## M- m- and em-square

On Typophile the technical aspects of the em-square have been repeatedly discussed, but the origin of the term seems to be unclear. I did some research and developed some models, of which I discuss and show a couple here. Because of lack of historical documentation, to a certain extend speculation is in this case unavoidable.

The illustration above shows the relation between the height and the width of the capital N from Jenson’s roman type applied in Epistolae ad Brutum from 1470 using a repetition, i.e. fence, of n’s. The counters in the m are in Jenson’s type identical to the one in the n. The height of the N also fits within the stems of the m and subsequently the N fits in a square. The illustration below shows the same relation for Griffo’s capitals from the Hypnerotomachia Poliphili. On top and rotated left is the m, at the bottom a repetition of n’s.

This ‘m-square’ is definitely something else than what is called ‘em-square’ or ‘em’ in contemporary typography. In digital typography, the em-square is a ‘real’ square based on the body size, normally the distance from the top of the ascender to the bottom of the descender and the ‘em’ equals therefore the body or type size. In foundry type casting on the edges of the body was technically not possible and hence the distance between the top of the ascenders and the bottom of the descenders was somewhat smaller than the body.
Nevertheless Moxon writes in Mechanick Exercises that ‘By Body is meant, in Letter- Cutters, Founders and Printers Language, the Side of the Space contained between the Top and Bottom Line of a Long Letter’, which is annotated by Davis and Carter as being ‘Not a good definition because letters are often cast on a body larger than it need be. It is the dimension of type determined by the body of the mould in which it was cast’ (Joseph Moxon [Herbert Davis, Harry Carter, ed.], Mechanical Exercises [New York, 1978]).
In digital type ascenders and descenders can stick outside the body without any (physical) problem. Parts will probably stick outside the em-square anyway, like for instance the diacritics on capitals. Nevertheless, some designers will basically copy the structure of foundry type, just to prevent clipping when zero line spacing is applied.

In the times of the hot metal and photographic composing machines, the em-square was a rectangle that could be square, depending on the design. Vertically the proportions were defined by the body size and in horizontal direction by the width of the widest character, which could be the M or W, which was divided in a certain number of units.

Although the term em-square is often related with the character width of the capital M, which provided the standard for the (division into units of the) em for composing machines, in for instance Monotype fonts the M is not always the widest letter; of a type family for instance the roman capital M could be placed on 15 units and the italic capital M on 18 units, as shown in the schematic representation of a matrix case above. The capital W seems to have been placed by definition on eighteen units and obviously that was part of the original idea: ‘[…] it was decided that the lower case i, l, full point, etc., could be commonly allotted a thickness of five units, the figures and average letter-thickness nine units, and the capital W, em dash and em quad eighteen units’ (R.C. Elliot, ‘The “Monotype” from infancy to maturity’ the Monotype Recorder, No. 243 Vol. xxxi [London, 1931]). The W of for instance of Monotype Poliphilus is much wider than the M.
On the other hand, in The Monotype System, ‘a book for owners and operators of Monotypes’ from 1912 one can read that: ‘The designer of Monotype faces divides the basic character of the font (the cap M) into eighteen equal parts, using one of these parts as his unit of measurement in determining the width of all the other characters in this font’.

Moxon mentions the ‘m Quadrat’: ‘by m thick is meant m Quadrat thick; which is just so thick as the Body is high’ and mentions ‘n Quadrat’ as ‘half as thick as the body is high’. In The history and art of printing from 1771, m and n Quadrats and related variants as ‘Three to an m’ and ‘Five to an m’ are blanks used for indenting and spacing. In An introduction to the study of bibliography from 1814, the function of the m and n Quadrats is described accordingly and furthermore as ‘the square of the letter to whatever fount it belong […] n quadrat, is half that size’.
If m and n stood and nowadays em and en stand for respectively the full and half size of the body, where does the term come from? In Monotype fonts the M is not always the widest letter, but in Moxon’s engraving in which he ‘exhibited to the World the true Shape of Christoffel Van Dijcks […] Letters’ the width of the capital M equalizes the height of the body. The N, however, has not been drawn of half the width of the M. Moxon notes ‘that some few among the capitals are more than m thick’ and he lists Æ, Œ, Q ‘and most of the Swash Letters’ as examples.

The question remains that if the sizes of m Quadrat, m-square and em-square are based on the width of the capital M, why are they not labelled M Quadrat or M-square or EM-square by Moxon and the other named authors? Do the terms ‘m’ or ‘em’ have a different historical background?

The term ‘m Quadrat’ is surely older than its use in Mechanick Exercises. A hypothesis: let’s assume for a moment that the origin of the (e)m-square lays in the lower case m. The relation with the n-square seems to make much more sense then, because the width of the capital N is never half the width of the M. The proportions of the m seem to have been the measure of all –or at least a many– things in Renaissance type. If a square is based on the outside stems of the m of Adobe Jenson and this ‘m-square’ is used to calculate a golden section rectangle (1:1.618) and the height of this rectangle is used for creating a new square, than the ascenders and descenders of (Adobe) Jenson’s type seem to fit perfectly into the latter, as shown above. This square is an extension of the ‘m-square’: an ‘extended-m’ or em-square, although it is perhaps more likely that ‘em’ originates from the rotated m, which reads like an E, in combination with the normally positioned m. If subsequently a square based on the x-height is made and extended to a golden section rectangle, than the proportions of the descenders can be determined.

Assuming that Jenson treated his roman type as a variant of the Textura, it is quite probable that Gutenberg’s type shows the same relation between the ‘m-square’ and the length of the ascenders and descenders. Gutenberg’s Textura from his 42-line Bible (see illustration) indeed shows the relation as in Jenson’s type. The length of the descenders can in this case be defined using a root 2 rectangle.

FEB

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Frank> A hypothesis: let’s assume for a moment that the origin of the (e)m-square lays in the lower case m.

Why not assume the origin of the lowercase m width is in the em-square instead?

Frank, I am guessing that the name came into being to label to spaces. An "em quad" in foundry type is a *space* that is square, and an "en quad" a space that is half-a-square wide. All foundry type is the same height, the body height, so the question is just what are you going to call a square space, which is the body height wide—and what you are going to call half that. They both have boxes in the type case, so they need a name.

The "em" and "en" are likely just convenient names, not tied to exact widths of the m and n. Since the M is also approximately square, you could take "em quad" as referring to that as well, but the reason for using the lower case "m" is probably because the lower case "n" is roughly half that, whereas the upper case N is not usually roughly half of the M.

The em quad is also called a "mutton" and the en quad a "nut" space, but I don't think you will learn much by taking pictures of sheep and nuts and measuring them :) I don't think the measurements of Jenson etc. are that relevant either. I suspect it is not named because of any exact measurement, but for ease of naming, and the rough widths of the m and n are good enough to suggest the names.

Em quad from m or M, En quad from n or N, fine.

_______________________________________________________

Be Careful Driving Elephants In Small Foreign Garages

Villans Usually Turn Space And Run

What was that third one?

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David: Why not assume the origin of the lowercase m width is in the em-square instead?

Because the (proportions of) written letters formed the basis for Renaissance type, I assume that the regularization and standardization started with the lower case m, but after the system was established it also worked the other way around, as you describe. In both cases the punch cutter probably defined a framework like I produced below for Adobe Garamond.

As reactions on my earlier posts on (possible) standardizations here on Typophile prove, not all contemporary type designers like the idea that the famous punch cutters from the past applied advanced regularizations and standardizations. The reactions seem to be in line with Fournier’s comment in his Manuel Typographique from 1764–1766 on the attempts of Jaugeon and his colleagues to standardize the design of type: ‘These gentlemen would have been well advised to a single rule which they established, which is chiefly to be guided by the eye, the supreme judge […]’.

When it comes to punch cutting, the patterns for the construction of a new series of types for the exclusive use of the Imprimerie Royale developed by the Académie des Sciences in eighteenth century France are generally considered a unique case. Updike in Printing types, their history, forms and use (Cambridge, 1937): ‘[…] every Roman capital was to be designed on a framework of 2304 little squares. Grandjean, the first type-cutter who attempted to follow them, is said to have observed sarcastically, that he should certainly accept Jaugeon’s dictum that “the eye is the sovereign ruler of taste” and accepting this, should throw the rest of his rules overboard!’.

The ‘RdR’ is merely treated as an isolated attempt to regularize and standardize type, and often it is disliked. For instance Fred Smeijers in Counterpunch (London, 1996): ‘The best known case of the separation of design from execution is the “romain du roi”. Here in France at the end of the seventeenth century, intellectual reason struggled in a dialogue with practice and human limitations’, and Albert Kapr in The art of lettering (München, 1983) : ‘A commission was appointed in 1692 to fix the proportions of the romain du roi. Under the chairmanship of the Abbé Nicolas Jaugeon, it went even further in determining the design of typefaces by mathematical rules and diagrams. We need not overrate all these attempts, for artistic success is scarcely achieved through geometric or scientific means’.

The framework of 2304 little squares was perhaps not so unique as many authors on type try to let us believe. The relation between the lowercase letterforms in Moxon’s engravings and the plates for the ‘RdR’ (see illustration; the red lines are Moxon’s contours) can be coincidental, but it seems that the Académie des Sciences thoroughly researched publications on type and it is quite possible that Moxon’s Mechanick Exercises was consulted also. And Moxon actually shows in his plates a 42-unit grid and this results in a framework of 1764 units. That is also a lot and Moxon remarks: ‘We shall imagine (for in Practice it cannot well be perform’d, unless in very large Bodies) that the Length of the whole Body is divided into forty and two equal Parts’ and ‘It may indeed be thought impossible to divide a Body into seven equal Parts, and much more difficult to divide each of those seven equal parts into six equal Parts, which are Forty two, as aforesaid, especially if the Body be but small; but yet it is possible with curious Working […]’. Just like Moxon, Fournier divided the body also into seven parts, but apparently without the subdivision: ‘I divide the body of the letter which I am to cut into seven equal parts, three for the short, five for the ascending and descending, and seven or the whole for the long letters’.

One wonders why Moxon’s grid seems to be overlooked; is it because he did not actually draw the grid lines, like I did in the illustration shown above? So, could it be that the conclusion by Robin Kinross in Modern typography (London, 2004) that ‘[…] The “romain du roi” can be seen as an innocent anticipation of the conditions of type design and text composition in the later twentieth century’ is incorrect and that the ‘RdR’ is actually just a formalization of an older process?

Recently I started measuring French Renaissance type at the Museum Plantin-Moretus in Antwerp to find prove for my ideas about the standardization of widths, which I discussed also in this topic. One of the types I measured was the Middelbaar Canon or Moyen Canon Romain, which is an adaptation by Hendrik van den Keere of Garamond’s Gros Canon Romain. The Gros Canon Romain appeared for the first time in 1555 and which was ‘extremely widespread over western Europe from about 1560 onwards’ according to H.D.L. Vervliet in Sixteenth-Century Printing Types of the Low Countries (Amsterdam, 1968). For the Middelbaar Canon Hendrik van den Keere made accompanying capitals, which appear in Plantin’s books from 1571 onwards and obviously he also shortened the ascenders and descenders.

In the 1960’s a small set of foundry type was cast from the original matrices of the Middelbaar Canon at the Museum Plantin-Moretus. The letters were apparently fitted according to Fournier‘s ideas about spacing in his Manuel Typographique: ‘The letter m of every fount is taken first, and when this is right it is used as a pattern for the others. Three m’s are put in the lining-stick and the first to be cast of every sort is put between them and made to tally with them. The necessary alterations are then made in the mould and the matrix’; the widths of all characters being different. Actually the widths are so different, that things are messed up, like the n and h show.

As I expected, the original sixteenth century type shows a clear standardization of widths and the letters can be placed in groups, like a,c,e and b,d,g,h,n,o,p,q,v,ﬁ and r,s,t. The results of the measurements (using a digital caliper) show deviations within these groups of approximately 0.2–0.4 mm. The deviations cannot be felt with one’s fingers, even when the nail is used to check differences in thickness when the letters are lined up. Also the widths of the characters within a group look the same. One can imagine that after casting the first letter of a group, this letter was used to empirically check the thickness of the other letters. There appeared to be also some deviations in the thickness of the letters, depending on where exactly they were measured.

As mentioned, Moxon describes in Mechanick Exercises a grid of 42 units for the body and this results in 24 units for the n. If the group of letters of the Middelbaar Canon with the same width as the n is placed on 5.3 mm, than 1/24 is 0.22 mm. If the width of the m is rounded to 8.8 mm, the resulting number of units is exactly 40. The group of the i, j and l is in general 2.3 mm and a little bit rounded this results in 10 units. The a, c and e are placed on in general 4.4 mm and this results in 20 units. The r, s and t take around 3.6 mm, which results in 16 units. The 1, 3 and 5 share the widths of the ‘i-group’, the 2, 4, 6, 8 and 9 the widths of the ‘a-group’ and the 7 and 9 the widths of the ‘n-group’.
A unit of 0.22 mm may look small, but when the smallest multiplication factor is for instance 10 (i, j and l), than working with such a system should at least theoretically have been possible.

FEB

Very interesting Frank. Then the other sort of meta-question, is whether this unitization in a systematic approach was taken for the benefit of the type design, or for the benefit of the typographer at composition-time.

David: […] the other sort of meta-question, is whether this unitization in a systematic approach was taken for the benefit of the type design, or for the benefit of the typographer at composition-time

The consequence of Fourniers method is that casting and composing becomes more complex than in case of standardizations of widths. Perhaps punch cutting becomes easier then, because the characters can be engraved independently of their final widths. The fitting becomes the problem of the caster (and the justification of lines the problem of the compositor). In the early days of typography the punch cutters were also the casters, but later on in history casting mainly became a separate profession, as you know.

During my research at the Museum Plantin-Moretus the technical expert at the museum, Guy Hutsebaut, showed me a collection of cardboard boxes with roles of mainly seventeenth century printed sheets, containing collections of foundry type. These loose letters were used as examples for the fitting of type during casting. Although some of the roles are numbered, they seem not to be catalogued.

The collections are identified by names as ‘pas letters’ and ‘Lettre de la justification’ plus information about the font in question. One can imagine that this material was only used if the punch cutter was not casting himself.

FEB

Frank:
So, could it be that the conclusion by Robin Kinross in Modern typography (London, 2004) that ‘[…] The “romain du roi” can be seen as an innocent anticipation of the conditions of type design and text composition in the later twentieth century’ is incorrect and that the ‘RdR’ is actually just a formalization of an older process?

Finding order in history, and seeing patterns of progress there, is a dangerous business. In the words you quoted from me here, I did my best to avoid the mistake of pattern building. The crucial word is "innocent". People in 1700, just as people in 2011, can anticipate nothing with any certainty, expect perhaps the rising of the sun the next day. And like your "could it be", I was careful to add "can be". I was really making a banal conclusion to my discussion of the RdR: "it reminds us of later conditions", and that one can see the RdR as standing in the broad sweep of modernity that developed over centuries.

Concerning the "older process". I take the point that there is a back-history to the RdR. Your research here is really interersting and I hope it fourishes. In my case it was Peter Burnhill's work that opened my eyes to this (I worked with him on the book published eventually in 2003 as Type spaces).

But your statement that "the ‘RdR’ is actually just a formalization of an older process" feels too strong. Yes, it's clear now that the forms of the RdR did not come out of nothing: they have some roots in writing, as I think James Mosley has suggested. And now one can see that there were habits of unitization that were in use in type manufacture already. But if the RdR is "a formalization of an older process", it can't "just" be that. The RdR did have clear after-effects. Type was cut from its models, was printed from. These printed images were circulated, reproduced, discussed ...

Frank: The collections are identified by names as ‘pas letters’ and ‘Lettre de la justification’ plus information about the font in question. One can imagine that this material was only used if the punch cutter was not casting himself.

This reminds me of the discussion we had over dinner with the URW guys regarding iterative auto-spacing and -kerning. What I had in mind is something like these lettres de la justification: a set of model glyphs, spaced by the type designer, that provide guidance to the auto-spacing and -kerning routines. Iteratively, after the auto- routines have run, the designer could adjust results on some glyphs and add them to the model set to refine the results of the next run of the routines.

John: What I had in mind is something like these lettres de la justification: a set of model glyphs, spaced by the type designer, that provide guidance to the auto-spacing and -kerning routines.

With Kernus 3.0 (1998) also auto-spacing was possible and the side-bearing or width values for a small range of key characters could be adjusted by the designer (see illustration). If everything goes well, this functionality will become available for Mac OS X and Windows as part of ‘GPOSMaster’ (the exact name of the application has not been defined yet actually) sometime this year. The ‘Kern Strength’ (as it is named in KernMaster) can be defined per group of characters in the new program.

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Robin, thanks for the clarification.

FEB

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One wonders why Moxon’s grid seems to be overlooked; is it because he did not actually draw the grid lines, like I did in the illustration shown above? So, could it be that the conclusion by Robin Kinross in Modern typography (London, 2004) that ‘[…] The ‘romain du roi’ can be seen as an innocent anticipation of the conditions of type design and text composition in the later twentieth century’ is incorrect and that the ‘RdR’ is actually just a formalization of an older process?

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Very suggestive point of view, Frank. In this way, the Romain du Roi could (just) shows visually the process, but carrying the older tradition.

Miguel

http://cg.scs.carleton.ca/~luc/oh/oh.html

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The RdR grid makes clear that the glyph is drawn on the grid ("snap to grid", as it were), rather than the grid being the traditional "squaring off" method of mapping used in art for drawing from life, perspective construction, and resizing.
For instance, the slope of the left stem of "M" is exactly one grid unit.
Even the "half square" width of the serif tips relates to the grid.

However, ultimately the functionality of the RdR drawings is questionable, because the cap-height is drawn to a height of 48 units, whereas the lower case ascender height is at a different scale, 63 units. So they are more of a proportional guide, albeit with high-tech cachet.

(I've come to this conclusion from online sources, not the originals, so I hope it's right.)

FB> Perhaps punch cutting becomes easier then, because the characters can be engraved independently of their final widths.

Engraved independently yes, but do you think letter definition and unitizing happen independent of each other in successful foundries?

>The fitting becomes the problem of the caster (and the justification of lines the problem of the compositor).

understood. But what better way to improve the quality "back then", than to have the letters designed for a specific width on a grid, and then to describe those widths to the caster, (painter, carver or scribe for that matter), in the form of an actual object for measurement?

There are some very interesting themes that you raise Frank.

However, it is perhaps worthwhile to look at Moxon's earlier work also (I have been looking at the work of Moxon, Fournier and the Academie of Sciences for my PhD, I also presented some findings in relation to this at ATypI Dublin – perhaps we should compare notes at some point?):

Moxon j. (1676) Regulea Trium Ordinum Literarum Typographicarum or The rules of three orders of print letters: viz. {The roman, italic, english} capitals and small. Shewing how they are compounded of geometric figures, and mostly made by rule and compas. Useful for Writing masters, Painters, Carvers, Masons, and other Lovers of Curiosity. By Joseph Moxon, Hydrographer to the Kings Most Excellent Majesty. London: Sign of the Atlas

It has to be borne in mind Moxon's scientifically inclined approach to work. This is also the period of enlightenment. Moxon's work is claimed to be based on a study of the letters of Christophel van Dijck. Influences are also drived from Albrecht Dürer's geometric rationalisation of captital letters and Vitruvius' The Rules of the Five Orders of Architecture (a survey of proportions found in Tuscan, Doric, Ionic, Corinthian and Composite columns etc.)

There is also something that has to be very carefully considered with regard to the purpose of what Moxon and the Academie set out to do by making such descriptions of letterform intended for typeface.

In terms of the Academie Jaugeon gives an account found in Jammes' excellent article in Journal of the Printing Historical Society No.1 1965:

'We began by making a collection of all letters made by means of punches, and which have been approved of in the finest printed books. Next we consulted those writers who have tried to provide rules and proportions for them and we saw when comparing the finest letters form the handsomest books with those proposed as models in treatise on the subject, that in every case there was room for improvement, and to do this one had to eliminate the defects of some and guard against the uncritical acceptance of others'.

'It was on this basis, and not empirically that engraved models were established.'

Moxon's preface to Mechanick Exercises also comes from the perspective of improving through mathematics and science that which he agruably considered otherwise malevolent perhaps:

'…I find that a Typographer ought to be equally qualified with all the sciences that become an Architect, and then I think no doubt remains that Typographie is not also a Mathematical Science. (Moxon 1683)

Moxon attempts to align his mathematical and scientific perspective as just with his obvious influence in Dr. Dee's Mathematical preface to Euclids Elements of Geometry.

As you correctly point out similarities in Moxon and Founrier's accounts of 'seven parts' etc. However, both are referring to the division of vertical space – so the height or depth of a letter in relation to working with the 'face gauge'. Lines that allow three parts for the body of the letter (our x-height today) two parts for the descenders and two parts for the ascenders.

Moxon's 'grid' as shown in Mechanick Exercises is obviously based on his work in Regulae Trium etc. However, you will notice that there is a convenient 'post-rationalisation' here. Moxon's original grid that surrounds the cap A in Trium etc. shows a width of 36 divisions, convincingly this appears in Mechanick Exercises extended to 42 wide, reinforcing his rationalist approach. Also of note are the serifs or 'footings' to the letter, these are much exaggerated in Mechanick Exercises. Moxon neither optically compensates for curves or points in his letters such as O V etc. On viewing letters drawn by Moxon some appear so badly rendered that his method of rule and compass can surely only indicate use as a guide. He espouses scientific and mathematic rule but this has to be questioned.

All this is not to say letters were not constructed to 'divine proportions' of course. However, Moxon and the members of the Academie who conducted their 'studies' were not expert in designing letters or cutting punches. The same cannot not be said of Fournier who's life and work was devoted to this. This is not to say that Fournier did not 'borrow' either. Fournier's account is a pragmatic one, one that cannot be ignored either.

Perhaps it is worth to consider a further point from Jammes:

'Jaugeon and his associates did not lose sight of the purpose of these models [RdR]. They conceived them as patterns destined to guide the eye of artist, afterwards to be transferred to steel as precisely as possible. They were well aware that their geometric grid was useless when reduced, for "in the making of punches, at least in the smaller sizes, it is very difficult to achieve perfect accuracy" and so it is the "eye of the craftsman that must decide"'. (Jammes 1965)

Perhaps it is worth also looking at the letters taken from the punches (1695) of Grandjean in relation to Simonneau's first copperplate engravings for the RdR (1695). These are more than imperfections of accuracy, these are deliberate or conscious changes that arguably Grandjean intended and at times disregards the work of the commission.

Well at least it's something to think about!
MH

Actually it was not my intention to put too much emphasis on Moxon and the ‘Romain du Roi’ in my attempts to prove the existence of unitizations in the work of Renaissance punch cutters, i.e. the modelers of the archetypes. My point is that the RdR is not a unique example of the appliance of a grid in the world of punch cutting. I underline ‘punch cutting’ here, because the attempts to capture the construction and proportions of the inscribed Roman imperial capitals from the first century into geometric models, like Dürer’s, were made by artists, scholars and calligraphers. For instance Dürer (1471–1528) was an artist, Fra Luca de Pacioli (1446/7–1517), who published a section on the ‘true’ shapes and proportions of classical Roman letters in his De Devina Proportione (‘Devine Proportion’, i.e., golden section) from 1509 was a mathematical scholar and Giambattista Palatino, who was a calligrapher, also made geometrical representations of the Roman imperial capitals.

Grids were applied on type before the RdR, as Moxon for instance shows in his Mechanick Exercises. I don’t believe that the 42-unit grid from this work or the 36-units grids from the Regulae Trium Ordinum Litterarum Typographic Arum were standards though. The fact that I could apply the 42-unit grid on the Middelbaar Canon could even be a coincidence. But if my theory is correct, any ‘natural’ division into any number of units could be made, using a simple system, which I describe below.
For me the most important question is how the division into the (number of) units, i.e. the grid, was actually made. Is there a clear relation between the units and the vertical and horizontal proportions of the letters? Is the vertical division of the body into seven parts by both Moxon and Fournier for instance related to the horizontal proportions of the letters? In other words, are the grids artificial, i.e. defined first, after which the letterforms are adjusted to the grid, or are the grids organic, i.e. derived from the proportions of the letters?

Fournier’s account on punch cutting in his Manuel Typographique has become a major source of information on the subject and besides Moxon’s Mechanick Exercises there seems not to be much info on this subject available. The dialogue on Calligraphy & Printing, which is attributed to Christopher Plantin (translated by Ray Nash [Antwerp, 1964]) does not provide much info on punch cutting. Fournier was certainly a trained punch cutter, but that does not imply by definition that he knew all rules that were applied earlier in the trade.

Letters are things, not pictures of things’ is a famous quote by Eric Gill from his Autobiography Nevertheless, in his An essay on typography Gill basically provides most info on the shapes of letters by using pictures with captions like ‘[…] normal forms; the remainder shows various exaggerations; […] common form of vulgarity; […] common misconceptions […]’. Any basic information on the underlying structures and patterns is missing. This is in line with the way type seems to have been treated since the establishment of typography in Renaissance Italy. The letter shapes and their proportions of the Italian Renaissance punch cutters were copied by French Renaissance punch cutters and their work formed the basis for the Dutch letterforms from the Baroque. This leads to the first question for which my PhD research is meant to provide an answer:

Could it be possible that somewhere during the development of type the knowledge of initial regularizations, standardizations and unitizations was lost and that subsequently letters became pictures of things instead of things and if so, can this information be retrieved from historical material, such as punches, matrices and prints since historical documentation on this subject is extremely scarce?

For answering this question, information about possible regularizations, standardizations and unitizations have to be distilled from historical material, such as prints, punches and matrices. To some extent making assumptions is inevitable and this makes this research also somewhat controversial. And, as I stated in earlier posts, not everyone likes the idea that the ruling of the eye is merely the result of a conditioning based on formalized sets of graphemes for –in our case– representing the Latin script. The models define the rules and their shaping is the result of culturally influenced ideas about harmony and rhythm and subsequently of beauty. As the graphemes worldwide in use to represent the different scripts prove, the ideas of what is harmonically and rhythmically balanced, clearly differ –as those who work on ‘global fonts’ probably will acknowledge.

To be able to describe the (possible) unitization, i.e. the applied grids, first I will have to describe here the factors that are crucial for defining the harmonics of type:
1. The relation between the proportions of the letters within a Harmonic system, such as roman, italic and capital and the required adjustments of these proportions to make the different Harmonic systems work together.
2. The relation between the horizontal and vertical proportions of the Harmonic systems.
3. The relation between the proportions of the members of a Harmonic system and their Rhythmic system, i.e. their widths (fitting).
4. The translation of the Rhythmic system into a grid.

I will try to keep this description as short as possible; it is absolutely not my intention to publish my thesis here or to reveal all the outcomes of my research. So, I just give a very compact summary of some of my ideas. At the end of this post I will discuss whether it is possible to distill a grid from an existing (digital) typeface, which has proportions related to the ‘Garamond model’ and give some info on ‘rhythmic’ fitting (as opposed to ‘optical’ spacing).

1. The proportions of the letters
There is no discussion possible about the fact that written letters were initially standardized and eventually formalized by the invention of movable type in the Renaissance. I can supply numerous quotations here, but I restrict myself to Johnston ([Heather Child ed.], Formal Penmanship and other papers): ‘The first printers’ types were naturally an inevitably the more formalized, or materialized, letter of the writer’. Bringhurst (The Elements of Typographic Style): ‘The original purpose of type was simply copying. The job of typographer was to imitate the scribal hand in a form that permitted exact and fast replication.’ Morison (Type designs of the past and present): ‘Handwriting is, of course, the immediate forerunner of printing, and some knowledge of its history is essential to any sound understanding of typography’.

For the formalization and standardization of written letters, Jenson and his colleagues (Sweynheym and Pannartz , Da Spira, Griffo) had to provide a structure for the relation of the proportions of the letters. I strongly believe that the Renaissance guys used the ‘primary’ (geometric) model for the roman (see illustration above), which is applied in LeMo.

The ‘n b c’ illustration shows the proportions of a couple of letters of Hendrik van den Keere’s Parangon Romain placed on the related ‘primary’ Harmonic model. The same relation between the proportions of the letters can be found in Jenson’s, Griffo’s and Garamond’s type.

Typefaces can be based on a single Proportional model, i.e. within the Harmonic model there is only one value used for the horizontal stretching, like in Van den Keere’s Parangon Romain, or contain multiple proportional models, like Van den Keere’s Canon Romain (see below). Multiple proportional models especially seem to appear in the larger point sizes during the French Renaissance. An example is the condensed m, of which I have the impression that it only was used for display purposes before the seventeenth century. The shape and proportions of the m seem to have been based always on ‘twice’ an n in the Italian and French Renaissance text types and the relatively condensed m seems to appear in text sizes in the seventeenth century also.

2. The relation between the horizontal and vertical proportions
After defining the proportions within the x-height using the primary Harmonic model, the next step is to establish the relation between the x-height and the length of the ascenders and descenders. This could have been done using the (e)m-square as follows:

The hierarchical relation between the size of the counters, i.e. the space in the letters and the length of the ascenders and descenders is catched in this (e)m-square model. Widening the m results in a relatively smaller x-heigth and condensing the m in a larger x-height within the (e)m-square. The Proportional model can be used to define the width of the m and thus the proportions of the (e)m-square.

The relation between the height of the capitals and the (e)m square and the actual lengths of the ascenders and descenders can be calculated using the n-square (see below).

The relation between the horizontal proportions of the (e)m-square and the widths of the capitals (like those of [Adobe] Jenson, which are shown in the illustration below) can be defined also using the m (or twice the n in case the m is relatively condensed).

3. The relation between the Harmonic system and the Rhythmic system

The modulation from Textura to Humanistic minuscule is not more than a matter of reversing the process of condensing and curve-flattening in combination with an increase in weight (see illustration above), which took place in the second half of the middle ages, and which transformed the Carolingian minuscule into the Textura. B.L. Ullman (The origin and development of humanistic script): ‘This Carolingian script reached its finest flower in the ninth century, then gradually decayed. By the thirteenth century its transformation into Gothic was complete. The characteristics of Gothic are lateral compression, angularity, and what I have called fusion, the overlapping of rounded letter’.
The transition from Textura to roman type is in the literature on type and typography mostly described as a matter of taste and preferences. Stanley Morison (Type designs of the past and present): ‘In Italy the gothic letter, though richly and magnificently used, soon began to show traces of influence exerted by the small round letter favoured by the humanistic scholars who thronged the courts and universities’. The technical consequences of the transition from Textura to roman type for the punch cutters and especially the casters seem to have been ignored completely in literature.

The fitting of Textura is basically fairly simple because of the vertical stressing of the letters; the vertical strokes can be placed at equal distances and hence the space between the strokes and the side bearings is also in almost all cases equal, as the following illustration shows.

The morphology is in basis the same for Textura and roman type, hence the round parts can be considered as overshoots of the straight strokes. Defining the side bearings for roman type can therefore be done in the same way as for Textura type (see below). It is not impossible that Jenson applied the fitting structure for Textura type directly on his roman type. The illustration below seems to prove the appliance of this fencing-method by Jenson.

The grids as shown in the previous two illustrations, are based on the division of the counter of the n into two equal space parts, i.e. the line is drawn exactly in between the stems of the n. This division comes forth from the design itself and the fact that the other letters belong to the same proportional system generates a simple unit arrangement in which the i is placed on one unit, the n, h, u and o on two and the m on three units.

The incorporation of other letters in the fitting system, like for instance the s and e, requires a refinement of the grid. For example the grid can be doubled, placing the o on five units and providing the three units required for spacing the s. The grid can be doubled again, because for the placement of the right side bearing for the e a further refinement of the grid could be necessary.
The distance from the centre of the n to the side bearing is identical to the distance from stem to stem (A). The division into finer units does not have to be the result of doubling; the forenamed distance can be divided into any number of units. One can imagine a smaller number for small point sizes.

4. The translation of units into a grid
The division into seven parts by Moxon seems to follow the scheme described above. In the illustration below the grid from his engravings in Mechanick Exercises is placed 1:1 on the ‘lower case’ letters. This implies that the size of the ‘seven equal parts which he used for the division of the body, was defined by the proportions of the n (and m). Here Moxon divides the distance from stem to stem into 12 units. One wonders if the developers of the hot metal typesetting machines knew this system. My guess is that they actually were aware of it.

Also in the type used by Gutenberg for his 42-line bible (an many other types), I could find a direct relation between the horizontal and the vertical grid, as the following two illustrations show. These grids are theoretically size-independent, like the (inorganic) m-squares used in CFF and TrueType fonts.

Rythmic spacing
To optically determine the character width, i.e. the space that ‘belongs’ to the character, (after spacing) an arbitrary side bearing can be drawn in between the characters, like has been done in the illustration below. This results in a distance between the right stem of the left n and the side bearing. By placing the side bearing at the same distance from the right stem of the right n, the character width is defined.

Theoretically this is enough information for spacing all other letters, and characters, because these can be placed optically correctly, i.e. within the defined rhythm, in between a range of n’s. The side bearings of the ‘n’ mark the side bearings of the spaced letters then. To make the fitting easier (and the combination of for instance roman and italic) the second step in the fitting process is normally to optically centre the ‘base’ letters. Letters that share (almost) the same forms, like the related curves of the b, d, p and q with the o, can be spaced identically. Therefore it is not necessary to space every character separately, because groups of related letters can be made.

Alternatively the fitting of letters can be done based on the Rhythmic system, by applying a grid on the fenced letters as described above. This actually implies that the letters themselves have to be designed on the fencing rhythm. This results in groups of equal widths, like I found in VdK’s Middelbaar Canon (digitally measured at the Museum Plantin-Moretus). A fencing rhythm or ‘fence posting’ standardises the distances between stems. The traditional approach in type design and typography is that the space between the counters of type for text setting is an optical repetition of the space within the counters. However one can question whether the differences in white spaces as the result of ‘fence posting’ can be seen at text sizes and also whether the casters in the past would have been able to apply the subtle differences, which are more visible for the digital type designer who enlarges the letters on screen for spacing. And could it be possible that at small sizes the rhythm of stems is more important than the rhythm of white space?

I did some test with the refinement of the grid and also looked if it was possible to translate the grid that originated from ‘fence posting’ into values for the placement of side bearings for letters that were not designed on groups of equal widths. A division of the width of the n into 36 units was refined enough to space for instance Adobe Garamond. In the illustration below the first text contains the original fitting by Slimbach and the second one grid fitting based on the 36 units for the n.

Spacing via cadence-units is an extremely simple and fast method when applied in a font editor (just put the grid into the background) and no knowledge of letters or any experience with spacing is required. For the more advanced type designers it could provide a starting point for further refining. Of course, I have been thinking of computerizing this simple system and it is already part of the latest version of LeMo. If everything goes well, further development will result in a small application (‘RhythmicFitter’[?]), which can be used for the fitting of digital fonts.

For those who want to apply the system on their roman type, I supply a range of units here (see also this pdf). These should work for a 36-unit grid for the n. My idea for the forenamed application is, that the user can define the resolution of the grid and the related units for fitting himself.

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Gotta love this thread! Thanks for sharing!
Somebody please put this on "Handpicked"?

Great work, Frank.

However, I'm not convinced that Jenson was a fence-poster.
In this example of letters culled from the same page printed by him, the distance between the stems of h, u, n and m is quite different, and it appears to be an aesthetic decision, not random deviation.

Seems odd that Jenson's u is more open than the n? I feel as though the u should be narrower than n or is that my astigmatism?

Chris, because the ink from those days is often much heavier on one letter than another it is hard to conclude anything from one set of letters.

"...because the ink from those days is often much heavier on one letter than another..."

I know that and I can see some acceptable variation in the spread on Nick's sample. I also see the position variation on the cyan guide lines indicates spread is not the culprit here. Yes, the u is a tad cleaner than the n with the n appearing to have recieved more ink perhaps due to its positioning visa vis the head of the form when locked up. Notice that even though the u received less ink and or less packing, it is still wider than the n. The m of course is typically narrower as an optical correction for overall width.

From what I can see from this low rez image, the packing does not seem to be severe and the inking difference is within tolerances for that era of printing technology.

Ink gain occurs on both sides of stems.
The blue lines are centred in the "h" stems.

It might just be a mistake or an imperfection from manufacturing. As exquisite as Jenson’s work is, it still suffers from the limits of the tools he had at his disposal.

Noticing the pull to the right of the u, perhaps some paper stretch is at work here, common for damp paper. From the gripper edge to the tail of the sheet, the sheet tended to stretch a tad wider at the foot. Glyphs on the lower left and lower right were subject to more of the effect than those at head above center.

No mistakes. Those are counter variations consistent with unitization of similar forms with differing spacial requirements wrought by x- ht serifs.

I tried to measure modern foundry type with the same equipment, and measurements smaller than about 1/4 point soon seemed irrelevant, regardless character size or even typeface, as differences in width between bodies of the same character were relatively too large, even after cleaning thoroughly, measuring exactly the same way, choosing similar samples, etc.

With the kindest of intentions and much goodwill I’d like to do something to introduce a little scepticism into the historical parts of Frank’s line of research.

Like many others, I am well aware that the type of the 42-line Bible, and Jenson’s, and perhaps Baskerville’s Great Primer too (the type of his Virgil, 1757), all seem to be designed to be cast in a way that will produce strokes that appear evenly spaced, and I am sure this effect gives printing with these types a special visual quality. But I find it less easy to believe that type makers of the 15th century did micro-analysis of the small details of their characters, involving the Golden Section.

I do know something of the often rather obsessive geometric constructions of Roman inscriptional capital letters that to our knowledge begin with Feliciano in about 1460 and of which Palatino’s, in about 1540, seems to have been among the last. Many of these schemes are closely linked up with attempts on the part of architects in Italy to interpret the text of the Roman theorist Vitruvius, who was writing about the proportions of buildings and the orders of columns, and was never concerned with letters.

I should like to draw Frank’s attention to the way humanity keeps breaking in to these theoretical constructions. Feliciano says of the letter R that the tail is a problem because there is no simple way of making it with a compass: ‘you must let yourself be guided by your eye’, he says. But then he tries again, showing a second R, saying that the tail must be made more by practice than by rules, so that to make it well, you must do it several times to get it right.

Palatino made one of the latest and craziest of the geometrical constructions, and more or less destroyed their credibility. Cresci, his great rival as a calligrapher and the designer of some beautiful big capitals, said, in effect, ‘loosen up’. Geometry destroys letters for inscriptions: to do them well, draw them freehand, over and over again. Cresci’s free-flowing script put Palatino’s stiff, cramped, system-made model out of business, and changed the history of handwriting.

Mind you, there are some schemes that are worth taking seriously, like those for the Romain du Roi, for example. But they need to be followed with intelligence. Frank quotes Updike: ‘Grandjean, the first type-cutter who attempted to follow them, is said to have observed sarcastically, that he should certainly accept Jaugeon’s dictum that “the eye is the sovereign ruler of taste” and accepting this, should throw the rest of his rules overboard!’.

Character width, or ‘set’. Those types that Guy Hutsebaut found for Frank are called ‘set patterns’ in English. (By the by, I think the wording on the wrappers of these examples needs closer examining: what has been quoted does not make sense). Once you have produced a good fount from a set of matrices in one mould, setting its registers, you keep sample types. To repeat the ‘set’ or spacing of a new ‘fount’ (a word that just means ‘casting’), you put the ‘set patterns’ back in the same mould, one by one, use them to set the registers again, and you can repeat the casting you did before. No measurement is needed: use your eyes and fingers. No punchcutter could ever dictate the spacing of a type: it was all done by judgement of the caster. Just possibly some punchcutters made trial founts to guide the caster, but Frank, how many punchcutters do you think ever cast a full fount of their own types, commonly 100,000 sorts or more? Very often they never even made their own matrices.

In any case, how could it be possible to learn anything about the original spacing of a type of Van den Keere’s from a casting done at the museum in the 1960s? Of course if their matrices are the same width so are some characters: that way you don’t have to keep resetting the registers.

In his own treatise of about 1700, the only major text about making types that we have in addition to Moxon’s and Fournier’s, Jaugeon says that Grandjean made registers for the mould that could be finely adjusted with a screw thread to avoid the casters’ normal practice of slackening the nut a bit and then using a hammer to shift the register, with predictable damage to the mould. Brilliant idea. But the new device was slow and it burned the caster’s fingers when the mould was hot, as it was during casting. The casters went back to their hammers. You can handle just so much ingenious logic, and then you have to get on with the job.

I rest my case. Yes, geometrical analysis is fascinating and it can probably give us real insights into some designs. But I am afraid that it often turns into a kind of enclosed system, isolated from the shop floor that we, as compositors and readers, work on.

The em quad by the way, as contributors to this thread have pointed out, is simply a ‘square’ space (which is what ‘quadrat’ means), determined by the body of the type that is being cast. The en is half its width. No direct relationship to any letter is intended: the terms are figures of speech. Compositors use them, and call them ‘muttons’ and ‘nuts’ to save confusion in the shop. No theory, no measurements. You use em quads, sometimes made in multiples like 3-em quads, to fill short lines and indent paragraphs. Welcome to the real world.

Best wishes.

"Yes, geometrical analysis is fascinating and it can probably give us real insights into some designs. But I am afraid ..."

I have always felt that rigid geometry was counterproductive as a way of working. I tried it numerous times and always found I needed to "fix" something a bit here and there. This is kind of like the measurement of moving quantum particles; there is a point where there is uncertainty and we need devise a probability instead of an exact measurement. As a way of working, I find this to be a waste of time. I would rather teach my eyes and hands to make the adjustment through human perception (learning to see).
I can understand how the manufacturing process of producing mats and castings, how a geometric system can help in the physical production of metal objects. In this age of bezier curves, we have no such need. Even when the type for screen hinting issues attempt to fit glyph to grid, the grid is a moving target and we once again institute some fudge factor to allow for differences. If the eye is the final arbiter in seeing it, then the eye should make the judgement in making it.

I am not saying this is a wasted process. I am keenly interested in it even if I do not use it myself. There are those with the right set of mathematical and perceptual gifts than can make a reasonable research of this and I hope they continue no-mater what they may find.

ChrisL

My hat is off to James. very very well put. Just in case someone reading this isn't sure what Cresci capitals are like here is an image. Contact me offsite if you need more.

Also looking over my many photos of Jenson type I can readily concur with Nick's observations. The stems don't picket in reality even if they mostly do when looking at the text. The u is a bit "too" wide and breaks the rhythm.

James: I find it less easy to believe that type makers of the 15th century did micro-analysis of the small details of their characters, involving the Golden Section.

I don’t think that the Renaissance punch cutters needed nanotechnology to apply the Golden Section on their type. The relations between the different Harmonic systems and their parts could have been drawn/calculated at any size and subsequently have been translated for instance to a ‘face gauge’.

James: I am well aware that the type of the 42-line Bible, and Jenson’s, and perhaps Baskerville’s Great Primer too (the type of his Virgil, 1757), all seem to be designed to be cast in a way that will produce strokes that appear evenly spaced […]

I am pleased to know that more people are aware of casting in a way that produce strokes, but my intention is to (try to) find out how exactly this stroke-system works and to prove for instance that the fence-posting in Textura type was directly translated to roman type.

James: I should like to draw Frank’s attention to the way humanity keeps breaking in to these theoretical constructions.

Yes, and that fact makes it quite plausible that the Renaissance punch cutters, who were gold smiths from origin, applied geometrical systems to standardize, regularize and unitize their type.

James: Feliciano says of the letter R that the tail is a problem because there is no simple way of making it with a compass [...]

A serious look at my models will show that these have nothing in common with the geometrical attempts by Feleciano, Pacioli, Palatino, Cresci, Dürer or any of their companions. I am not trying to reconstruct specific letterforms (in case of forenamed men specifically the Roman imperial capitals) using rulers and compass, but I try to describe the general underlying patterns and constructions of type, either Gothic or roman.
By generalizing geometrical attempts this way, I fear that the door is closed by definition for any research in this direction, which does not help science I think.

James: [...] I think the wording on the wrappers of these examples needs closer examining: what has been quoted does not make sense

What I quoted can be read on the photograph, which I place here again. And I will do a close examination of these sets and their wrappers, of course.

James: how could it be possible to learn anything about the original spacing of a type of Van den Keere’s from a casting done at the museum in the 1960s?

Actually I measured the original Renaissance type (both the Gros Canon Romain and the Moyen Canon Romain), as you can read above. I only showed the type casted in the 1960’s as an example of ignorant fitting.

James: But I am afraid that it often turns into a kind of enclosed system, isolated from the shop floor that we, as compositors and readers, work on.

The shown models will be applied in software for analysing type and in software for designing type. So, there will be no isolation in this case and this makes this project part of the real world, I reckon.

After measuring the Gros Canon Romain and the Moyen Canon Romain and finding the expected standardizations of widths, the next question to answer was whether the matrices would show the same standardization. In that case the fitting of only one set letter of each group (like b,d,g,h,n,o,p,q,v,ﬁ) would be necessary and all the other letters of the group could be casted without any additional adjustments of the fitting.

On Tuesday the 11th of January 2011, I measured the matrices in question and found the same regularization as in the sixteenth century casted type. The strikes of the punches were placed exactly in the ‘optical’ centre of the matrices.
Below I show a couple of photo’s of the matrices I made with a digital microscope camera (specifically meant for checking circuit boards). One can clearly see that the images are centered. The following two photo’s show matrices of the Gros Canon Romain by Garamond.

The matrices of the Gros Canon Romain are much more refined than those of the Moyen Canon Romain of Van den Keere, as one see below.

Still, when casting the matrices of Van den Keere could be used directly in the system of the Gros Canon Romain, without any adjustments of the fitting. The casting was done by Guy Hutsebaut, and I placed a short movie (made with my iPod) on YouTube.

Because there are no moulds available which support the bodies of the Gros Canon Romain and Moyen Canon Romain, the letters were cast on a body which was too small. For testing the (standardization of the) width of the letters, the used mould was perfectly suitable though.

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Wednesday 28 August in the presence of my Expert class Type design (Plantin Institute of Typography) students, I tested (again) my theory on standardized and systematized Renaissance matrices (you’re all familiar with my PhD research, I reckon ;-) at the Museum Plantin-Moretus.
As always my friend and former Plantin-Society student (almost 20 years ago) Guy Hutsebaut did the actual casting. We used Garamont’s original matrices of the Gros Canon Romain. By just centering the lower-case l and adding a little bit of space at both sides of the serifs, it was possible to properly cast the complete lower case with the same registers setting for the mould.
EcTd-student Kees Kanters made a couple of marvelous photo’s and placed them on his Flickr page

With the registers of the mould the character-width is adjusted. Fournier describes this in his Manuel Typographique as follows: ‘The lateral spacing of letters is called the set. The correct set is achieved by casting the shanks to the exact thickness necessary to make regular intervals between the letters. The thickness is regulated by the two registers of the mould, which hold the matrix between them. Their position determines the width of the cavity between the bodies of the mould, into which ﬂows the metal destined to form the shank with the letter on its end.’*

If the distances measured from the edges of the matrices to the bows and stems are handled identically for a range of matrices (like in the example with matrices of Granjon’s Ascendonica Cursive above), one only has to adjust the registers once for this range. That is my hypothesis. In that case one can set words with the matrices, and although the spacing is too wide, the amount of space between the characters is identical. To obtain a spacing that preserves the stem interval, i.e., which matches the size of the counters, one has to apply ‘tracking’. See illustration with 16th-century matrices of Garamont’s Gros Canon Romain below; for reducing the spacing I used cadence-units.
In case a character from a range is not exactly cast in the center of its width, all other characters will show the same deviation, of course.

*Harry Carter, Fournier on typefounding (New York, 1973) p.158

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In my post of 7 January 2011 I showed the transition from textura type to Renaissance roman type, and the subsequent limited range of widths of matrices for the latter. By limiting this, the striking of the punches (not in single lumps, as is written often [always?], but in strokes of copper), which were precut like chocolate bars, and the justiﬁcation of the matrices was subsequently easier.

The early punch cutters had to set up the complete system in a relatively short period. The outcome was basically comparable with the widths-standardization (i.e., simpliﬁcation) for the Monotype hot-metal system. The fact that designs of roman type were in general easy to adjust by the Type Drawing Ofﬁce for the Monotype 18-units arrangement system, could actually be caused by the fact that roman type was initially made for a system that required a comparable standardization.

Why do 17th- and 18th-century descriptions of the type-founders’ practice by for instance Moxon and Fournier not mention the standardization of matrices, which I measured in Renaissance type? Could there be a direct relation to the appliance of ‘set patterns’ for the setting of mould registers and the change of proportions in type, such as due to the goût Hollandais? The photo above of matrices from Rosart’s Garamonde Romaine obviously doesn’t show the forenamed standardizations anymore.

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Standardized Casting 2013: The Movie