Letterform Analysis: The Oval and Compound Curves

In this new series of articles, I would like to discuss my approach to letterform analysis. A prerequisite for understanding the proper formation of letters in any script discipline is to first identify the fundamental shapes that make up a given set of letterforms. To simplify the discussion, I will focus on Engrosser’s script as the model for this analysis. The basic concepts discussed can be applied to other forms of script as well.

The structural building blocks of Engrosser’s script are the oval (Fig. 1A), the compound curve (Fig. 1B) and to a much lesser degree, the straight line. Of these three basic shapes the oval dominates since, as we shall soon see, it defines the symmetry of almost every letter. Curiously, a properly formed and slanted oval is one of the most difficult fundamental shapes to achieve (Fig. 1A) Note that the long axis of this oval is on the slant angle. As seen from the illustration the slant angle will bisect a properly formed oval into two equal halves (Fig. 1A).

Let us now consider the compound curve (Fig. 1B). Making this stroke correctly is essential to the proper formation of many Engrosser’s script capital letters. Even this important fundamental stroke is dependent upon the oval. Notice how the seemingly identical entry and exit angles, indicated by the double arrows, are defined by imaginary symmetrical ovals having their long axis on the slant angle (Figure 1B). Thus, the oval forms the basis of my approach to letterform analysis.

Letters formed without proper regard to their component ovals will appear 'off' to the eye. To illustrate this concept, consider a compound curve formed with imaginary ovals each having a different slant angles (Fig. 1C). This compound curve appears asymmetrical. Furthermore, the entry and exit angles are no longer equal (see double arrows in Fig. 1C). Let us now apply these basic concepts to an actual letter.

Figure 2A illustrates a properly formed capital ‘P’ in the Engrosser’s script style. Please note that this is a somewhat simplified ‘P’ form to aid in illustrating the concept. First, let us examine the primary shade of the ‘P’, namely the compound curve (Fig. 2B). You will notice that the compound curve is exactly on the slant angle (dotted line Fig. 2B). Furthermore, the entry and exit angles of the compound curve (double arrows Fig. 2B) are essentially identical. The question is, “why is this stroke so well formed?” The answer is, “because this compound curve traces the curvature of imaginary ovals (dotted ovals Fig. 2B) that are properly formed and on the main slant angle.”

We will now turn our attention to the component shades of the ‘P’, namely the rear shade and the front shade (Fig. 2A). When properly formed these shades harmonize with each other and are parallel. Once again this is due to the fact that the component ovals are properly formed on the main slant angle (Fig. 2C). Finally, the overall result is a letter that is symmetrical and properly formed. Notice how the upper portion of the ‘P’ also forms a larger imaginary oval (Fig. 2D). These rules also apply to both the capital ‘B’ and ‘R’.

We can further break down this letterform to provide additional insight into refinement of this particular letterform. Let’s look at the rear shade indicated by the arrow (Fig. 3A). Please note how this shade ‘harmonizes’ with the main compound curve. This effect is achieved by forming the rear shade on an imaginary oval whose long axis is rests on the main slant angle (Fig. 3B). As a result, the gap between the rear secondary shade and the compound curve will have equal space at the top and bottom as indicated by the double arrows (Fig. 3B). The final effect is achieved by forming the front shade of the ‘P’ using the same principles involving the imaginary oval (Fig. 3C). This results in front and rear shades that are parallel and harmonious.


Let us consider what would happen to the symmetry of the letter ‘P’ if these rules were not followed. Figure 4A shows the properly formed letter ‘P’ using the principles previously discussed. The ‘P’ in Figure 4B looks almost perfect; however, something should appear slightly ‘off’ to your eyes. Yes, some may think this overly critical but this type of critical evaluation is essential to making progress. Notice how the rear shade no longer fully harmonizes with the compound curve as seen previously in Figure 3B. In addition, the top and bottom spaces formed between these two shades are no longer equal (Fig. 4C double arrow and dash). If we examine the slant of the oval used to form this rear shade we notice it has a less angled than the main slant angle (Fig. 4C). The last problem we will consider is pictured in Figure 4D. You should notice that this ‘P’ (Fig. 4D) seems much more asymmetrical than the form pictured in Figure 4B. The imaginary oval used to form this rear shade is at a greater angle relative to the main slant angle (dotted lines Fig. 4E). The result is greatly unequal spaces formed between the rear shade and the main compound curve as indicated by the double arrows (Fig. 4E). Furthermore, the front and rear shades no longer harmonize with each other as they do in Figure 4A.


In the next installment I will use this approach to evaluate letters that would seem to have nothing in common with an oval. Yet their very grace and elegance are dependent upon adherence to the rules discussed above.