In typographical terms, the axis of a letter refers to the axis of the stroke of the tool used to create the letter. If a letter has thick and thin strokes, the axis can be found by connecting the midpoints of the thin strokes and connecting them. A letter may have multiple axes as well if multiple tools (uncommon) or angles were used with the tool. A tool could consist of anything that can mark, usually a broadnib pen, brush, pencil, etc. Usually a pen or brush of some kind will be employed but, depending on the effect desired by the designer, other tools are possible.
Since type styles fall into general classes with particular properties, there are different names for the commonly used axes. For example, a Humanist axis generally runs from upper left to lower right while a Rational axis usually runs completely vertical. Some faces completely lack an axis.
The axis is sometimes confused with the slope of a letter which is defined as the angle of inclination of the stems and extenders. Italics are often sloped in a direction opposite to their axis. This might not make a lot of sense in technical terms so,
How about some examples?
..f""7TMN, .JTMN,
.MF ?MN, .@` MMr
.M# dMN. .d# JMF
JMN .MM\ JMt JM$
,MM| .MM` MM| .MD
?MM, .MM' JMb .d=
?YMa..d9^ TMNsY^
Bembo Bembo Italic
.J#"""NJ. .gT""TNJ.
.MMF .MMb .MM^ JMM,
.MMMr MMMb dMMF JMMN
.MMMr MMMM JMMM` dMM#
.MMMr MMMF dMM# .MMM^
,MMb .MM@ .MMN .MM#!
?Wm...M"! TMm...M"!
Bodoni Bodoni Italic
..
..+gNNgJ. .JMMMMMMMNJ
.MMM""77TWMMm. .MM9^ ?WMM,
.MMD` ?MMe .MM3 ,MM,
.MM$ .MMr .MM! dMF
JM# JM# MM% dMF
JM# JM# .MM. .MM`
.MM, MMF MMp .MM^
JMM, .MMF ,MMa. .MMD
.TMMa......MM#^ TMMNag&gMMM"`
?"MMMMMY"` .7""""!
Avant Garde Avant Garde Oblique
Here I've rendered the lowercase "o" of three different typefamilies into ASCII, each from different time periods and styles. In each case, I've supplied an italic as well as a roman so as to show the difference between slope and axis. Let's see each one in detail:
Bembo - This is a Renaissance typeface ca. 15th century Italy. Like most faces of its time, it was designed using a broadnib pen, essentially the same as the standard calligraphy pen (think of a metal fountain pen that comes to a short line instead of a point). If you consider an imaginary line running between the thinnest points, you'll see the line runs from approximately NNW to SSE. This shows that the axis is a right-handed Humanist one since it's the same axis a right-handed person would get if he wrote with such a pen.
Notice that the thin points are essentially the same in the italic even though the shape clearly leans to the right. This demonstrates the difference between the axis, inherent to the tool and angle of the designer's hand, versus the slope which is subject to the shape the designer writes.
Bodoni - This was based on typefaces of the 1780s and is representative of Romantic faces. Romantic and Neo-Classical faces (a contemporary to Romantic) are based on the a pointed quill pen. In the case of these figures, the designer usually drew instead of wrote the figure. This was intentionally done as the prevaling art movement of the time held rigorous consistancy and rationalism as its chief tenents. As a result, a the vertical, Rationalist axis was employed. This axis is considered to be no-handed since it isn't an axis one can comfortably maintain while writing.
The italic also shows a essentially a vertical axis as well but, in this case, seems to lean very slightly in the direction with the slope. This may be a result of making an italic closer to simply a sloped roman which would modify the axis via the sloping/sheering transformation.
Avant Garde - Representative of the Geometric Modernist faces of the 1920s, Avant Garde was created not with a pen but with a ruler and compass. Geometric Modernism put purity of form over reflection of humanity as its goal and therefore believed in geometric precision. Since a compass was used to make a perfectly circular shape, no axis exists because the human hand was completely uninvolved in the creation.
In the case of the oblique, there is still no axis. The only thing visible is slope which almost causes the appearance of one due to the distorted form; the thickness of stroke is still the same all around.
In closing, here is a paid, public service announcement from a fellow noder:
"This business about grotesque 19th-C faces, this might be related to the fact that they went completely mad and designed this shitty New Face crap and lost any sense of... well, you know… It was a horrifying massacre around 1804. (I really do think New Face was an intellectual crime of the millennium, like breaking stained glass windows.)"
In short, that means earlier, Renaissance faces with their Humanist axis are generally more appealing than the Neo-Classical / Romantic faces. I agree with this sentiment but others may not. Oddly enough, that may partly be a matter of nationality and will be found in my eventual writeup on serif fonts.
Remember to use your text figures, kids!