Problem with scale of imported glyphs

Question

Traying to obtain the Times 4-Line Mathematics used in old math books of Springer (and many other scientific textbooks) I downloaded the mtpro2 lite package. However, this package doesn't include a varg option, like newtxmath, as far as I know.

So, following Egreg's answers and, I have imported the glyphs varg, varv and varw to my document.

The problem is that it seems they are quite smaller than the mtpro2 fonts:

The following image corresponds to the Springer's book of Morris W Hirsch Differential Topology:

Certaily, the glyph looks different, but the main problem I see is that the \varg and especially \varv seem quite smaller; in my opinion the $x$ is quite taller.

Do you know a way to correct that? I thought in using the package newtxmath instead of mtpro2 and import the z glyph (with the upright base). The problem is that I would have to change also the italic z in normal text.

Here I attach the mwe:

\documentclass{article}
\usepackage[scaled=0.92]{helvet}    % set Helvetica as the sans-serif font
\renewcommand{\rmdefault}{ptm}      % set Times as the default text font
\usepackage[lite,subscriptcorrection,slantedGreek,nofontinfo]{mtpro2}

%var letters
\DeclareFontFamily{U}{ntxmia}{\skewchar\font=127 }
\DeclareFontShape{U}{ntxmia}{m}{it}{
  <-> ntxmia
}{}
\DeclareFontShape{U}{ntxmia}{b}{it}{
  <-> txbmia
}{}
\DeclareSymbolFont{ntxmia}{U}{ntxmia}{m}{it}
\SetSymbolFont{ntxmia}{bold}{U}{ntxmia}{m}{it}
\DeclareMathSymbol{\varg}{\mathord}{ntxmia}{49}
\DeclareMathSymbol{\varv}{\mathord}{ntxmia}{51}
\DeclareMathSymbol{\varw}{\mathord}{ntxmia}{52}
\AtBeginDocument{\mathcode`g=\varg}
\AtBeginDocument{\mathcode`v=\varv}
\AtBeginDocument{\mathcode`w=\varw}


\begin{document}

\[
gxv \qquad \{(x,g(x)):x\in U\} \qquad v(x)
\]

\end{document}

Thanks in advance and happy new year.

Answer 1

It is possible to provide a scale factor while loading a font by inserting s * [<factor>] (or just [<factor>]) in the fifth argument of \DeclareFontShape. This is documented in the fntguide (section 4).

I don't think I've got much more to say about this, so I'll just include an example. I'm using a factor 1.5 below, just for the purpose of illustration/comedic effect, and I've commented out the line loading mtpro2 because I don't have this font.

\documentclass{article}
\usepackage[scaled=0.92]{helvet}    % set Helvetica as the sans-serif font
\renewcommand{\rmdefault}{ptm}      % set Times as the default text font

%% I don't have this font:
% \usepackage[lite,subscriptcorrection,slantedGreek,nofontinfo]{mtpro2}

%var letters
\DeclareFontFamily{U}{ntxmia}{\skewchar\font=127 }
\DeclareFontShape{U}{ntxmia}{m}{it}{
  <-> s * [1.5] ntxmia
}{}
\DeclareFontShape{U}{ntxmia}{b}{it}{
  <-> s * [1.5] txbmia
}{}
\DeclareSymbolFont{ntxmia}{U}{ntxmia}{m}{it}
\SetSymbolFont{ntxmia}{bold}{U}{ntxmia}{m}{it}
\DeclareMathSymbol{\varg}{\mathord}{ntxmia}{49}
\DeclareMathSymbol{\varv}{\mathord}{ntxmia}{51}
\DeclareMathSymbol{\varw}{\mathord}{ntxmia}{52}
\AtBeginDocument{\mathcode`g=\varg}
\AtBeginDocument{\mathcode`v=\varv}
\AtBeginDocument{\mathcode`w=\varw}

\begin{document}

\[
    gxv \qquad \{(x,g(x)):x\in U\} \qquad v(x)
\]

\end{document}

---

Edit:

Here's a little demonstration to show that this works in subscripts and at different font sizes:

\documentclass{article}\pagestyle{empty}
\usepackage{newtxtext,newtxmath}

\DeclareFontFamily{U}{ntxmia}{\skewchar\font=127}
\DeclareFontShape{U}{ntxmia}{m}{it}{<-> s * [1.5] ntxmia}{}
\DeclareFontShape{U}{ntxmia}{b}{it}{<-> s * [1.5] txbmia}{}
\DeclareSymbolFont{ntxmia}{U}{ntxmia}{m}{it}
\SetSymbolFont{ntxmia}{bold}{U}{ntxmia}{m}{it}
\DeclareMathSymbol{\varg}{\mathord}{ntxmia}{49}
\DeclareMathSymbol{\varv}{\mathord}{ntxmia}{51}
\DeclareMathSymbol{\varw}{\mathord}{ntxmia}{52}
\AtBeginDocument{\mathcode`g=\varg}
\AtBeginDocument{\mathcode`v=\varv}
\AtBeginDocument{\mathcode`w=\varw}

\begin{document}

{\tiny gxv, $gxv_{gxv}$}

gxv, $gxv_{gxv}$

{\Huge gxv, $gxv_{gxv}$}

{\fontsize{60}{72}\selectfont gxv,$gxv_{gxv}$}

\end{document}