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Is there anything inherently wrong with a square image composition?
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Mike, nothing is wrong or right about any size or dimension in and of itself. You could even have a circle composition that is beautiful. The Golden Mean is a guide not a steadfast rule. Square compositions can be hard in many ways, but as an illustrator, I have had to do a few (CD and before that album covers are square). Also, anyone who has done a collectors plate illustration can tell you a circle can have its own composition problems as well. When faced with a square it is most important to include ether some strong horizontal or strong vertical to offset the rather boring, even dimensions; but that is not a stead fast rule either. Also try never to center anything within a square - but again, not a steadfast rule either. If formality is desired, a very balanced composition may be what you want.
The rules of informal subdivision can help make a rather boring composition sing. What is this rule? It is simple. You just divide the space unequally and interestingly, avoiding placing a line at a point which would be one half, one third or one forth of the whole space. You can then continue to divide your divisions with diagonals that intersect at points of interest within your divisions. It sounds complicated but it's not really, and it offers great freedom to the artist in makng interesting compositions within a variety of shapes.
In book illustration, a long vertical rectangle is common, and it is usually taller than the golden mean would have you design in. Tri-folds are much wider then a normal landscape, and must function as a unified composition when viewed as a whole; the front cover alone needs to work as a vertical composition.
Every painting is a challenge, no matter what the shape of the canvas. In the end, if you are conscious of line and value areas, you can get a good composition within any shape. The golden mean is just the most visually pleasing proportion and for the most part the easiest to work within - but it is not by any means the only proportion to use. I have seen paintings that are much taller then they are wide and vice-versa.