which divides the picture into two equal vertical sections. Each of these sections can be folded in half again, creating two secondary midline folds (m) and two secondary centerline folds (c), or six folds in all.
I've also shown, as an orange box, the outermost eighth folds (cc and mm), which are halfway between c or m and the nearest edge of the sheet or frame. These establish an implicit content boundary inside the image; as I explain later, strong forms in the image usually should not extend beyond this frame, unless the forms extend beyond the image boundaries or represent flow or dynamic movement.
The compositional importance of these divisions is roughly C > M > c > m. This is revealed in the esthetic effect of edges that match the folds. It is visually more distracting if a vertical edge (the side of a building) coincides with C across most of the height of the picture, than it is when a horizontal edge (the horizon) coincides with M across most of the width of the picture; this implies M is a weaker division. Placing a pictorial edge along C seems to split or unbalance the image, while an edge along M does not.
The second system of format proportions is based on squares constructed from the smaller format dimension the height of the sheet in the landscape format, the width in portrait format and from the "edges" created by the centerline and midline folds.
The diagram (above) shows these three divisions: the square defined by the height of the format (which creates the vertical division h'), the square defined by the width of the half sheet on either side of the centerline (which creates the horizontal division c'), and the square defined by the height of the quarter sheet above or below the midline (which creates the vertical division m'). These square proportions are constructed from both the top left and bottom right corners, producing six more proportional divisions.
In general, the visual emphasis carried by these divisions is h' > c' > m'.
In the portrait orientation the height of the image is larger than its width, so a square based on the larger format dimension falls outside the image. However, when hanging a painting, this square is useful to determine the minimum distance between the painting and objects on either side of it (diagram, below).
These various divisions rarely duplicate each other to divide the format into precise subsections. Instead, they indicate stronger and weaker lines of emphasis, which suggest the effective placement within the image of strong edges, important detail shapes, or accenting changes of contour.
constructing the format proportions
Now I'll explain different methods for defining or constructing the format proportions on your painting surface or photographic image.
Construction by Measurement. The easiest method for making the divisions is to use a straightedge premarked with the divisions for a specific format.
Watercolor blocks are glued at the edges and bound with a paper cover: the format divisions can be marked on the outside of the cover, and transferred to the sheet from these marks. A yardstick can be marked with a colored felt pen with the divisions for a full or half sheet. These divisions would be indicated very lightly with pencil on each new sheet before outlining or painting the composition. These prepared guide marks or measuring sticks are especially useful when you habitually use the same format to make many works.
Larger or unusually sized sheets require individual measurement. The most accurate way to do this is with a ruler or tape measure, as follows:
1. Measure the long and short dimensions of the sheet.
2. Divide these two dimensions by 4.
3. Mark the centerline, midline and quarter folds from these divisions. Measure on four sides of the sheet and connect to create six lines.
4. Mark the shorter dimension of the sheet along the longer edge to locate the square h'.
5. Mark the centerline and midline dimensions, along the edges parallel to each fold, to define the squares m' and c'.
Constructing With "Compass" and Straight Edge. Classical methods avoided working with numbers. In this approach, you can use a long piece of string tied around the tip of a pencil, or a cardboard strip fixed at one end with a push pin, as both compass and ruler.
1. Put the pencil point at the upper left corner of the format (at 1 in the diagram, above), then gently stretch the string to the lower left corner (at 4) and anchor it firmly at the corner with your left thumb.
2. With your right hand, bring the pencil across and down the sheet toward the bottom edge, keeping the string taut. As you do, lightly draw a short arc at three places: around the approximate centerline of the sheet, around the approximate midline of the sheet, and at the bottom edge (blue marks in the diagram).
3. Repeat this procedure three more times, fixing the string at each of the remaining three corners, and keeping the string the same length. This will produce matching edge marks for the h' divisions at the top and bottom of the sheet, and four "x" marks within the sheet where two arcs cross at the midline or centerline.
4. Lay a straightedge or long ruler across the paper between matching edge marks at the top and bottom of the sheet, and make faint vertical line on the sheet for the two square divisions h'. C is defined by a vertical line through the two arc "x"'s on the centerline; and M is indicated by a horizontal line through the two arc "x"'s at the midline, as shown above.
5. To find the quarter divisions, lay the straightedge or ruler so that one end is lying on the midline or centerline, and the other edge at an opposite corner. Then draw a faint line where the ruler crosses the centerline or midline (black dots in the diagram, above). These indicate the placement of the horizontal and vertical quarter folds.
6. Again fixing the string at each corner, place the pencil on the midline M, then swing this distance up or down to the top or bottom edge; these marks define m' on both sides. Connect with two vertical lines.
7. Finally, fixing the string at each corner, take the distance to the centerline down to the side edges; these marks define c' on both sides. Connect with two horizontal lines.
Rabattement des petits côtés. Charles Bouleau describes a method he calls rabattement des petits côtés ("folding down of the smaller sides"), as shown in the diagram (below).
1. Measure and mark the length of the shorter sides of the rectangle along the longer sides, from the corners at both ends, and connect the marks to define the divisions h'.
2. Construct the two diagonals inside each of the squares formed by h'.
3. These diagonals will form a small diamond or rotated square in the center of the format. A vertical line through the top and bottom corners of this square defines C; a horizontal line through the left and right corners of this square defines M; horizontal lines through the top or bottom corners define the two m' divisions; vertical lines through the two side corners define the two c' divisions.
4. Using diagonal lines, as described in step 5 of the previous method, construct the quarter folds on all four sides.
In the diagram, the rabattement of the short sides locates the division h', point 1 determines the midline and the vertical division m', and point 2 defines the centerline and the horizontal division c'. This construction method creates more lines on the sheet than necessary, although the diagonal bands may be useful as compositional guides.
composing with the format proportions
If you are working at any stage with digital photographs, then the format proportions are most easily implemented as an image overlay onto the reference or original photograph, using graphics or image editing software.
Computer Format Templates. You must first determine the file image size (pixel height by pixel width) appropriate for your working methods. This means you have format templates for:
1. each of the paper formats you use most often,
2. sized to accommodate the projection or copying method(s) you use to transfer the image outlines to the paper.
The first issue arises because different brands of paper define the standard formats differently (the double elephant in Arches is not the same as the double elephant in Saunders Waterford, for example); some brands (Zerkall) use nonstandard dimensions; and all handmade sheets can be quirky.
The second issue arises because optical projection systems have different focal lengths or enlargement ratios. If you want to project an image onto a full sheet paper, for example, then the image you are projecting should be large enough to produce a large, bright image for copying, but not be so large that it cannot be brought into crisp focus across the entire format area.
The following images show the format proportion templates for two common watercolor paper formats and the classic golden rectangle. These also illustrate what happens to the format proportions as the rectangle becomes more elongated. (For comparison, the horizontal and vertical divisions by thirds are shown as small blue dots.)
If you open these templates in a new window, you will find they are actually 450 pixels wide. I use that standard width because when it is printed at 100% size it is the largest image that will fit into the window of my opaque projector without optical distortion. You may need a larger or smaller template for your particular equipment and methods.
Computer Image Editing. Once the format proportions have been constructed or templated, then fitting the image into the format and aligning the image elements with the format proportions is a matter of experience, artistic style and the specifics of the image.
I use the format proportions to edit the composition of a digital photograph, as described next. However the logic of the method applies as well to composing the image by eye in a freehand drawing or through a camera viewfinder.
First do any major image editing in the full size image before working with format proportions. For example, in landscape photos, I typically correct for foreground expansion caused by the camera optics, so I do this before adjusting to format proportions. I may also delete or reposition (cut and paste) objects in the photo to improve the image composition and legibility before using the format proportions, or to bring everything into better aligment with the folds and squares when the format proportions are added.
Here, step by step, are the menu and keystroke commands for Adobe Photoshop in the Mac OS:
1. Open as separate files the art image and the format template for the support you intend to use for the painting or drawing.
2. In the format template file, Select All (Command+A) and Copy (Command+C) the format template. Close this file.
3. Switch to the digital image file and Paste (Command+V) the template as a new layer on top of the digital image.
4. In the Layers window, set the transparency of the format template to 50%. (If you do not see the Layers window already open with your files, it is found in the Windows > Layers pulldown menu.)
5. In the Layers window, click on the digital image layer. Then Select All (Command+A) and choose the Free Transform function (Command+T). The image will be outlined by an animated dashed box, with small squares at each corner and the center of each side. Note that I resize the photo rather than the template, because the template has been presized to accommodate my printing and projection tools.
At this point your working image will appear similar to the upper image above. You will see the digital image and, floating in front of it, the semitransparent format template.
6. Hold down your shift key and option keys (Shift+Option) at the same time, then click on and hold a corner box of the image with your mouse cursor.
Move this corner toward or away from the center of the image to resize the image.
Release the shift and option keys, then click and hold anywhere inside the image to grab the image to move it up, down, left or right. (You can also use your keyboard arrows to make these repositioning adjustments.)
Continue resizing and/or repositioning the image until you get the image proportions you want within the format outline.
7. Double click inside the image to resize it. The Free Transform guides will disappear.
8. Using the Layers window, click on the template layer.
9. Using the magic wand tool, click on the area outside the template. Then Select Inverse (Shift+Command+I) to select the template itself.
10. Crop the image (from the pulldown Image > Crop menu). Your file will now look like the bottom image, above.
11. In the Layers window, grab the template layer and drag it to the layer trash can. The template disappears.
12. Mark the corners of the image with black dots if they will not be easily visible when the image is projected, so that the image can be correctly sized, focused and registered over the support for tracing.
Note that the resizing and repositioning may produce an empty border along one side of the image (as you see along the lefthand edge in the example above). This area is usually small enough so that it can be completed freehand during the process of tracing or painting. If it is much larger, you can use the image editing program to fill the area by copying and pasting elements of the image.
Format Design Principles. Step 6, the actual resizing and repositioning, is a subjective and exploratory process. It is important to play around with the image, trying different sizes and different positionings of a new size, before you find a solution that "clicks" (and you double click on it).
I sometimes just observe the effects of resizing until I notice a solution that seems to work, then I reposition and resize to the template guidelines. If the result does not seem satisfying, I return to the original image size (Control+Z) to find another one. Often, the size of the major form dictates the approximate enlargement required, and it's just a matter of moving the resized image around to position it against the template guidelines.
A reliable method is to start with the most dominant image element(s), and work from those to the less important image elements. In the example image, the cat, bookshelf and window created an obvious vertical point of interest, so first I positioned the image so that these fell against the righthand h' and c divisions. Then I resized the image to find a good placement against the lefthand h' and c, and finally moved the resized image up or down to find a good placement against the horizontal guidelines.
Do not center important large forms. Avoid centering any dominant object, either around the midpoint of the format or on the centerline or midline. The major exception is when the object is isolated in the image and is the sole focus of attention (for example, the animal skull in the O'Keeffe painting below, or any portrait by Chuck Close). In the example image, no object is centered.
Do not place strong edges along the centerline or midline. For example, in a landscape, do not place the horizon or rooftops along the midline, or the edge of a building along the centerline. In the example, there is no strong edge along the centerline or midline.
Emphasize the edges or dimensions of important large forms, or the center of important small forms, by placing them on or next to the format folds or squares (other than C and M). The goal is to place the dominant forms and edges in the image so that they seem to fit into or hang from the format guidelines. How you approach this depends on your choice of important or interesting forms and their spatial relationships within the image. During digital editing you can resize the image so that the dominant objects correspond to the template guidelines, and use cut and paste or drawing tools to move or edit less important objects or edges into better alignment.
For partial balance, place two important but contrasting forms along the two strong vertical lines (h' and c) or (h' and m'). In the example, these are the front left corner of the table, the paintings propped on the table top, and the nearby front right corner of the cardboard box (on the lefthand h' and c), and the edge of the bookshelf, window and the inquisitive cat (on the righthand h' and c).
For asymmetry, place a single important form or strong edge along only one strong vertical line (h' and c) or (h' and m'). In the example, the bookshelf and cat at the righthand h' and c, and the illumination flowing into the frame from the window, provide stronger visual interest and greater emphasis than the corner and leg of the table at left. All the forms are arrayed in relation to the compact, bright window puncturing the shadowed wall, and the large, diffuse area of illuminated wall and floor.
Place the center of attention off center but inside the central rectangle. The central rectangle is defined by the dominant vertical lines h' or c on either side and by c' and/or m above and below. Note that these lines may be close together (as are h' and c in the image above) or may be separated (c' and m in the image above), which I feel defines gradations in emphasis that are unique to each format.
The central rectangle is typically the place in the composition where the principal subjects (including strong contrasts of value, color, texture or visual detail) are located. In the full sheet format (used in the example above), this area is large and well structured, allowing for an expansive visual interest including the cat, the bookshelf, the chair and the table.
Notice that the same image could be resized and cropped in many other ways to emphasize the cat, the table, the cat and the window, and so on. As is, the image implies a broad view of the whole room. (The photo was taken as my wife and I were unpacking in our retirement home, and for me evokes a moment of nostalgia, which is not a detail state of mind.)
Enclose at least one visually interesting or important form inside the central rectangle. The quarter sections of the central rectangle are usually the smallest inner rectangles formed by the format divisions. These keystone rectangles often include a local center of interest in the painting but do not have to do so (as we'll see in a painting by Caravaggio). In the example, the back of the wooden chair, with its pattern of closely spaced vertical posts, provides visual interest to balance the cat, window and table.
If perspective or spatial depth is implied, space distance markers along the format lines. In landscape the horizontal lines are especially important. Do not link the horizontal and vertical lines in nested rectangles toward the center unless you want to create a tunneling effect.
In the example, the nearest table leg falls on the lower eighth fold (mm), the far front leg and the hind feet of the cat on the lower m, the seat of the chair and far table leg on c', the corner of the table top on M, the window frame and top of propped paintings approximately on the upper c', and the top of the lamp and bookshelf on the upper mm.
Do not extend or place important static forms outside the "frame" of eighth folds (cc and mm) unless the forms are cropped by the image borders. This is not a hard and fast rule, though it usually contributes to a good result. In the example, the tops of the torchere lamp and rowboat bookshelf lie on the top eighth fold; the corner of the table and cardboard box lie on the lefthand eighth fold; the leg of the table and bottom of the box lie along the bottom edge fold.
The window extends outside the righthand eighth fold, but it (actually, the molding around it) is cropped by the image boundary. Although the window placement up against the format corner was an unanticipated result of the resizing, I decided it worked in context to "hang" the window around the cone of light entering the room. And this suggests a final principle:
Place important forms outside the "frame" of eighth folds (cc and mm) to create a sense of dynamic movement across the image or into space outside the image. In the example, the window symbolizes the flow of light into the room and the presence of a landscape beyond its confines. In other situations a strong form of that shape in that location would probably look wrong, and this would need to be addressed by editing (deleting or moving) the offending object into a better position.
other format proportion schemes
Many other format proportion schemes are possible and several deserve mention here.
The most common approach is the intuitive arrangement of major forms or shapes in the image. The criterion here is just "a good effect" for the specific image, without relying on general principles. In the simplest approach, the most interesting part of the image is located on a sweet spot a point displaced to one side and above or below the center of the image and then the image is resized or cropped to fill the rest of the format in a pleasing way.
Another approach is the mise en scène strategy of stage managing the forms within the image to emphasize dramatic relationships, tell a story, highlight main characters or character contrasts, and so forth. A delightful example is Weegee's The Critic, in itself a carefully staged "class encounter" that was cropped in two versions to emphasize the character contrast between attenuated socialites and a disheveled street character.
There is nothing wrong with either approach; in fact, by playing around with the resizing and positioning of any image within a format template, you are simply using "what works" or "what looks good" to find an effective solution. But even with the two intuitive methods, the format proportions operate in the background, as can be used a reference and to critique specific ways in which the composition does or does not work.
A third compositional strategy is a geometrical arrangement of dominant forms. It is common in art history to hear a painting analyzed into a simplified geometrical framework, such as the golden rectangle, the square, two or more overlapping circles, the main diagonals, a triangle or pyramid, nested triangles or pyramids, and so on. I have never had sympathy for this brutish and simpleminded analysis and, excepting the analysis of paintings from the Italian Renaissance, don't see much relevance in it.
In his book, Bouleau contrived many complex variations on the square divisions, including the use of harmonic intervals across the format dimensions proportions that match the whole number fractions of musical intervals: 1/2 (the musical octave), 2/3 (the fifth), 3/4 (the fourth), 4/5 (the third), supplemented by diagonals drawn from the major divisions. I find the result (diagram right) to be so cluttered as to be useless.
My dissent from this approach is that it creates formalisms that have little relevance to the way we look at the world or at art. In particular, most of the geometric formalisms really define solutions to composition and design, not to the specific problem of fitting the image within a format.
Our visual experience is not aimless, ad hoc or mathematically prissy: it is consistently skilled, motivated and pragmatic. It's my claim that the format proportions represent a form of visual field, and the structure of the visual field represents the structure of our interests and aims in relation to the world. We identify the most important features of our world within our continuous stream of experience, then apportion or balance our looking among these features in a way that reflects how we believe they relate to each other and to our immediate priorities of enjoyment, understanding or action. We also commonly do this from a distance that allows us to see the important forms within a situating context.
diagonal (quarter) divisions of the rectangle
Bouleau's "armature du rectangle"
I believe the whole point of compositional systems based on the rectangle format is that they shape our attention dividing visual strategies. Looking directly at something emphasizes its importance. Dividing attention often means we balance our looking across competing things available to view, which tends to center them in a wider view. Disregarding or discounting means we push things into our peripheral vision. This is basically what the format proportions do they divide up the support into competing areas of unequal interest. A simple interpretation is that the h' squares represent the overlapping retinal areas of a binocular field of view, the outer eighth folds the widest area of view, and the central rectangles the focus of attention (at right, in the full sheet format). This dictates that more elongated formats are appropriate for forms viewed from a distance or as a series or progression, while squarish formats are appropriate for forms viewed as exemplars or individuals, separate from context and movement.
The compositional guides are not an empty or arbitrary geometry. They suggest how the viewer should look within the image, as he or she were actually inside the world of the painting or photograph. They do this because they mimic our habitual strategies of visual attention. By placing the important parts of the image along or inside strong divisions and keystone rectangles, the artist implicitly directs the viewer's selective exploration and appreciation of the total information in the image. This is why format based composition turns up in photographs or images even cinematic or advertising images that were created by artists who may have rejected the classical formalisms of composition and design.
Why not just divide the format by thirds (the musical interval of a fifth) and be done with it? As you can see in the format templates above, formats with an aspect ratio around 1:1.5 (the half sheet or emperor) place the h' and m' vertical divisions at the vertical 1/3 divisions. But in many compositions based on the thirds, the central rectangle is crowded into too small an area in the middle of the sheet, so that the focus of attention is, as it were, viewed from too far away. In most formats, two of three vertical divisions c, m' or h' and both horizontal proportions (m and c') are closer to the edge than the divisions by thirds. Placing compositional elements on these outer divisions seems more pleasing.
The major exception is the square format or formats that are nearly square. In a square the square division h' disappears, c' = M and m' = C, and the sheet is defined entirely by the half folds. In that case the division by thirds can supplement the half fold divisions.
The illustration (a CD cover for the album Animals by Pink Floyd) illustrates use of the third and half fold proportions in a nearly square (1:1.15) format. I offer this as an especially convincing example because the flying pig is placed exactly at the point where the upper and left third divisions cross. But nearly all the format lines are aligned with or centered on some important architectural edge or form. The monumental impression created by the old London power plant is emphasized by its harmonious, stable placement within the image dimensions.
format proportions in western paintings
At this point there will be two critical questions: Do the format proportions really produce a better design? And are the format proportions so complex as to be arbitrary? The most direct way to answer these questions is to make a review of images from western painting.
I have done this with a large number of published paintings over the years, and have been impressed by how consistently the format proportions anchor important image elements in paintings by a wide variety of artists in a wide range of styles. I suggest you test this for yourself: leaf through any art historical book or photographic magazine, or freeze frames from your favorite wide screen film, and pick out images that seem to be effectively or badly composed. Then use the image outline to construct the format proportions in the image, and see whether the pleasing composition can be explained by the guidelines.
the format proportions as symbols of binocular attention
In this section I offer analysis of 15 paintings from the western canon, both to show how they respect the format divisions (whether intended or not by the artist), and to illustrate how departures from the formatting principles are interesting for the effects or insights they can reveal.
In all images, white or gray lines are used to show the six format half and quarter folds (C, M, c, m), red lines the six square folds (h', c' and m'), and orange the eighth fold frame (mm and cc). The square folds h' and c' (w' and m' in portrait format) are shown as bold lines.
Two cautions are necessary when doing this. First, paintings may have been trimmed during relining, stretching or restoration, or arbitrarily cropped to fit page formats in books, and these proportions will give a distorted idea of the format proportions of the original work. Second, paintings are rich with detail, which means only large or important forms should be interpreted.
The first example, a large oratory panel of The Martyrdom of Saint Sebastian (1475) usually attributed to Piero del Pollaiuolo, is famous for its arbitrarily formal design devices a triangular arrangement of figures including six archers in three poses viewed two ways. As you can see, the design also builds on the format proportions. The heads of the four central archers lie very close to the four corners of the central rectangle (defined top and bottom by the strong division at w'/c') and this rectangle roughly defines the height of the back two archers. However, the keystone rectangles are empty of visual interest, which pushes the structural emphasis outward, to the triangular lines of aim taken by the four archers. The left standing archer is as high as M and the balance of both corner archers is along cc. The position of St. Sebastian does not correspond well to the format divisions the placement would be stronger if his shoulders were at mm but as I will explain later, this displacement appears to have an important expressive purpose.
The second example, Sandro Botticelli's Birth of Venus (c.1485), has exactly the aspect ratio of a golden rectangle, and it captures the "portal" implications of that format in the arrangement of attending immortals on either side of the newly created figure of Venus. On the right, the two hands and face of Hora (and the coast behind her) fall on h', m' and c respectively, and Hora's figure leans into but does not cross c. The centerline C, which runs through the left side of Venus, her raised thigh and her weight bearing foot, emphasizes the tilt to her left that prepares her first step on land; most of her torso falls within two of the four keystone rectangles. (An interesting compositional detail is that, in the golden rectangle format, the central rectangle formed by h' and c' is also a golden rectangle, as are the two rectangles outside the h' divisions.) The location of the horizon, just above the waist of the two standing figures, implies that we viewers are kneeling on the shore. The shell carrying Venus is not centered between c and m' (as if pushed backwards and to the left by her step), but the width of the shell exactly equals the distance between Hora's face and the blowing mouth of Zephyr. On the left, the major features in the figure of Zephyr (blowing mouth, right shoulder) and his companion (face, left shoulder, right knee) also lie along the lefthand format lines. All three major figures are arranged parallel to three upward converging lines (in green) defined as diagonals from edge intersections of the major format folds; by tilting the figures in this way the emphasis on the lefthand division is reduced and space is opened below to receive the implied forward movement of the Venus figure. The divisions m and c' are not clearly accented above or below, which reduces the spatial layering of the image. I think it's more common for c' top and bottom to define the height of standing figures in the 1:1.6 format, but here the measure is the eighth fold frame mm top and bottom which seems to bring us and the figures closer together. In addition, the feet or legs of the companion gods extend outside this frame, which creates a kind of spatial expansion away from Venus, and this is supported by the beautiful flow of her hair into Hora's upraised and windblown drape. Finally, Venus's head pokes above the mm line at top, which gives greater vertical emphasis to her already elongated (more than 8 heads high) proportions.
Another secular image of beauty, the Venus d'Urbino (1538) by Titian, with an aspect ratio of about 1:1.4, is interesting for the ways it "violates" the design principles outlined in the previous section for example, by placing the edge of the drapery along the centerline C. Figure nudes are difficult generally because the landmarks are created by the continuous curves of the figure. The points of emphasis depend on the posture of the figure and how it has been cropped. Usually the top of head, eyes, shoulders, breasts (in females), elbows or hands, hips, groin, knees, and ankles or feet are the points of emphasis horizontally or vertically. The point of greatest inflection in the spine, or the center of gravity of a standing or sitting figure, can also be marked. In this horizontal Venus (as in the vertical Venus of Botticelli) the figure pushes outside the eighth folds on both sides, though the girl's heel and head mark them. Recession is marked by placing the base of the back wall on M and the ledge above on c'. The format lines clarify the balanced assymetry in the composition: the heel of the lady's foot and the head of the servant are at the top and bottom mm at right, while her head and hand are bracketed by the upper and lower c' at left.
Caravaggio's paintings, for all their violent contrasts and dramatic action, often have an overall visual balance that seems painstakingly planned. In the The Taking of Christ (1598) there is a general shoving of humanity across the picture plane, but this dynamic flow is controlled by the format placement. The key event, the Judas kiss between two faces, is placed on the lefthand strong lines, and the actors' eyes are gathered along the upper c' and their shoulders along M. Especially significant are the picture details that lie outside the eighth folds (orange rectangle). The shout and upraised hand of the disciple explode to the left like water splashed from an impact, balanced by the portrait profile of Caravaggio as the disciple pushing in from the right. The keystone rectangles are completely empty of interesting content, so our attention is forced to the edges of the format as if jostled back and forth by the action. The format lines also help the viewer appreciate other points of conceptual symmetry behind the visual asymmetry that is characteristic of Caravaggio's carefully designed pictures. I especially like the variety of hands outside the frame two hands joined below, two hands separated above, one arm stretched across the picture vs. two raised arms above on either side, three heads geometrically balanced on either side of the interlaced fingers, two foreground heads facing one another matched by two foreground heads facing in the same direction, and so on. (All of Caravaggio's compositions merit close study.)
There is a huge number of classicizing landscapes that I find difficult to tolerate, such as Nicholas Poussin's Summer (Ruth and Boaz) (1664). Some might admire the spatial staggering of trees and fluffy clouds, or the contrived figure placements. It seems obvious, however, that Poussin was not much concerned with the format proportions: the disjointed, stagey feel of the painting reveals it. I especially dislike the placement of the foreground figures along the bottom edge of the picture, well below the lower eighth fold mm. These are esthetic decisions consistent with Poussin's aim, which was to present a familiar (Biblical) story in familiar dramatic terms, not to dissect or recreate our perception of the physical world. In fact, the flatness of everything behind the three foreground figures looks remarkably like the painted backdrop to a three actor morality play: I wonder whether contemporary dramatic conventions and perspective principles of set design influenced Poussin's concept.
In contrast, Vermeer's Woman in Blue Reading a Letter (1664) has a stillness and harmony that must have been conceived in terms of the format proportions. Too many features coincide to be coincidental, and there are too few edges and forms to create random correspondences. Broad, rectangular forms are placed outside the eighth fold frame and all are cropped by the format (except for one chair, which is cropped by the table); the figure is slightly off center, enclosed within a narrow column defined by the midline square m' on the left and the centerline fold c on the right. The woman's head is topped by h', her eyes by m, her hands by c' and her elbow by M. Even the lower centerline square c', which doesn't seem to indicate anything visible, runs directly through the hidden fetus corresponding to the c' above, through the hands holding the letter.
The Rokeby Venus (c.1650) of Diego Velázquez is closely modeled on Titian's pose but viewed from the back! Like Titian, Velázquez places the major accents at the knees, hips and shoulder, the head against one cc, with the elbow and foot jutting beyond the eighth fold frame. But he adds several important innovations. The format itself is elongated horizontally, reducing its visible headroom and drawing both h'/m', and c'/m closer together. To compensate, Venus's legs are slightly flexed (not fully extended as in Titian), the curve of the buttocks is accented, not the point of greatest weight at the hips, and the torso is contracted upwards to bring the left shoulder and right margin of the rib cage (accented below by darkened folds in the gray bedsheet) into h'; in this way the whole figure is made larger within the format (closer to the viewer). Velázquez also emphasizes the opposing h' and m' format lines through the relationship between Venus and her reflection and Venus and the putto, whose heads are symmetrically placed around C. Velázquez places the reflected portrait of Venus within one of the keystone rectangles, and the contrivance is revealed by the fact that this is optically implausible (it allows us to see Venus, but does not let her see herself). The righthand dominant verticals are marked by the putto's knee, crossed hands, the fabric dangling from his wrist, the edge and corner of the mirror frame, and the right foot peeking under Venus's crossed leg. The upper boundary made by m/c' is marked by the top edge of the glass, the amorino's elbow and wing, and the top of Venus's head and reflected head. The gray and crimson fabrics are separated by M. The lower boundary is marked by her feet and rib cage; the sag of her hip below this line, reinforced by the broad curve in the gray bed cover, creates an erotic focus on this part of her figure.
The Oath of the Horatii (1784) by Jacques-Louis David utilizes the format proportions in an explicit way that does not require detailed explanation. Note that the aspect ratio of 1:1.28 (in watercolors, typical of the medium or demy sheets) creates an unusual spacing system: a strong vertical emphasis at c/h' (where h' is actually closer to the edge than c) linking the three warriors with their three wives opposite; the contrasting horizontal division of the image into nearly equal intervals (approximately corresponding to the feet, knees, waist/heads, shoulders, upraised swords, capitals and arch centers); and the small, nearly square central area created by the midline square m' and centerline square c'. As in Poussin, the figures extend below mm and again the effect (with the lighting) suggests a dramatic stage. I like the way one keystone rectangle contains the nexus of upraised swords and hands, symbolizing the oath; the way that the strong emphasis at h'/c unites the group of warriors at left, but divides the group of grieving women at right; and the bridging function of the central archway and the feet of the foreground figure, which connect the two m' lines and pull the figures and background into a single, continuous frieze.
There are many Impressionist and later painters, from Edouard Manet to Paul Cezanne to Pablo Picasso to Barnett Newman, who do not seem much aware of the format proportions. In every case the question is how this disregard affects the impact of the image. In Le Dejeuner sur l'Herbe (1863), Manet has chosen a format that spaces out the format lines into an almost even grid, but unlike David he uses them haphazardly. There are a few points of obvious correspondence the capped man's head and hand on h', his upraised hand and the bathing woman's head on m', the line of feet, knee, hand and hip along the lower m, etc. But look at the way the upper format lines are lost in vague foliage, or the way the basket and picnic covers spill out of the frame at lower right, the random placement of tree trunks. One of the things that always puzzles me about this picture is that peculiar alley of lawn and shade that recedes along the lefthand h', between trees and bushes on that side. (If there is water back there, its shadowed color disconnects it from the water in which the woman is wading.) That recession always has an unsettling effect on me, a tunnel of obscurity contrasting with the field of light on the opposite side. (I will show later that these oddities have a good purpose.)
Format proportions can be wildly disregarded in paintings by Edgar Degas, as in his The Rehearsal (1873-78). But Degas was among the 19th century artists whose design sense was strongly influenced by photographic materials, and this shows in his bold use of empty space, cropping, and unusual points of view or strong perspective. Here, except for the edge and central support of the large window at right, which fall along h'/c and mm respectively, the line of heads along c', and perhaps the location of the two front dancers at left, it's hard to see many format correspondences. But I think this illustrates two basic points about the format proportions: (1) they seem to represent or symbolize the natural distribution of human visual attention, and (2) they tend to produce balanced, somewhat static images. In Degas's conception the cropping of the windows and the violinist at right seem to assert a flat, photographic rather than human focus, and the composition is dramatically off kilter (like the position of the dancers). However, the warm, analogous color scheme seems to place the emphasis on light itself flowing through the windows, across the floor, and through the gossamer dresses of the dancers and it's possible that strong format markers would disrupt this effect of gradation and flow, captured so beautifully in the colors of light along the floor and walls.
The eternally happy Danse au Moulin de la Galette (1876) by Pierre-Auguste Renoir shows how the format proportions can control an image that is dense with competing details. This lovely format, which is very close to the full sheet, places the h' and c intervals close together, and puts m' halfway between them and C. The closest two female faces are placed like cameos within two keystone rectangles, facing the male whose head is against the righthand c/h'. On the opposite side, the strong h'/c division is marked by a dancing couple (actually, the back of the man, who seems to lean against it); the m' division is marked by a second dancing couple behind them. On the right, a man in a blue coat leans against c/h' in the opposite direction, and his angle carries up into the tree trunk and down into the back of the seated man, lending the composition a wonderfully lightheaded, lilting effect. All the legible faces of the background figures fall within the m/c' divisions at the top of the sheet; everything above m is an indistinct crowd, and the foot of the male dancer is on m below.
Another painter who seems to have consciously used the format proportions was Paul Signac, as shown in his Quai de Clichy (1913). Composed in a format close to a half sheet, there are too many precise alignments to be due to chance: the placement of h' on the trees on opposite sides of the street, of m' with the distant smokestack, c' with the top of the roof at right and the base of the two trees, M with the horizon and top of the fence at right, C with the distant house and c with the side of the fence at right and the row of trees at left. This picture also gives a sense for the feeling of balance, stability and spatial recession that is created when the format proportions are explicitly accented by major image elements.
The format proportions work just as well in portrait format, as this lovely painting of Lady Agnew of Lochnaw (1893) by J.S. Sargent demonstrates. The only difference in the portrait orientation are that the largest square in this format (equivalent to a demy or medium sheet) is formed by the width of the canvas (w'), and what used to be the midline (the horizon in landscape format) is now the centerline C. Lady Agnew's eyes and the top of the chair are perfectly aligned with the area of emphasis created by m and w' at top, matched by the location of her left hand below. Her nose, pendant and left eye lie along C, her torso is bracketed by m' on both sides. Her right forearm is flexed to lie with her crossed leg along the lower c', while her neckline dips down to the upper c'. The top of her head does not extend above the top eighth fold (mm), while her left forearm and hand lie exactly along the right eighth fold (cc). The edge of the chair and the shadow behind it push outside the eighth fold on the right, just as the woman's left arm and the shadow behind it push out on the right; this seems effective to accent the Lady's turned position in the chair and draws attention to the angular flow of her waist sash. Her skirt flows outside the bottom mm, but this is fine because it is cropped by the bottom of the picture.
Typical of many modern paintings, Summer Days (1946) by Georgia O'Keeffe shows less interest in the format proportions, despite the strong centering of the major form and the sprawl of the antlers. These do roughly hang on the upper m (usually a weaker line than w') to match the location of the red blossom below, the lower antler curve is along c' the skull eye orbits are within two keystone rectangles, and the upper border of blue sky is along the lower h', but the overall sense of floating is created by the curvature of the horns and the broad background of undifferentiated clouds. In cases where the image does not seem strongly formatted, it is instructive to digitally alter it to make it so, then assess the differences between the two images.
Finally, there is Bill Latham's House (1927) by Edward Hopper, in a format close to a half sheet. As we've seen, this format tends to create an "opposition" emphasis, which Hopper exploits in the strong placement of the tree on the left and the house (and small fencepost) on the right. Hopper places the visually most delicate and active details of branches and foliage within the central rectangle; each keystone subdivision contains a contrasting visual pattern. The upper division at m/c' is accented by the widest part of the dark foliage, the lower division only weakly, by the lowest branches in the tree. The midline M defines the eaves of the roof and tops of the windows, and is positioned exactly between the ocean horizon and the horizontally extended branch extending left from the tree.
are the proportions "real"?
These "analyses" invite the obvious and legitimate rebuttal that geometrical interpretations applied after the fact can always be made to match some aspects of a painting: that doesn't mean the proportions actually highlight key aspects of the composition.
That's a fair challenge, and a fair test is to find a composition that does not seem to correspond to the format proportions in an obvious way, then change the major elements to coincide with those proportions and see what effect this has on the image.
To illustrate the basic procedure, I will use a painting by Edward Hopper: Portland Head Light (1923).
The original image is at top; the three lower images above show the editing process. The second shows the format proportions scribed over the original image; the painting is in the half sheet proportions (1:1.47). The composition seems based primarily on the horizontal thirds; the vertical divisions do not correspond to strong image elements.
To accent these proportions, the center of the lighthouse was shifted left to fall on the closely spaced h'/m' lines. The base of the tower and small house were dropped to the lower m/c' lines, and the top catwalk in the light tower was moved down to the upper m/c' lines. The small house was moved inward between c and m', and the main house was shifted slightly to bring the join between large and small parts of the house to h' and the porch to cc along the right edge of the picture (third image). The bottom image shows this altered painting with the proportion lines removed.
To me, the revised composition has a less dramatic and compact effect than the original, but it has a greater feeling of openness and visual stability. There is a distinct tension between the tower and house, and a more interesting rhythm connecting the buildings with the rocky beach. The weight of the horizon is greater, partly because the height of the tower has been reduced and the ocean's area within the central rectangle has been increased. (In my experience, emphasizing the format proportions often creates a stronger sense of recession and a greater feeling of space.)
I chose this example partly because the original seems to have been painted (or sketched for painting) in a open field. The altered image would closely correspond to the view that Hopper could have taken by standing about 50 feet to his left. Although the site today has been heavily landscaped and fenced, there is a sea cliff and steep walkway at that location which would have made an inconvenient perch even in Hopper's time. Therefore his design was at least in part dictated by site specific obstacles, yet the format analysis still identifies the resulting compromises in his painting.
As another example, here is the Pollaiuolo panel analyzed above, with the saint lowered to bring his shoulders onto mm, his hips to m, his groin to w' and his feet to M. Although the changes are very minor, they significantly alter the image. The archers do not seem to be working as hard, nor the saint suffering as much: tension has been lost. In the original the saint's unseen heart is at the intersection of mm and C and at the apex of the archers' aim; his head pushes against the picture limits much as his spirit strains to leave its body. In the revised version he just seems to be having a bad day.
By making the archers correspond closely to the format divisions, Pollaiuolo invested the displacement of the saint's body from these divisions with greater expressive significance: the misalignment symbolizes the agony. More generally, the effect of using the format proportions consistently throughout a design is to produce a more balanced and integrated image, which can also cause the picture to seem static or tidy. For some painting goals this will not be desirable!
And here finally is the Manet painting I complained about earlier. Here the changes, though clumsy, are more substantial and involve almost all parts of the image. In particular the sky has been opened behind so that the arc of four heads leads into the bright distance, and landscape layers have been aligned with the divisions to accent this recession. The basket has been moved up and in, the figures shifted and edited, the near trees brought to the strong picture divisions, and that strange alley of lawn diverted to run off the side rather than into the picture.
The composition has become more balanced and stable, and in the process more domesticated. The grouping of figures is tightened in a way that seals them off from the uncanny woods around them, there is more light and bourgeois interest in keeping food nearby. One misses the unsettling effect in the original of the strong tilt of the figures and lawn downward to the left, which doesn't consciously register until it has been removed. The revised version makes it seem as if ladies go naked in the park because men are docile and the lawn free of insects. The insouciance of the avant garde has been lost.
use what works
I conclude with a hazard that is obvious by now: that one can "explain" any random distribution of forms in a rectangle with some system of proprotional or geometrical divisions, provided you can use as many lines or curves as necessary. The problem is especially vexing in Charles Bouleau's Charpentes, because he applies circles, ellipses, triangles, interval divisions, musical ratios, diagonals and other constructions differently from one painting to the next, with no systematic justification and often imprecise results.
Reproduced below as one example is his "explanation" of Vermeer's Allegory of Painting, which requires a "framework" of 45 unique lines!
Most of these lines do not define any important edge or form in the painting. Analytic clarity is lost in the complexity, and we have no reason to believe Vermeer ever considered such a network or that these lines indicate how most viewers would look at the painting. In other words, the Boileau principles are not fundamentally analytical.
A more elegant explanation has been developed by Robert DiCurcio as the Grail Geometry in Vermeer's images. I can't do justice to his ideas here, but the pictorial analyses that result are substantially simpler than Boileau's; the flavor can be conveyed in DiCurcio's anchoring of a hexagram in the image geometry (image below).
DiCurcio's point is not that we can derive patterns from the image, but that Vermeer (said to be represented by the painter in the image) arranged pictorial elements as a covert code in this case, of his secret religious beliefs in a violently contentious historical epoque. Again, however, Vermeer's religious symbolism is probably not of interest to a modern painter, and methods of symbol encryption are not useful methods of painting design.
How does my modest system of format proportions fare? The illustration (below) indicates several points of convergence, although there is no guarantee that the digital image dimensions match the original either as it was framed by Vermeer, or as it exists today after centuries of curatorial trimming and relining.
However my system catches alignments missed by the others, and in particular nicely characterizes the location of the female subject within the c' and m' defined keystone area and the painter between the h' and c' folds outside it.
However, it seems to me the assumption that the painter in the image is actually Vermeer raises an obvious question: what kind of compositional framework is the painter using? Vermeer shows enough of his painter's work for us to impose his canvas formats onto the image (green rectangle). And from this we can construct the format proportions of the painter's composition (image, right).
Not only do my format proportions locate several significant features of the female image her eyes, wrists, hat, book corners, etc. within the painter's painting, the major horizontal divisions h' and M correspond closely with the horizontal divisions c' and M of Vermeer's painting! If there is a visual code hidden in this painting, it seems to be a key to the way Vermeer himself constructed his images.
My approach has been to choose the proportional constructions in advance, apply them consistently to historical examples or my own works, and from this study develop principles that describe the effects that result when a design adheres to or ignores the format proportions. This minimizes the arbitrariness of the activity and increases my understanding of design decisions.
In that spirit, I urge you to browse any book of art reproductions, choose paintings that seem especially well composed or satisfying to you, then establish the format proportions in the image to see how well these correspond to significant guidelines. Try them in your own paintings, too.
the format proportions in the painter's painting