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Wikipedia defines counter then gives examples. Then it proceeds to give examples of open counter without having given any definition of it:

In typography, a counter or aperture is the area of typeface anatomy that is entirely or partially enclosed by a letter form or a symbol (the counter-space/the hole of). Letters containing closed counters include A, B, D, O, P, Q, R, a, b, d, e, g, o, p, and q. Letters containing open counters include c, f, h, i, s etc.

So, what is the proper definition of open counter?
To illustrate, could you give a handful examples of characters that contain no open counters?

Is it synonymous with aperture? Fonts and Encodings, O’Reilly 2007 says on page 4:

The counter, which is the inner part of a letter, for example, the space inside an 'o' and 'O', a 'D', etc. The counter of an 'e' is commonly called an eye. When the letter is open at one end, as is the case with 'n' we speak instead of an aperture.

I have drawn my interpretation of open counter in green below, is it correct?

enter image description here

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Using a map metaphor:

A counter is a lake.

An open counter is a bay.

enter image description here

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  • So there are not so many examples of characters that contain no open counters I guess? Except 0 o 。. ・ - _ \ / ` | ' – Nicolas Raoul Apr 17 '14 at 1:04
  • Correct. Actually, I'm not entirely sure what wikipedia considers the open counter in an 'i' to be. Remember that type terminology tends to be a little fuzzy in nature. The definitions are more along the lines of 'mostly accepted conventions' but there's always room for debate. – DA01 Apr 17 '14 at 1:06
  • I'd think an i can have an open counter if it curves towards the bottom-right. But it's an uneducated guess. – Yisela Apr 17 '14 at 2:06
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Adding to DA's great answer, some more info about open counters and legibility.

First of all, as mentioned a counter is the partially (open) or fully (closed) enclosed space in a letter. As I see it, all these letters have counters: b,d,g,o,p,q,A,B,D,O,P,Q and R. An these have open counters: a,c,g,s,C,G and S.

Another example of an open counter to add to the 'cartography a":

enter image description here

Source

Counters can help with legibility, although they need to be combined with other properties such as x-height:

Taller x-heights (usually) result in an overall increase in legibility, thus causing a direct correlation between counters and x-height.

Compare the difference between a typeface with small short counters and a typeface with large counters and taller x-height:

enter image description here

While the first one has large counters, the second one has smaller ones, but larger x-height. Of course larger x-heights is just part of the equation. The most efficient typefaces with the best ratio of x-height and cap height seem to be between 67 to 69 percent of the cap height.

A nice related article on legibility and the related study where the previous information came from.

Source

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  • So, small counters can imply legibility, and small counters imply large open counters, right? In the image, is it intended that the blue zone does not reach a bit further right? This image invalidates the definition I was thinking about, which was "every point that is not part of the letter but can be reached by drawing a line between two points belonging to the letter". – Nicolas Raoul Apr 17 '14 at 2:14
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    @NicolasRaoul I don't think such hard math-based rules will work well with typographic definitions. Again, we're a bit loose with our terms and definitions in the world of type. – DA01 Apr 17 '14 at 2:15
  • I have to agree. I had a more flexible concept of open counter in mind, you last example made it trickier for me. I wouldn't consider those spaces as structural parts of the glyph, but I like to think of a and e as good examples of open counters. – Yisela Apr 17 '14 at 2:30
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So, what is the proper definition of open counter?

First note that such terms for letter anatomy are usually not strictly defined, because there is no need for it. What follows is an attempt to formalise this concept by me that covers common features upon which all the sources I am aware of (implicitly) agree, namely:

  • Open counters are essential features of the skeleton of a character, which is its basic form.

  • An open counter can be almost closed, without the character becoming unrecognisable.

Consider the following example of the two-storey a:

Concepts illustrated on the letter a

  • The green area marks an open counter, because it is part of the skeleton (2), even when reduced to its most basic (3). When we alter the skeleton so much that this area is not enclosed anymore (4), the character is not recognisable anymore. Finally, we can almost close the counter (5).

  • The red areas are not open counters as they are lost in the minimal skeleton (3). They are not essential to the shape of the character.

  • The yellow area is not a counter because almost enclosing it (5) would change the essence of the character. You can see this by rotating the character to obtain a p. Enclosing would destroy this. If we rotate Part 5, this is not a p by any standard.

Therefore your variant letter p has no open counters. The only variants of the letter p with open counters are when the usually closed counter in the centre (the red area in your sketch) is opened for stylistic or technical purposes (e.g., a stencil typeface).

Is it synonymous with aperture?

There appears to be no agreement on this. Some sources treat the two as synonymous. Some sources say the aperture only describes the opening of the counter, not the area (e.g., the straight line between the two ends of the letter c in Part 5 below). In yet more sources there seems to be an (implicit) distinction between open counter and aperture that is based on whether the opening can be closed in the skeleton of the character (open counter) or only with decorative elements (aperture). For example:

Concepts illustrated on the letters c and n

In the sense in question, the letter n has an aperture as it can only be almost closed with decorative elements such as serifs (2). When we almost close the opening by modifying the basic skeleton (3), this is not recognisable as an n anymore. By contrast, the letter c (4) has an open counter as we can almost close with modifying the basic skeleton (5).

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An entire alphabet and number font set can be designed with open counters. In that case, there would usually be a small space in a part of the letter/number. For instance, the d loop would generally not join to the straight line at either the top or bottom.

This is usually preferable for ease of weeding die-cut letters, words and numbers (i.e. Cricut, Silhouette or other machine cutters) and for cutting stencils.

For an entire example, check out the stencil version of Indulgence 2 or the Alba stencil fonts.

See an example of Indulgence 2 by Stacey's Digital Designs at https://fontbundles.net/stacysdigitaldesigns/382140-indulgence-2-the-stencil-version

Note the arrows pointing to small apertures in otherwise closed counters.

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