Appearance of \tiny or \scriptsize Fontsize in LaTeX (horizontal stretch)

Question

The fontsize commands for fontsizes smaller than \normalsize stretch the aspect ratio of the letters or stretch the letters itself plus their spacing instead of properly scaling the text in width and height (with respect to \normalsize) - an effect that becomes really extreme for \scriptsize and especially \tiny.

The following minimal example shows the basic problem and a possible solution/workaround to it (to which I need an improved, global turn on / turn off - solution):

 \documentclass[12pt,a4paper,ngerman]{scrbook}
 \usepackage[T1]{fontenc}
 \usepackage{lmodern}
 \usepackage[utf8]{inputenc}
 \usepackage{amsmath,amsfonts,amssymb,amsxtra}
 \usepackage[ngerman]{babel}
 \usepackage{graphicx}

 \newcommand{\tinyb}[1]{\scalebox{0.5}{{\normalsize #1}}}
 %\newcommand{\scriptsizeb}[1]{\scalebox{0.66667}{{\normalsize #1}}}

 \begin{document}
 \begin{itemize}
      \item {\tiny{Tiny tiny Tiny TINY tiny (original \textbackslash tiny)}} \hspace{.2cm} {\tinyb{Tiny tiny Tiny TINY tiny (custom \textbackslash tinyb)}}
      \item {\tinyb{Tiny tiny Tiny TINY tiny (custom \textbackslash tinyb)}}
      \item {\normalsize{Tiny tiny Tiny TINY tiny (original \textbackslash normalsize)}}
      \item {\tiny{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (original \textbackslash tiny)}} \hspace{.2cm} {\tinyb{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (custom \textbackslash tinyb)}}
      \item {\tinyb{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (custom \textbackslash tinyb)}}
      %\item {\scriptsize{Scriptsize SCRIPTSIZE (original \textbackslash scriptsize)}} \hspace{.2cm} {\scriptsizeb{Scriptsize SCRIPTSIZE (custom \textbackslash scriptsizeb)}}
      %\item {\scriptsizeb{Scriptsize SCRIPTSIZE (custom \textbackslash scriptsizeb)}}
 \end{itemize}
 \end{document}

The result will look like this:

You will notice that the original \tiny stretches the textwidth extremly, while the workaround with \tinyb uses the scalebox command from the graphicx-package and scales both - height and width of the text - exactly by 50 percent. The fontheight of both styles (\tiny and \tinyb) are exactly identical. Especially in the equation \tiny looks pretty ugly stretched, which is a big problem in small figure's legends or annotations, where only very few letters fit into the legend, even when using \tiny.

The solution with \tinyb (scalebox trick) isn't sufficient for me because I won't be able to change settings globally. I can only change a certain textpattern to \tinyb locally and things like line breaks etc. won't work. It is not a turn on / turn off solution like \tiny or \normalsize, which is what I want: For example I want to use tikzfigures / pgfplots and change the annotation style of all axis legend entries, ticks and graph annotations to \tinyb with only one command but as \tinyb uses a scalebox (which uses a \mbox) I can only use it in specific command lines and code like

\begin{tikzpicture}
\tinyb
\begin{axis}[...
...
xlabel={frequency (Hz) $U_{\infty}$ $\frac{\alpha}{\beta}$},
ylabel={frequency (Hz) $U_{\infty}$ $\frac{\alpha}{\beta}$},
...
\end{axis}
\end{tikzpicture}

won't work (while the same code with \tiny instead of \tinyb would work and change every annotation, label, ticklabel etc. to \tiny)! So I need to redefine \tiny in a way that it behaves like \tinyb or create a newcommand \tinyc that behaves like \tiny but looks like \tinyb. But I could't find out how to change the streching behaviour for different fontsizes. Basically I want that LaTeX properly scales the text in width and height as it would look for \normalsize - specificly for the \tiny and \scriptsize command because the stretching effect is extreme there... and I need a command for that, which must be defined globally and can be set on and off easily for whole sections.

Does anyone know how to do it?

I guess there must be an easy solution, maybe with some packages that allow changing of letterspacing and/or kerning but I actually don't know the right search term for the problem that the letters seem to be stretched with respect to their width... (neither letterspacing nor kerning seem to fit to the problem)

Answer 1

You should look up what "optical sizing" of fonts entails. (Computer Modern is an example of a font family with optically sized letters at various font sizes.) Letters that are sized optically for \tiny are not ordinary letters reduced linearly by 50%, and they are not simply horizontally stretched either. Instead, they are individually re-drawn, with proportionately thicker strokes, and they are spaced more loosely, all so that they remain legible even though they're only half as tall as \normalsize letters. Conversely, optically-sized \huge letters are deliberately drawn with thinner strokes, and they are spaced more tightly, all so that they don't look too "heavy" even though the height of \huge letters is more than twice that of \normalsize.

The following table shows various words typeset at their "native" 10pt size on the left and linearly enlarged or reduced from having been typeset at \tiny, \scriptsize, \footnotesize, etc through \huge sizes. Note that the letters in the resized words look progressively thinner and are spaced more tightly as you move down the right-hand column of the table.

\documentclass{article}
\usepackage{graphicx,lmodern}
\begin{document}
\begin{tabular}{rl}
basic 10pt    & scaled \\
\hline
five    & \scalebox{2}{\tiny five}\\
seven   & \scalebox{1.429}{\scriptsize seven}\\
eight   & \scalebox{1.25}{\footnotesize eight}\\
twelve  & \scalebox{0.833}{\large twelve}\\
fourteen& \scalebox{0.694}{\Large fourteen}\\
twenty  & \scalebox{0.482}{\huge twenty}\\
\end{tabular}
\end{document} 

---

Addendum: Another way to think about what optical scaling does is to superimpose words natively set at \normalsize with the same words, linearly scaled from their optically sized \tiny, \scriptsize, etc through \huge versions. In the following screenshot, the native-\normalsize letters are rendered in black and the rescaled optically sized words are rendered in red. Observe that optical sizing entails (a) changing the widths of the strokes used for various glyphs as well as (b) changing the kerning between letters in word. It's far more sophisticated than performing a horizontal stretch.

\documentclass{article}
\usepackage{lmodern,graphicx,xcolor}
\begin{document}
\obeylines
five\kern-15.6pt\textcolor{red}{\scalebox{2}{\tiny five}}
seven\kern-23.45pt\textcolor{red}{\scalebox{1.429}{\scriptsize seven}}
eight\kern-21.4pt\textcolor{red}{\scalebox{1.25}{\footnotesize eight}}
twelve\kern-27.18pt\textcolor{red}{\scalebox{0.833}{\large twelve}}
fourteen\kern-35.8pt\textcolor{red}{\scalebox{0.694}{\Large fourteen}}
twenty\kern-29.05pt\textcolor{red}{\scalebox{0.482}{\huge twenty}}
\end{document}

Answer 2

As has been explained in comments and other answers, it is not latex that is scaling the fonts, it is just choosing the fonts designed for that size.

If you do not like the font choice you can change it here I specify that the 10pt font is to be used scaled for all sizes (I just did roman and math italic, you may need to do more) In general such scaling is considered to make a poorer less legible result than using optically scaled fonts at their design size, but all these things are a subjective choice.

\documentclass[12pt,a4paper,ngerman]{scrbook}
 \usepackage[T1]{fontenc}
 \usepackage{lmodern}
 \usepackage[utf8]{inputenc}
 \usepackage{amsmath,amsfonts,amssymb,amsxtra}
 \usepackage[ngerman]{babel}
 \usepackage{graphicx}

 \newcommand{\tinyb}[1]{\scalebox{0.5}{{\normalsize #1}}}
 %\newcommand{\scriptsizeb}[1]{\scalebox{0.66667}{{\normalsize #1}}}
\DeclareFontFamily{T1}{lmr}{}
\DeclareFontShape{T1}{lmr}{m}{n}%
     {<->    ec-lmr10
      }{}

\DeclareFontFamily{OML}{lmm}{\skewchar\font127 }
\DeclareFontShape{OML}{lmm}{m}{it}%
     {<->  lmmi10
      }{}

 \begin{document}
 \begin{itemize}
      \item {\tiny Tiny tiny Tiny TINY tiny (original \textbackslash tiny)} \hspace{.2cm} {\tinyb{Tiny tiny Tiny TINY tiny (custom \textbackslash tinyb)}}
      \item {\tinyb{Tiny tiny Tiny TINY tiny (custom \textbackslash tinyb)}}
      \item {\normalsize Tiny tiny Tiny TINY tiny (original \textbackslash normalsize)}
      \item {\tiny{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (original \textbackslash tiny)}} \hspace{.2cm} {\tinyb{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (custom \textbackslash tinyb)}}
      \item {\tinyb{$U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ (custom \textbackslash tinyb)}}
      %\item {\scriptsizeScriptsize SCRIPTSIZE (original \textbackslash scriptsize)} \hspace{.2cm} {\scriptsizeb{Scriptsize SCRIPTSIZE (custom \textbackslash scriptsizeb)}}
      %\item {\scriptsizeb{Scriptsize SCRIPTSIZE (custom \textbackslash scriptsizeb)}}
 \end{itemize}
 \end{document}

Answer 3

Perhaps something like this, with the use of \DeclareFontShape, to tell LaTeX to always use the the 10pt font to construct everything else.

EDITED to employ the otherwise unused "bold-scshape" as the placeholder for the fixed-width version of the font (which is invoked in the tinyb environment).

RE-EDITED to make math font of fixed shape in tinyb environment. Originally, it substituted the fixed shape operators in non-tinyb math, as well. THis was remedied by declaring a new math version to be invoked in the tinyb environment only.

Shown for LMODERN (a scalable T1 encoded font)

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{lmodern}
%%% TEXT FONT FIX
\rmfamily
\DeclareFontShape{T1}{lmr}{bx}{sc}{<-> cmr10}{}% USE BOLD SCSHAPE NOT OTHERWISE DEFINED
%%% MATH FONT FIX
\DeclareFontFamily{OML}{zlmm}{}
\DeclareFontShape{OML}{zlmm}{m}{it}{<-> lmmi10}{}
\DeclareFontShape{OML}{zlmm}{b}{it}{<->ssub * zlmm/m/it}{}
\DeclareFontShape{OML}{zlmm}{bx}{it}{<->ssub * zlmm/m/it}{}

\DeclareMathVersion{Tinyb}
\SetSymbolFont{operators}{Tinyb}{T1}{lmr}{bx}{sc}
\SetSymbolFont{letters}{Tinyb}{OML}{zlmm}{m}{it}
%%%
\newenvironment{tinyb}{\bgroup\tiny\bfseries\scshape\mathversion{Tinyb}}{\egroup} % edit: now with \tiny included
\begin{document}
\newcommand\mytext[1]{\normalsize This is a test #1\par
  \small \scalebox{1.11}{This is a test} This is a test \par
  \footnotesize \scalebox{1.25}{This is a test} This is a test \par
  \scriptsize \scalebox{1.425}{This is a test} This is a test \par
  \tiny \scalebox{2}{This is a test} This is a test\par\normalsize
}
\newcommand\mymath{\normalsize$y = mx + b - 3f^2 + \sin (\omega x - \tau)$\par
  \tiny$y = mx + b - 3f^2 + \sin (\omega x - \tau)$\par\normalsize}

\mytext{of the normal}

\begin{tinyb}
\mytext{of the fixed scale}
\end{tinyb}

\mymath

\begin{tinyb}
\mymath
\end{tinyb}
\end{document}

The OP seems very much to not want to use a tinyb environment, but rather a \tinyb macro. Here is a possibility that suffers one shortcoming...and that is any font size changing command will place the font in \mdseries\upshape mode, as well.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{lmodern}
%%% TEXT FONT FIX
\rmfamily
\DeclareFontShape{T1}{lmr}{bx}{sc}{<-> cmr10}{}% USE BOLD SCSHAPE NOT OTHERWISE DEFINED
%%% MATH FONT FIX
\DeclareFontFamily{OML}{zlmm}{}
\DeclareFontShape{OML}{zlmm}{m}{it}{<-> lmmi10}{}
\DeclareFontShape{OML}{zlmm}{b}{it}{<->ssub * zlmm/m/it}{}
\DeclareFontShape{OML}{zlmm}{bx}{it}{<->ssub * zlmm/m/it}{}

\DeclareMathVersion{Tinyb}
\SetSymbolFont{operators}{Tinyb}{T1}{lmr}{bx}{sc}
\SetSymbolFont{letters}{Tinyb}{OML}{zlmm}{m}{it}
%%%
\def\invokemode{\bfseries\scshape\mathversion{Tinyb}}
\def\restoremode{\mdseries\upshape\mathversion{normal}}
\newcommand\adapt[1]{%
  \expandafter\let\csname sv#1\expandafter\endcsname\csname#1\endcsname%
  \expandafter\def\csname#1\endcsname{\restoremode\csname sv#1\endcsname}
  \expandafter\def\csname#1b\endcsname{\invokemode\csname sv#1\endcsname}
}
\adapt{tiny}\adapt{scriptsize}\adapt{footnotesize}\adapt{small}\adapt{normalsize}
\adapt{large}\adapt{Large}\adapt{LARGE}\adapt{huge}\adapt{Huge}
\begin{document}
 \tiny Hello World \par 
 \tinyb Hello World \par 
 \tiny Hello World \par 
 \tiny $a^{2} + b^{2} = c^{2}$ \par 
 \tinyb $a^{2} + b^{2} = c^{2}$ \par 
 \tiny $a^{2} + b^{2} = c^{2}$ 
\end{document}

Answer 4

Edited to add: If zooming by the user is an allowed solution, an extreme example is at How to get an even smaller font?. Just make the scale factor an inverse of the zoom (and use a scalable font, of course).

Or even better: An experiment:

Some ordinary text, actual size:

Zooming in to the notes:

And then the notes to the notes (this is x19462% magnification):

Conclusion: TeX is brilliant!

This method uses nested minipages, where the linewidth adjusts to the outer minipage's width. But the baselineskip doesn't auto-adjust (for obvious reasons: original design), so is adjusted manually.

Nesting is unlimited, I presume (well, the wavelength of visible light is a constraint). Next potential step is a TikZ-path version following the inside contours of a letter.

MWE:

\documentclass{article}
\usepackage{fontspec}
\usepackage{xcolor}
\usepackage{lipsum}
\setmainfont{Noto Serif}
\newfontface\ftsmall[Scale=0.25,Colour=blue]{Noto Serif}
\newfontface\ftvsmall[Scale=0.02,Colour=red]{Noto Serif}
\begin{document}
\begin{enumerate}
\item Here is some text, with some notes $\to$
\begin{minipage}{0.1\linewidth}
x\baselineskip2pt
{\ftsmall{\tiny \lipsum[2] And here is another InfoDot:}}
\begin{minipage}{0.1\linewidth}
{\ftsmall{\tiny y}}\par\baselineskip0.2pt
{\ftvsmall{\tiny \lipsum[3] And that is the end of the demonstration.}} 
\end{minipage}
\end{minipage}
\end{enumerate}
\end{document}

=== Original post:

For text, generally sans-serif seems easier to read at smaller sizes than serif. Verdana was designed for small size readability. Scaling the font does not add any value in this context.

For maths, the experimental mathspec package, using fontspec in the background, might be worth a look. It has too many options and switches for a quick mastery in one post though, so would repay careful study. An alternative is unicode-math, which also uses fontspec but in a different way. The nub of the question seems to be about scalable fonts.

Here is mathspec, with a random font and default settings:

An abundance of fonts to choose from, in combinations of various subsets, does not make the task easier.

MWE:

\documentclass{article}
%\usepackage{fontspec}
\usepackage[MnSymbol]{mathspec}
\setmainfont{Noto Serif}
\setmathsfont(Digits,Latin){Noto Serif}%TeX Gyre Termes Math}
\setmathsfont(Greek){FreeSerif}
\setmathrm{TeX Gyre Bonum Math}%Symbola}%Cambria Math}%TeX Gyre Schola Math}
%STIX Math}%Quivira}%Noto Sans Symbols}%Libertinus Math}%Hayashi-Serif}%FreeSerif}%DejaVu Math}%Arial Unicode MS}%Minion Pro}%Cambria Math}%GFS Porson}
\usepackage{xcolor}
\newfontface\ftsmall[Scale=0.5,Colour=blue]{Noto Serif}
\newfontface\ftverdana{Verdana}
\newfontface\ftvsmall[Scale=0.5,Colour=blue]{Verdana}
\begin{document}
Noto Serif
\begin{tabular}{rl}
\tiny abc wqerty & \ftsmall\tiny abc wqerty \\
\scriptsize  abc wqerty &  \ftsmall\scriptsize abc wqerty \\
\footnotesize  abc wqerty & \ftsmall\footnotesize abc wqerty \\
\small  abc wqerty & \ftsmall\small abc wqerty \\
\normalsize  abc wqerty & \ftsmall\normalsize abc wqerty \\
\large abc wqerty & \ftsmall\large abc wqerty \\
\Large abc wqerty & \ftsmall\Large abc wqerty \\
\LARGE abc wqerty & \ftsmall\LARGE abc wqerty \\
\huge abc wqerty & \ftsmall\huge abc wqerty \\
\Huge abc wqerty & \ftsmall\Huge abc wqerty \\
\end{tabular}

\ftverdana
Verdana
\begin{tabular}{rl}
\tiny abc wqerty & \ftvsmall\tiny abc wqerty \\
\scriptsize  abc wqerty &  \ftvsmall\scriptsize abc wqerty \\
\footnotesize  abc wqerty & \ftvsmall\footnotesize abc wqerty \\
\small  abc wqerty & \ftvsmall\small abc wqerty \\
\normalsize  abc wqerty & \ftvsmall\normalsize abc wqerty \\
\large abc wqerty & \ftvsmall\large abc wqerty \\
\Large abc wqerty & \ftvsmall\Large abc wqerty \\
\LARGE abc wqerty & \ftvsmall\LARGE abc wqerty \\
\huge abc wqerty & \ftvsmall\huge abc wqerty \\
\Huge abc wqerty & \ftvsmall\Huge abc wqerty \\
\end{tabular}

\newpage
\normalfont
Maths
\begin{tabular}{r}
\tiny $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\scriptsize $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\footnotesize  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\small   $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\normalsize  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\large  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\Large  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\LARGE  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\huge  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\Huge  $U_{\infty}=f\cdot a\cdot \frac{\alpha}{\beta}$ \\
\end{tabular}

\begin{tabular}{r}
\tiny $a^{2} + b^{2} = c^{2}$ \\
\scriptsize $a^{2} + b^{2} = c^{2}$ \\
\footnotesize  $a^{2} + b^{2} = c^{2}$ \\
\small   $a^{2} + b^{2} = c^{2}$ \\
\normalsize  $a^{2} + b^{2} = c^{2}$ \\
\large  $a^{2} + b^{2} = c^{2}$ \\
\Large  $a^{2} + b^{2} = c^{2}$ \\
\LARGE  $a^{2} + b^{2} = c^{2}$ \\
\huge  $a^{2} + b^{2} = c^{2}$ \\
\Huge  $a^{2} + b^{2} = c^{2}$ \\
\end{tabular}




\end{document}