Alternative separate font to mathfrak for small letters

Question

I am looking for a second set of alphabets for my article.

I have seen this post which looks great but it does not cover small letters (only capitals).

\mathfrak is a good option too, except for a very ugly and ambiguous x letter:

I am wondering if there is another alternative which covers small letters.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\usepackage{yfonts}

\begin{document}
\begin{align}
&\mathfrak{abcdefghijklmnopqrstuvwxyz} \\
&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} 
\end{align}
\end{document}

The font should be different enough to be distinguished from normal default font but readable enough so no ambiguity happens.

Answer 1

Here are some freely available fonts included in TeX Live. But Fraktur is inherently ambiguous, see C, E and G, for instance or A and U.

\documentclass{article}
\usepackage{amsfonts}

\newcommand{\alphabet}{abcdefghijklmnopqrs\/tuvwxyz}
\newcommand{\Alphabet}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

\DeclareMathAlphabet{\mathpgoth}{OT1}{pgoth}{m}{n}
\DeclareMathAlphabet{\mathesstixfrak}{U}{esstixfrak}{m}{n}
\DeclareMathAlphabet{\mathboondoxfrak}{U}{BOONDOX-frak}{m}{n}

\begin{document}

\subsubsection*{amsfonts}
$\mathfrak{\alphabet}$\\
$\mathfrak{\Alphabet}$

\subsubsection*{pgoth}
$\mathpgoth{\alphabet}$\\
$\mathpgoth{\Alphabet}$

\subsubsection*{esstixfrak}
$\mathesstixfrak{\alphabet}$\\
$\mathesstixfrak{\Alphabet}$

\subsubsection*{boondox-frak}
$\mathboondoxfrak{\alphabet}$\\
$\mathboondoxfrak{\Alphabet}$

\end{document}

The \/ is in order to avoid ligatures.

Answer 2

This is compiled in LuaLaTeX. I can use \setmathfont with the range specifier to limit the extent of the font substitution. Here, I set the math font to Old English Text MT found by default on Windows systems, but limit it to the range of \mathfrak. In essence, it substitutes only for \mathfrak, until the \setmathfont is used to later reset the feature to the Latin Modern Math defaults.

\documentclass{article}
\usepackage{fontspec,unicode-math}
\setmathfont{Latin Modern Math}
\begin{document}
\setmathfont[range=\mathfrak]{Old English Text MT}
Here we have $\mathfrak{x}^{55}+1 \ne(x^5)^{11}+1$

$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

$\mathfrak{abcdefghijklmnopqrstuvwxyz}$

\hrulefill

\setmathfont{Latin Modern Math}
Here we have $\mathfrak{x}^{55}+1 \ne(x^5)^{11}+1$

$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

$\mathfrak{abcdefghijklmnopqrstuvwxyz}$
\end{document}

---

Alternately, if the new fraktur font replacement is already available for pdflatex, then an approach like this can be used (based on the answer at Is it possible to use the DeclareFontShape command with kpfonts?):

\documentclass{article}
%\usepackage{fourier}
\DeclareFontFamily{U}{jkpmia}{}
\DeclareFontShape{U}{jkpmia}{m}{it}{<->s*jkpmia}{}
\DeclareFontShape{U}{jkpmia}{bx}{it}{<->s*jkpbmia}{}
\DeclareMathAlphabet{\mathfrak}{U}{jkpmia}{m}{it}
\SetMathAlphabet{\mathfrak}{bold}{U}{jkpmia}{bx}{it}
\begin{document}
Here we have $\mathfrak{x}^{55}+1 \ne(x^5)^{11}+1$

$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

$\mathfrak{abcdefghijklmnopqrstuvwxyz}$
\end{document}