The letter S

I found this old article today, which was originally published in the Periodica Polytechnica (scientific journal of the Budapest University of Technology and Economics) in 1979. It covers issues regarding the designing of the letter S. The text from a PDF along with some illustrations are provided below.

What are you think?


J. Gróh
Department of Drawing and Composition, Technical University, Budapest
Received: March 15, 1979

The characters S in “Hypnerotomachia Poliphili” printed in the shop of Aldus Manutius are excellent. Among patterns arisen in the first century of printing, the designs by Vicentin, later by Cresci, show a dynamic letter S. Construction of the letter S by Durer is, however, faulty, the character falls backwards. In later periods, up to present, many good and bad examples are found, the difference between them slowly fading out.

Forming of the letter S is unparalleled in our alphabet. The floating statics of the intertwining arcs makes it the most problematic character, ahead in difficulty of the construction of characters inexistent in the Roman alphabet therefore uneasy to be fitted into its form system.

It is well known that S forms (both capital and lowercase) are built of two superposed circles. The two circles are joined, opened on top and bottom, in general by applying a tangent arc (a). The obtained initial form is not bad. If, however, the letter is less wide than the circles, the character tips over; vertical chords adjusted to the endings make the cause of this phenomenon evident (b). The S tilts less to the left when only the upper part is shorter than the length of the diameter (c). Just as deficient a form results from enlarging the lower part for the sake of an apparent, optic equilibrium of the two parts; thus the character obtains a vertical tangent on the left but none on the right (d). The correct solution is evident; the upper circle has to be slid to the right (e). Even with identical circles, a balanced form tending to the right is achieved.

Fig 1

Fig. 1

S varieties are easy to construct from joining identical circles slid on each other (Fig. 1). In drawing four squares, not only those enveloping the circles but also their reflections along the horizontal bisector, diagonals of the overlapping squares intervene in constructing the letter. They provide numerous points and refer to other ones suitable as centres for circular arcs to be composed at will. Thus the letter may be formed optionally to match the given alphabet. The construction is simplified by adhering to the enveloping circular arc for the outer arcs, rather than to join both circles by an arc, necessarily empoverishing the form. These letters have in common to always keep the statics of S and mostly also its impulse.

Full article: download original pdf file or OCR text

initial letter Hypnerotomachia Poliphili

Initial letter (Hypnerotomachia Poliphili)

Roman capitals inscription at Via Appia

Roman capitals inscription at Via Appia.



  • Chris LozosChris Lozos Posts: 1,458
    The S is still my favorite letter to draw.  Yes, it is demanding but also satisfying. I must admit that I just draw it rather than construct it.  It is interesting to see this theory, however.
  • Ray LarabieRay Larabie Posts: 1,374
    In summary: Dürer's compass/straightedge rationalization was wrong. Tilt the S a bit and make the top smaller.
  • Ah, my old nemessssisssss... (sorry!) Damn hard letter(s) to draw, especially if you're using a mouse. This circle method is so much easier, producing usable results nearly instantaneously, with very little work. Plus, its authenticity is impeccable, being millennia old. Very nice!
  • Geometric construction works very poorly, even for monoline geometric typefaces. All of Gróh's examples depart radically from the underlying circles. (And they're still not very good.)  Meanwhile, constructing an S out of circles doesn't work at all for most styles of letter. You can't make grots, garaldes, didones, transitionals that way, to say nothing of more calligraphic forms.  You sure can't make an s for Michael's M75 face (which, fwiw, I think is shaping up very nicely).

    Michael, if you think the circle method produces usable results fast, I suspect you're not looking hard enough. Drawing an s is a basic type design skill. Trying to find a trick to avoid learning it will not help you develop.
  • Chris LozosChris Lozos Posts: 1,458
    To me, this is the fun part! Ahh, at last, I get to draw an S!  Forget about that damn W! ;-)
  • Well, in all fairness they're more usable than what I draw... the bar isn't exactly high. :/ I never could get the upper left and lower right curves to look decent, not without hour after hour of work, deleting points and moving off-curve points.

    Anyway, I think I unconsciously adapted a method of resizing and stacking the letter /o, rather than a circle -- already shaped for/by/with pen angles and such, and more oval than circular. This looks better than circles.

    But I think Max has it right.
  • Chris LozosChris Lozos Posts: 1,458
    You only need to complete your 10,000 hours now ;-)
  • Stephen ColesStephen Coles Posts: 994
    edited August 2015
    Interesting, John. That’s the opposite of the sign painters’ technique taught by John Downer where they do the spine first.
  • ...but sign painters don't use Bézier curves ;)
  • Do you have to start with Béziers?
  • PabloImpallariPabloImpallari Posts: 775
    edited August 2015
    Besides the shape, another thing to consider is the width of your /s.
    It's a letter that gives you some freedom to

    Some examples:

    Sans: Narrow: Avant Garde, Eras, Frutiger, Kabel / Wide: Franklyn, Helvetica, Titling
    Serifs: Narrow: Garamond, Bembo, Baskerville, Stone / Wide: Fenice, Century, Stika
  • Do you have to start with Béziers?
    For what little it's worth, if I have to draw an S or any other glyph where organic flow is important, I personally have to start with pencil or ink, some method that lets me make whole forms with a sweep of my fingers and/or hand. Once I've got the essence, béziers are brilliant for editing. But compared to a drawing tool in my hand, I find, even after 30 years of practice, that using béziers to create complex curves from scratch is a bit like pushing strands of al dente spaghetti around with chopsticks.
  • David, that wouldn't work for me. I don't mind the /s, but the section mark never looks right to me.  ;o)
  • Chris LozosChris Lozos Posts: 1,458
    What a wonderful dissection of the problem, David ;-)
  • Chris LozosChris Lozos Posts: 1,458
    Maybe I was born with a bezier chromosome but I rather like starting straight away drawing with the mouse.
  • Is that strange to have done the section mark and/or dollar sign before both Ss?
  • Chris LozosChris Lozos Posts: 1,458
    Mr Berlow was enjoying a bit of humor, Michael.
  • Maybe I was born with a bezier chromosome but I rather like starting straight away drawing with the mouse.
    You crazy kids with your computer gadgets.
  • Evie S.Evie S. Posts: 74
    Ray's method is pure gold! You could even start a font by these steps (in Glyphs)
    1) Ray's method, only with a monoline (no serifs if serif typeface)
    2) Apply Broad Nibber plugin for serif typeface or plain Offset Curve in sans typeface.
    3) Tweak as necessary. (Add serifs if needed now.)
  • Evie S.Evie S. Posts: 74
    Polygonal templates have the most tweaking freedom. (Rotating and slanting artificially not worrying about extrema is really helpful.) The result of adding serifs and broad-nibbing the template has a certain charm I can't place my hand on.
    On the left is the serif-and-broad-nibbed /s, on the right is a bold tweaked version (with more bézier curves. Also, sorry for the incompleteness.)

  • Evie S.Evie S. Posts: 74
    Definitely, Mark. I can't make my mind up on my bézier /s either leaning forward or backwards. (Only have 1-2 years of messing around with fonts.)
  • And, I’ve found that a spine with a straight segment gives me a lot more control.

    How well does that interpolate? 
  • John HudsonJohn Hudson Posts: 2,940
    edited August 2015
    Interesting, John. That’s the opposite of the sign painters’ technique taught by John Downer where they do the spine first.
    If you look at where sign painters (or calligraphers) start and finish the spine section, it isn't so different. The key thing is that the left and right extrema of the curves are in a known position, either because they've been made already (as in my bezier method) or because the sign painter or writer is experienced enough to know where the stroke is going to end up. The position of those extrema is really what determines everything else about the S: how wide or narrow it is, how it leans, how steep or shallow the middle bend, how rounded or flattened the top and bottom, and whether, ultimately, it all works as a whole, i.e. it will work or not relative to the position of those two extrema.
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