Our definition of proportion as a comparative relationship of size is so broad that any sizes may be in proportion. The quality of proportion in design is always assumed to be a pleasing relationship of sizes. It thus becomes necessary to determine what relationship of sizes will be most pleasing.
The use of equal masses in a design is monotonous. The eye finds variety of size more interesting. But to determine what form of variety is most interesting we must find, if possible, the ideal area relationship between masses in a design. This problem has of necessity been solved by the designers of all nations and all periods, and it is interesting to note that the result has everywhere been practically the same.
Let us arrive at the expression of good proportion by the simple means of dividing a rectangle into two parts which will have the most interesting relationship. This rectangle is A in [Fig. 8]. B shows a division into equal parts, the result being uninteresting and monotonous. In C the division gives a feeling that the lower part is too large; it is crowding the upper and the result is not pleasing. The relationship in D is so nearly equal that the division seems to have been an inaccurate effort to locate the center. Somewhere between the division point in C and that in D will probably be the best point. Repeated trials will locate the point about as in E, which will be found to lie about two-fifths of the distance down from the top. This will give the upper area in E an area of 2 and the lower an area of 3. Hence the relationship or proportion is said to be as 2 is to 3. By the term “good proportion,” or merely the word “proportion,” in speaking of design this ratio of 2 to 3 is assumed.
Fig. 8. The division of a rectangle, A, to secure spaces of interesting
relationship. Equal division in B. Overbalanced effect in C. Too nearly
equal in D. More interesting in E, where the relationship of spaces is as 2 is to 3.
It is interesting to note that when a space has been divided into the ratio of 2 to 3, the relationship of the smaller to the larger is practically the same as the relationship of the larger to the original whole. Or, mathematically, if the original, having an area of 5, is divided into parts of 2 and 3, then 2 is to 3 as 3 is to 5,—a ratio which is approximately true.
The student of architecture finds the most careful consideration of proportion in the relationship of spaces throughout all the architectural orders. In printing, the designer must be guided by the same traditions.