# What are the fontdimen s13,s14,s15,s16,s17 exactly?

What do different \fontdimen<num> mean” lists but does not mention how these three font dimensions are used. I could not find this information anywhere. All I could figure out was that changing s14 affects the usual superscript position, but could not find out how s13 and s15 were used. Even “Redefine the default depth of superscript and subscript document-wide” does not bother to change s15. So what are they really?

Edit: I've provided my own rough answer after seeing cfr's examples and fiddling with many more.

• See The TeXbook, Appendix G, page 447, Summary of parameter usage. Also, rule 18c on page 445. – Gonzalo Medina Jul 22 '15 at 17:52
• @GonzaloMedina: And where can I find that? Is it available online? If not, do you know the answer to the question? – user21820 Jul 22 '15 at 17:56
• No, the source code is available in CTAN but compilation is forbidden. You can buy it. I provided the reference, but I'd rather let a TeX font expert to answer this. – Gonzalo Medina Jul 22 '15 at 17:59
• They are all to do with the positioning of superscripts. if we are talking about sigma 13-15 (sup 1-3). Which one is used depends on the current style used for typesetting. (I think one is used in display, one is used for scriptscript, one is used for other cases. But it is a while since I read this last.) – cfr Jul 22 '15 at 22:25
• @Werner Do you think that is right? – cfr Jul 22 '15 at 22:58

Okay so here's my own answer, which I think is good enough for all those people like me who just want a rough guide as to what the numbers mean.

\textfont2 = normal math font

\scriptfont2 = script math font

\scriptscriptfont2 = script-script math font

\fontdimen13 = display-style superscript height

\fontdimen14 = text-style non-fraction superscript height

\fontdimen15 = text-style fraction numerator/denominator superscript height

\fontdimen16 = subscript normal depth

\fontdimen17 = subscript changed depth if superscript is too close

script math = superscript/subscript/tfrac/overset/... at first level (text-style by default)

script-script math = script math from second level onwards

display-style = displayed equations or when \displaystyle is used in the current group

text-style = inline equations or when \textstyle is used in the current group

Don't ask me why s13,s14,s15 are so different from s16,s17. I expected corresponding parameters for superscripts and subscripts, but obviously the designer didn't think so.

Maybe an illustration would help...

\documentclass{article}
\newdimen\savedimen
\begin{document}
Control
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\hrule
\verb|\fontdimen13| $\sigma_{13}$
\savedimen=\fontdimen13\textfont2
\fontdimen13\textfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen13\textfont2=\savedimen
\savedimen=\fontdimen13\scriptfont2
\fontdimen13\scriptfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen13\scriptfont2=\savedimen
\hrule
\verb|\fontdimen14| $\sigma_{14}$
\savedimen=\fontdimen14\scriptfont2
\fontdimen14\scriptfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen14\scriptfont2=\savedimen
\savedimen=\fontdimen14\scriptscriptfont2
\fontdimen14\scriptscriptfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen14\scriptscriptfont2=\savedimen
\hrule
\verb|\fontdimen15| $\sigma_{15}$
\savedimen=\fontdimen15\textfont2
\fontdimen15\textfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen15\textfont2=\savedimen
\savedimen=\fontdimen15\scriptfont2
\fontdimen15\scriptfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\fontdimen15\scriptfont2=\savedimen
\savedimen=\fontdimen15\scriptscriptfont2
\fontdimen15\scriptscriptfont2=25pt
$x^{x^{x^{x^x}}} \frac{1}{x^{x^{x^x}}}$
\end{document}