<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Bruno,<div class=""><br class=""></div><div class="">Thanks for providing all this information. The LaTeX Companion (2nd Ed) is a reference I consult frequently. But I have to admit that I just skimmed the NFSS section. I’ll go back to it.</div><div class=""><br class=""></div><div class="">I ran some tests of scale-factor/font-size specifications and thought you and others may be interested in the results, which I summarize below. I typeset a variety of text and math expressions (mostly math) and printed the output to avoid possible screen-induced effects. Then I evaluated the appearance of the printed output. </div><div class=""><br class=""></div><div class="">I used the AMSART document class and toggled between 10pt and 12pt font-size option and Scale=.92 and 1.0. Here are the results:</div><div class=""><br class=""></div><div class="">1. 10pt, <span style="color: rgb(78, 75, 35);" class="">\defaultfontfeatures{Scale=.92}:</span><font color="#000000" class=""> The printed output looks too small. </font></div><div class=""><font color="#000000" class=""><br class=""></font></div><div class="">2. 10pt, <span style="color: rgb(78, 75, 35);" class="">\defaultfontfeatures{Scale=1.0}:</span><font color="#000000" class=""> </font><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class="">The printed output is noticeably larger and more readable. </span></div><div class=""><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class=""><br class=""></span></div><div class=""><div class="">3. 12pt, <span style="color: rgb(78, 75, 35);" class="">\defaultfontfeatures{Scale=.92}:</span><font color="#000000" class=""> The printed output looks just right and easy to read.</font></div><div class=""><font color="#000000" class=""><br class=""></font></div><div class="">4. 12pt, <span style="color: rgb(78, 75, 35);" class="">\defaultfontfeatures{Scale=1.0}:</span><font color="#000000" class=""> </font><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class="">The printed output looks good and is very easy to read but is too big.</span></div></div><div class=""><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class=""><br class=""></span></div><div class=""><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class="">So, in my estimation, 12pt/scale=0.92 is the sweet point.</span></div><div class=""><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class=""><br class=""></span></div><div class=""><font color="#000000" class=""><span style="caret-color: rgb(0, 0, 0);" class="">I’ll continue delving into font technicalities. Thanks for pointing me in the right direction.</span></font></div><div class=""><font color="#000000" class=""><span style="caret-color: rgb(0, 0, 0);" class=""><br class=""></span></font></div><div class=""><div class=""><font color="#000000" class=""><span style="caret-color: rgb(0, 0, 0);" class="">Best wishes,</span></font></div><div class=""><font color="#000000" class=""><span style="caret-color: rgb(0, 0, 0);" class=""><br class=""></span></font></div><div class=""><font color="#000000" class=""><span style="caret-color: rgb(0, 0, 0);" class="">Raúl </span></font></div></div><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On May 4, 2022, at 11:40 AM, Bruno Voisin <<a href="mailto:bvoisin@icloud.com" class="">bvoisin@icloud.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class=""><blockquote type="cite" class="">On 4 May 2022, at 16:23, Raúl Martínez <<a href="mailto:rm.tech@mac.com" class="">rm.tech@mac.com</a>> wrote:<br class=""><br class="">But there’s an issue still open that I thought about after posting my query. The issue is that the document class specifies the font size, either as an option or by default. It’s not clear to me how font scaling plays with the font-size specification by the document class.<br class=""></blockquote><br class="">The basic idea is actually quite simple:<br class=""><br class="">- On one hand there is the document class (.cls or .clo), which defines the standard font sizes such as \normalsize, \small, \large, etc. This is where the [10pt], [11pt] and [12pt] options come into play. This is not related to any specific font, and there is no scaling involved.<br class=""><br class="">- On the other hand there are the font definition files (.fd), which associate these standard sizes with specific fonts in specific sizes, scaled or not.<br class=""><br class="">The implementation, however, is all but simple.<br class=""><br class="">Let's assume you write say (from lucida-sample.tex):<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>\documentclass[11pt]{article}<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\usepackage[T1]{fontenc}<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>\usepackage{textcomp}<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\usepackage[altbullet]{lucidabr}<br class=""><br class="">First comes the "class" part.<br class=""><br class="">The [11pt] option calls<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">        </span>/usr/local/texlive/2022/texmf-dist/tex/latex/base/size11.clo<br class=""><br class="">which says<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\renewcommand\normalsize{%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>   \@setfontsize\normalsize\@xipt{13.6}%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>[...]<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\DeclareRobustCommand\small{%<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>   \@setfontsize\small\@xpt\@xiipt<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>[...]<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\DeclareRobustCommand\footnotesize{%<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>   \@setfontsize\footnotesize\@ixpt{11}%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>[...]<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\DeclareRobustCommand\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}<br class=""><span class="Apple-tab-span" style="white-space:pre">        </span>\DeclareRobustCommand\tiny{\@setfontsize\tiny\@vipt\@viipt}<br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\DeclareRobustCommand\large{\@setfontsize\large\@xiipt{14}}<br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\DeclareRobustCommand\Large{\@setfontsize\Large\@xivpt{18}}<br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\DeclareRobustCommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>\DeclareRobustCommand\huge{\@setfontsize\huge\@xxpt{25}}<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>\DeclareRobustCommand\Huge{\@setfontsize\Huge\@xxvpt{30}}<br class=""><br class="">Given<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>/usr/local/texlive/2022/texmf-dist/tex/latex/base/latex.ltx<br class=""><br class="">has defined<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\def\@vpt{5}<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>\def\@vipt{6}<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\def\@viipt{7}<br class=""><span class="Apple-tab-span" style="white-space:pre"> </span>\def\@viiipt{8}<br class=""><span class="Apple-tab-span" style="white-space:pre">        </span>\def\@ixpt{9}<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\def\@xpt{10}<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\def\@xipt{10.95}<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\def\@xiipt{12}<br class=""><span class="Apple-tab-span" style="white-space:pre">        </span>\def\@xivpt{14.4}<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\def\@xviipt{17.28}<br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\def\@xxpt{20.74}<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\def\@xxvpt{24.88}<br class=""><br class="">this means<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\normalize<span class="Apple-tab-span" style="white-space:pre">  </span>font size 10.95 pt<span class="Apple-tab-span" style="white-space:pre">  </span>line spacing 13.6 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>\small<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 10 pt<span class="Apple-tab-span" style="white-space:pre">     </span><span class="Apple-tab-span" style="white-space:pre">    </span>line spacing 12 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\footnotesize<span class="Apple-tab-span" style="white-space:pre">       </span>font size 9 pt<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>line spacing 11 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\scriptize<span class="Apple-tab-span" style="white-space:pre">  </span>font size 8 pt<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>line spacing 9.5 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>\tiny<span class="Apple-tab-span" style="white-space:pre">       </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 6 pt<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>line spacing 7 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\large<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 12 pt<span class="Apple-tab-span" style="white-space:pre">     </span><span class="Apple-tab-span" style="white-space:pre">    </span>line spacing 14 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\Large<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 14.4 pt<span class="Apple-tab-span" style="white-space:pre">   </span>line spacing 18 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\LARGE<span class="Apple-tab-span" style="white-space:pre">      </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 17.28 pt<span class="Apple-tab-span" style="white-space:pre">  </span>line spacing 22 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\huge<span class="Apple-tab-span" style="white-space:pre">       </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 20.74 pt<span class="Apple-tab-span" style="white-space:pre">  </span>line spacing 25 pt<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>\Huge<span class="Apple-tab-span" style="white-space:pre">       </span><span class="Apple-tab-span" style="white-space:pre">    </span>font size 24.88 pt<span class="Apple-tab-span" style="white-space:pre">  </span>line spacing 30 pt<br class=""><br class="">(the odd non-entire font sizes come from the early days of TeX, when fonts were bitmaps and sizes above 10 pt were created in advance at 1.2-multiples of 10: 10 * sqrt(1.2), 1.2, 1.2^2, 1.2^3, etc.).<br class=""><br class="">Now comes the really tricky part: the "font" stuff. <br class=""><br class="">Given \usepackage[T1]{fontenc} makes T1 encoding the default, and given<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>/usr/local/texlive/texmf-local/tex/latex/lucidabr/lucidabr.sty<br class=""><br class="">says<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\renewcommand{\rmdefault}{hlh}<br class=""><br class="">this calls<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">        </span>/usr/local/texlive/texmf-local/tex/latex/lucida/t1hlh.fd<br class=""><br class="">which says<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>\DeclareLucidaFontShape{T1}{hlh}{m}{n}{ hlhr8t }{}<br class=""><br class="">The default in lucidabr.sty is [lucidascale], namely<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>\DeclareOption{lucidascale}{%<br class=""><span class="Apple-tab-span" style="white-space:pre">  </span> \def\DeclareLucidaFontShape#1#2#3#4#5#6{%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span> \DeclareFontShape{#1}{#2}{#3}{#4}{%<br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>  <-5.5>s*[1.04]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre"> </span>  <5.5-6.5>s*[1.02]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>  <6.5-7.5>s*[.99]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>  <7.5-8.5>s*[.97]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>  <8.5-9.5>s*[.96]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>  <9.5-10.5>s*[.95]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>  <10.5-11.5>s*[.94]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>  <11.5-13>s*[.93]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>  <13-15.5>s*[.92]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>  <15.5-18.5>s*[.91]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>  <18.5-22.5>s*[.9]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre">      </span>  <22.5->s*[.89]#5%<br class=""><span class="Apple-tab-span" style="white-space:pre"> </span>  }{#6}}}<br class=""><br class="">Accordingly the above means<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>for font sizes below 5.5, use the font metrics hlhr8t.tfm scaled by 1.04<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>for font sizes between 5.5 and 6.5, use the font metrics hlhr8t.tfm scaled by 1.02<br class=""><span class="Apple-tab-span" style="white-space:pre">     </span>etc.<br class=""><br class="">And finally the even trickier part:<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre"> </span>/usr/local/texlive/texmf-local/fonts/tfm/bh/lucida/hlhb8t.tfm<br class=""><br class="">is a virtual font metrics, which<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>/usr/local/texlive/texmf-local/fonts/vf/bh/lucida/hlhr8t.vf<br class=""><br class="">defines in terms of the actual metrics<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>/usr/local/texlive/texmf-local/fonts/tfm/bh/lucida/hlhr8r.tfm<br class=""><br class="">Then<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>/usr/local/texlive/texmf-local/fonts/map/dvips/lucida/lucida.map<br class=""><br class="">writes<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>hlhr8r LucidaBright " TeXBase1Encoding ReEncodeFont " <8r.enc <lbr.pfb<br class=""><br class="">telling that the metrics hlhr8r.tfm (i) corresponds to the Type 1 file<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">    </span>/usr/local/texlive/texmf-local/fonts/type1/bh/lucida/lbr.pfb<br class=""><br class="">containing the PostScript font named LucidaBright, and (ii) reencodes it to the TeXBase1Encoding defined in<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre"> </span>/usr/local/texlive/2022/texmf-dist/fonts/enc/dvips/base/8r.enc<br class=""><br class="">Such is the joy of Type 1 fonts in classical (La)TeX!<br class=""><br class="">Fortunately there are now OpenType fonts and XeTeX and LuaTeX, which together with the immensely convenient and powerful fontspec and unicode-math packages make things much much much easier.<br class=""><br class="">The above is much better explained in the LaTeX Companion, by Frank Mittelbach and others. Frank, together with Rainer Schöpf, introduced the above font selection design, originally known as NFSS (New Font Selection Scheme), in 1989. This led to the replacement of the original version of LaTeX, 2.09, by LaTeX 2ε in 1994.<br class=""><br class="">The LaTeX Companion is currently in its second edition, which is an invaluable resource for all things LaTeX. See<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">    </span><a href="https://www.latex-project.org/help/books/" class="">https://www.latex-project.org/help/books/</a><br class=""><br class="">Franck has been working for some time on a 3rd edition, which is scheduled for release next year. Don't believe the sites that allow pre-order already or give a release date, like<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">   </span>https://www.lehmanns.de/shop/mathematik-informatik/38861146-9780134658940-the-latex-companion-3e<br class=""><span class="Apple-tab-span" style="white-space:pre">       </span>https://www.pearson.com/store/p/latex-companion-the-tools-and-techniques-for-computing-typesetting/P100000261198/9780134658940<br class=""><br class="">The second link, in particular, announces a release on May 5th, 2023, but that shouldn't be trusted. See<br class=""><br class=""><span class="Apple-tab-span" style="white-space:pre">  </span>https://tex.stackexchange.com/questions/612573/the-latex-companion-3rd-edition<br class=""><br class="">Bruno<br class=""><br class=""></div></div></blockquote></div><br class=""></div></body></html>