About em
出典: DoubleType
This document is licensed under a Creative Commons License. This is a translation of document I originally wrote in Japanese.
Contents |
Introduction
There is nothing more confusing in typography than em. First of all, the name is misleading. Both the typeface creators and users are not clear what it is. For metal type craftsman, it should be the most concrete, physical thing, but for a creator of digital typeface - especially em of a typeface that doesn't exist yet - it is very vague. A unit is destined to be value when it measures something relative.
Again, the name is really bad. It's unavoidable to mislead people into thinking that em is an M; To make the matter worse, it is not even completely wrong.
In this document I explore the variance of the definitions of em, the keystone of typography that continues to confuse people.
Patterns of common mistakes
Mistake pattern 1
The rectangle surrounding capital M.
All letters must fit into an em-square. Hopefully, one would soon question "what about p?"
Mistake pattern 2
The set width of the letter M.
This is by far the most common mistake, but a mistake nonetheless. Consider a monospace typeface, such as the one used for doubletype logo. The definition does not hold because it is unlikely that the uniform width of the body size of the typeface matches its own uniform height. The detail of the body size is covered later.
It is generally wrong when em is defined by a width of something. The problem is that this mistake pattern actually is the namesake of em. In the olden day of the Roman Empire, the set width of M was close to em, and that is where em got its name. Moreover, 1/2 em is called en; thus, many tend to misunderstand that is a width of something.
However, after the invention of lowercase alphabets, even for classic typefaces, em would rarely match the set width of M. Set width of M is generally much narrower than em.
Mistake pattern 3
The set width of Asian full-width character.
A variation of this common mistake is presented by QuarkXpress, which defines em as twice the width of 0, but that's also incorrect. In the western (horizontal) typesetting, the set width varies from letter to letter, and it's not reliable.
Mistake pattern 4
The distance between the highest point of the ascender of h and the lowest point of the descender of q.
This definition is close, but no cigar. If one defines em as above, the letters would touch the other letters above or bellow them when set without any leading.
Definition of em
Well then, what's em?
Em is a square metal block used for spacing, called em quad. When it is used as a linear unit, em is the length of a side of the em quad, which is also known as em space; it is written as 1 em as unit.
The constant height of the face of types is called body size, and that's what 1 em is defined as. For example, 1 em of 12 pt font is 12 pt. In other words, all TrueType fonts are defined by the height of typeface as if it were cast in metal type.
It gets harder to estimate em from handwritten letter like h or q.
The complexity comes from thinking about the letters first. Seeing things from the point of view of carving craftsman would clarify the situation. First, there is em. Suppose the craftsman is designing a 12-point font. 1 em equals 12 pt. The craftsman finds a metal block of 12 pt square and carves h on it, leaving enough space on the top and the bottom so it can align with letters like p. That's a 12 pt h.
Verification
English language readers are lucky because they have direct access to many typography classics.
Finding many mistakes in Japanese source, and I suspect it is due to the lack of good reference books in typography; however, even in English some books spread incorrect definition of em, in particular, TeX related sources.
References
The Elements of Typographic Style
One of my primary references is Bringhurst's The Elements of Typographic Style, 2.5 ed. p.291:
Em Em In linear measure, a distance equal to the type size, and in square measure, the square of the type size. Thus an em is 12 pt (or a 12 pt square) in 12 pt tpe, and 11 pt (or an 11 pt square) in 11 pt type. Also called mutton.
The Elements of Typographic Style is one of the reliable standards recommended by many. The definition is properly based on type size.
How does it define type size?
p. 298:Type Size See body size.
Body Size In graphic terms, the height of the face of the type, which in letterpress terms is the depth of the body of the block on which each individual letter was cast. In digital type, it is the height of its imaginary equivalent, the rectangle defining the space owned by a given letter, and not the dimension of the letter itself. Body sizes are usually given in points - but European type sizes are often given in Didot points, which are 7% larger than the points used in Britain and North America.
It defines body size based the face of the type, and that is called em. Note that it does not mention set width at all. The reason is the way western types are set. Each type varies in its set width, but by keeping the height of the face constant, one can align them horizontally.
Note that it denies all the mistake patterns.
Designing with type: A Basic Cource in Typography
In Designing with type: A Basic Cource in Typography, 4th ed., James Craig mentions em around p. 22 in the text, but the index has better coverage. p. 166:
Em. Commonly used shortened term for em-quad. See also Em-quad.
Em-quad. In handset type, a metal space that is the square of the type body size; that is, a 10-point em-quad is 10 points wide. The em gets its name from the fact that in early fonts the M was usually cast on a square body.
The text mentions that em quad is used for the indentation at the beginning of the paragraph. This book is not as famous as The Element, but it was picked up from the bookstore because it looked like a textbook that's easy to understand.
w3c: Cascading Style Sheets
Next are online resources. How about w3c as a reliable source. World Wide Web Consortium is an organization that draws up standards on the Internet.
Cascading Style Sheets, level 2 4.3.2 Lengths:
em: the 'font-size' of the relevant font
Cascading Style Sheets, level 2 15.2.1 Font specification properties
Font size
The font size refers to the size of the font from baseline to baseline, when set solid (in CSS terms, this is when the 'font-size' and 'line-height' properties have the same value).
CSS is a standard on specifying the typefaces and layouts of web pages. Among the length unit used in CSS is em. For example, one can specify the beginning of the paragraph indentation as 1 em.
The definition is legitimate. To avoid the concept of imaginary type, it introduces the notion of solid. With no leading in between, the baseline distance will equal to the height of typeface.
Note that em could be used for measuring vertical or horizontal distance, but in the definition of em, there is no mention of set width or the letter M.
TrueType Reference Manual
Let's look at what TrueType's author Apple Computer has to say on em in TrueType Reference Manual.
TrueType Reference Manual ch 2 The Font Engine::
The scaler converts values in the master coordinate system to values in the pixel coordinate system by multiplying them by a scale. This scale is:
pointSize * resolution / (72 points per inch * units_per_em).
This is a little tricky. Glyphs in TrueType font is defined in coordinate system with FUnit, which is a fraction of em. It skips the physical coordinate and it goes directly into pixel coordinate system. Resolution is used to convert from physical coordinate system to pixel coordinate system.
Let's verify by putting values in. Suppose the resolution is 96 dpi (dots per inch), and 1024 FUnit per 1 em.
y [px] := x [FUnit] * pointSize * 96 [px/inch] / (72 [pt/inch] * 1024 [FUnit/em])
Pixels are noted as px; point as pt. Let's calculate the number of pixels in 12 pt.
y [px] = 1024 * 12 * 96 / (72 * 1024)
= 16 [px]
In the resolution of 96 dpi, 16 px is 0.1666 inch, and it is 12 pt, so we can verify that 1 em is 12 pt.
y [px] := x [em] * pointSize * 96 [px/inch] / (72 [pt/inch])
y [inch] := x [em] * pointSize / (72 [pt/inch]) Convert y into inch.
y [pt] := x [em] * pointSize Convert y into point.
The above illustrates that 1 em always matches the length of point size; also, it turns out that the unit of pointSize is [pt / em].
The Complete Manual of Typography
After reading some books and web pages, I decided to get another reliable book to verify my understanding. James Felici's The Complete Manual of Typography was selected. There's a chapter dedicated for this topic, called Units of Typographic Measurement, and em is explained there. p. 24:
The Em
The fundamental relative unit in typography is the em. An em is the same size as the type currently being set, so if you're setting 11-point type, an em equals 11 points. Despite the sound of its name, an em is not the width of an M; in fact, an M is rarely a full em wide (see Figure 2.4).
The Ms in the bottom row (each shown within an em square corresponding to its typeface and point size) illustrate that the width of an em has nothing to do with the width of an M.
Not only does Felici define em as body size, but also it completely negates the set width of the letter M'. In the book, there is a figure illustrating M in three typefaces printed with em square.
Basic "old timers" typesetting practices
I found Jan Roland Eriksson's Basic "old timers" typesetting practices from Luc Devroye's Font Measurements. The explanation on font height and em-quad was very informative. It's long, so I would quote part of it.
The required height of a lead block, that is cast to make room for all possible characters in a font, is traditionally called font height. Normally the height of the block is little bit larger than the characters printing face since the character, cast on top of the block, is slightly tapered to make it easier to get it out of its mould during the casting process.
The font height is in it self such a significant unit of length for a typesetter, that it has been used to define a universal unit of relative length by the name of one em, where the name may stem from the fact that the letter M in the Roman alphabet did in fact have a width that filled the full width of the square based on the height of the type in use.
To meet this document's purpose, I only quoted the part relevant to the definition of em, but Eriksson gives clue to the name em. The first is Capitalis Quadrata, a typeface that completed around 200 BC by the Roman Empire. It consisted only of uppercase letters and it was designed based on the square of body size, and for the letter "C, G, M, O and Q," body size was chosen as their set width (Mistake pattern 1 and 2). However with the invention and adoption of lowercase letters and diacritical marks, em stretched both up and down, but the letter M remained the same size (Mistake pattern 4). Next, metal type was invented and em streched again in order to take the metal block out of the cast (correct definition).
Eriksson also mentions that the printed impression of a letter becomes slighly larger since the paper absorbs some ink.
TeX related
This document is for my better understanding of typography, and I have nothing against TeX, so please don't take this personally. Having said that, TeX and many TeX books and resources use incorrect definitions of em.
There are two problems. First, older implementation of TeX and/or TeXbook seemed to defined em based on the set width of M, and people still misunderstand em. Second, TeX and/or TeXbook changed the definition but it still uses typographically incorrect definition of em.
A Gentle Introduction to TeX: A manual for Self-study
Michael Doob's A Gentle Introduction to TeX: A manual for Self-study is a popular tutorial of TeX. p. 19:
The ex is about the height of a small "x" and the em is a little smaller than the width of a capital "M". TeX book 60
As you can see, it cites TeX book p. 60 as its source. The definition is obviously incorrect.
LaTeX
LaTeX books including the LaTeX author Leslie Lamport's LaTeX: A Document Preparation System defines em as approximate set width of M.
The TeXbook
Donald E. Knuth's The TeXbook is the official manual for TeX. Millennium ed. p. 60:
em is the width of a "quad" in the current font; ex is the "x-height" of the current font.
Each font defines its own em and ex values. In olden days, an "em" was the width of an 'M', but this is no longer true; ems are simply arbitrary units that come with a font, and so are exes.
I do not know when Knuth changed his definition of em from the approximate set width of M to the width of a "quad", but many people didn't get the announcement I suppose. If you have older edition, please let me know what p. 60 says.
The hard cover Millennium edition denies the set width of M, but to my surprise, it defines it as an arbitrary value set by the font designer.
The way Knuth defines quad makes it even confusing.
p. 166:
A quad used to be a square piece of blank type, 1 em wide and 1 em tall - approximately the size of capital M, as explained in Chapter 10. This tradition has not been fully retained: The control sequence \quad in plain TeX is simply an abbreviation for '\hskip 1em\relax', so TeX's quad has width but no height
Apparently, TeX fonts are designed based on body size called "DESIGNSIZE", but 1 em is defined by a value called "QUAD."
According to The TeXbook p. 433 a 10 pt font called cmr10 has 1 em set as 10.00 pt; however, cmbx10 has 1 em set as 11.50 pt. Clearly, this breaks the definition of em as body size. By nature, em is supposed to be typeface independent. But in TeXbook definition, em changes as one change to cmbx10 from cmr10. It may made sense to some people, but he shouldn't have named it em.
In the traditional definition, set cmbx10 and skip 10 em would mean skip 100 pt; however, in TeX's definition skip 10 em means 115 pt.
QuarkXpress related
Quark Knowledge Base #4081
After searching for em on Quark's web site, a Support Database article regarding the definition of em was found.
Definition of Em space, En space, and Flex space:
The Standard Em Space is based on a typographer's em space (point size = em space value). QuarkXPress uses the width of two zeros in a particular font to define the width of an em space.
The default for the Standard Em Space check box in the Typographic Preferences dialog is unchecked. When you select the check box, em spaces will be equivalent to the point size for your text. For instance, 24-point text will have a 24-point Em space.
Although the definition of using the width of two zeros is blatantly wrong, Quark was smart enough to admit the "standard em space" is defined as the "typographer's em space" (point size = em space value), let its users know what the rest of the world thinks em means, and give them the option to use the standard em. It is likely for the backward compatibility with the existing data that they had to uncheck the standard option by default.
