According to the user guide of the memoir package, the following default font sizes (in points) are provided: 9, 10, 11, 12, 14, 17, 20, 25, 30, 36, 48, and 60. For each of these sizes, a file called mem?.clo ìs provided, where ? can be 9, 10, 11, etc and clo stands for "class option". One needs to set the document class option extrafontsizes for font sizes that exceed 25pt.
For new font sizes, e.g., 13pt, you'll have to set up a file named mem13.clo along the lines explained in the user guide. For the case of 13pt, I'd like to suggest you use mem12.clo and mem14.clo as "templates" and, specifically, average the values used in those two files for the new file.
Addendum: Here's my attempt to create mem13.clo as a convex combination of the parameter settings used in mem12.clo and mem14.clo. Save it either in the directory that contains your main tex file or in a directory that's searched by your TeX distribution. If you choose the second option, do also perform a refresh of the filename database of your TeX distribution.
%% This is file `mem13.clo', generated as a convex
%% combination of mem12.clo and mem14.clo
%%
%% This work may be distributed and/or modified under
%% the conditions of the LaTeX Project Public License,
%% either version 1.3 of this license or (at your
%% option) any later version.
%% The latest version of the license is in
%% http://www.latex-project.org/lppl.txt
%% and version 1.3 or later is part of all distributions
%% of LaTeX version 2003/06/01 or later.
%%
%% This work has the LPPL maintenance status "maintained".
%%
\ProvidesFile{mem13.clo}%
[2016/05/17 v0.01 memoir class 13pt size option]
\renewcommand{\normalsize}{%
\@setfontsize\normalsize{13.2}{16.0}%
\abovedisplayskip 13.2\p@ \@plus3\p@ \@minus7.5\p@
\abovedisplayshortskip \z@ \@plus3\p@
\belowdisplayshortskip 6.75\p@ \@plus3.5\p@ \@minus3\p@
\belowdisplayskip \abovedisplayskip
\let\@listi\@listI}
\normalsize
\newcommand{\small}{%
\@setfontsize\small\@xiipt{14.0}%
\abovedisplayskip 11.5\p@ \@plus3\p@ \@minus6\p@
\abovedisplayshortskip \z@ \@plus3\p@
\belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
\def\@listi{\leftmargin\leftmargini
\topsep 10\p@ \@plus3.5\p@ \@minus5.5\p@
\parsep 5.25\p@ \@plus2.5\p@ \@minus\p@
\itemsep \parsep
%% \itemindent\z@
}%
\belowdisplayskip \abovedisplayskip
}
\newcommand{\footnotesize}{%
\@setfontsize\footnotesize\@xipt\@xiipt
\abovedisplayskip 10.5\p@ \@plus2.5\p@ \@minus5.5\p@
\abovedisplayshortskip \z@ \@plus3\p@
\belowdisplayshortskip 6.25\p@ \@plus3.25\p@ \@minus3\p@
\def\@listi{\leftmargin\leftmargini
\topsep 6.25\p@ \@plus2.75\p@ \@minus2.5\p@
\parsep 3.5\p@ \@plus2.5\p@ \@minus\p@
\itemsep \parsep
%% \itemindent\z@
}%
\belowdisplayskip \abovedisplayskip
}
\newcommand*{\miniscule}{\@setfontsize\miniscule\@viiipt{8.8}}
\newcommand*{\tiny}{\@setfontsize\tiny\@ixpt{10}}
\newcommand*{\scriptsize}{\@setfontsize\scriptsize\@xpt\@xipt}
\newcommand*{\large}{\@setfontsize\large{14.5}{20}}
\newcommand*{\Large}{\@setfontsize\Large{18.5}{23.5}}
\newcommand*{\LARGE}{\@setfontsize\LARGE{22}{27}}
\newcommand*{\huge}{\@setfontsize\huge{27}{33}}
\ifextrafontsizes
\newcommand*{\Huge}{\@setfontsize\Huge{33}{40}}
\newcommand*{\HUGE}{\@setfontsize\HUGE{40}{48}}
\else
\let\Huge=\huge
\let\HUGE=\huge
\fi
\setlength{\onelineskip}{16\p@}
\if@twocolumn
\setlength\parindent{1em}
\else
\setlength\parindent{1.5em}
\fi
\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}
\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}
\setlength\headheight{16\p@}
\setlength\headsep{.3in}
\setlength\topskip{13.2\p@}
\setlength\footskip{33\p@}
\setlength\maxdepth{.5\topskip}
\setlength\@maxdepth\maxdepth
\setlength\footnotesep{9\p@}
\setlength{\skip\footins}{11.9\p@ \@plus 4\p@ \@minus 2\p@}
\setlength\floatsep {13.2\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\intextsep {14\p@ \@plus 4\p@ \@minus 4\p@}
\setlength\dblfloatsep {14\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\@fptop{0\p@ \@plus 1fil}
\setlength\@fpsep{10\p@ \@plus 2fil}
\setlength\@fpbot{0\p@ \@plus 1fil}
\setlength\@dblfptop{0\p@ \@plus 1fil}
\setlength\@dblfpsep{10\p@ \@plus 2fil}
\setlength\@dblfpbot{0\p@ \@plus 1fil}
\setlength\lxvchars{372\p@} % standard 390pt
\setlength\xlvchars{264\p@} %
\if@twocolumn
\setlength\marginparsep{10\p@}
\else
\setlength\marginparsep{7\p@}
\fi
\setlength{\marginparpush}{7\p@}
\endinput
%%
%% End of file `mem13.clo'.
And here's an MWE that makes use of this new class option file. (Incidentally, I think the sizing command should be named \minuscule rather than \miniscule...)

\documentclass[13pt]{memoir}
\newcommand\qbf{The quick brown fox jumps over the lazy dog.}
\newcommand\qbfshort{The quick brown fox jumps over\dots}
\setlength\parindent{0pt}
\begin{document}
\obeylines
\miniscule\qbf
\tiny\qbf
\scriptsize\qbf
\footnotesize\qbf
\normalsize\qbf
\large\qbf
\Large\qbf
\LARGE\qbf
\huge\qbf
\Huge\qbfshort
\HUGE\qbfshort
\end{document}
~/texmf(equivalent to/home/<username>/texmf) directory and do atexhash ~/texmf<Enter>at the command prompt. This is a wonderful answer, and I know a lot of work went into it. – A Feldman May 18 '16 at 02:48kpsewhichutility from a command line to locate any file of the TeX distribution. E.g.,kpsewhich mem12.clowill return the fully qualified path name ofmem12.clo. – Mico May 18 '16 at 07:26mem13.cloto the directory which contains your main tex file, you should be in business. – Mico May 20 '16 at 05:15mem13.clo. – Mico May 20 '16 at 05:34mem13with the extensionclo. Saved it in the same folder I have theMain.texfile.However, it does not seem to recognize the command
13ptafter the\documentclass[]due to the resulting fontsize being 12pt.[http://i.imgur.com/1P3bT7K.jpg]
– Adriano May 20 '16 at 05:41\documentclass[13pt]{memoir}? – Mico May 20 '16 at 06:02C:\Users\Adriano\AppData\Local\Programs\MiKTeX 2.9\tex\latex\memoirThat is where the packages hide themselves.I have managed to put this edited file there, and made some comparisons... [http://i.imgur.com/IIqlXln.png]
The author really enjoyed the outcome of the
– Adriano May 26 '16 at 06:19\usepackage[fontsize=13pt]{scrextend}package....However, I am the programmer and understand the consequences...so, is it possible to make themem13.closame font sizes as the package mentioned above? If yes, how?