Upright Greek letters in textmode and default font

Question

I want to produce a few upright Greek letters in the latex default font. I would use math mode for this purpose, however, it only displays Greek letters in italics. Since I am already using xelatex, I thought it would be easy to produce a few Greek symbols using the polyglossia package. Unfortunately, polyglossia reports this:

! Package polyglossia Error: The current latin font does not contain the "Greek" script!

Solution form the docs: specify a font for Greek. OK. That worked. But I want to use the default font. Since it is possible to output Greek letters with the default font in math mode, it should somehow be possible to get Greek letters in text mode with polyglossia.

\documentclass{article}
\usepackage{polyglossia}
\setmainlanguage{english}
\setotherlanguage{greek}
\title{}\date{}
\begin{document}
\maketitle

This is math mode with default font $\tau\acute{\epsilon}\mu\nu\omega$. 
The Greek should, however, be set in regular font.

% This is polyglossia \textlang{greek}{τέμνω}, reporting an error.
\end{document}

Answer 1

You need to load a text font that features polytonic Greek letters. As you've discovered, Latin Modern Roman -- the default font if the fontspec package is loaded -- does not. Not knowing which text font preferences you have, I can't provide an informed recommendation. Just to get you started, you might try using EB Garamond.

\documentclass{article}

\usepackage{polyglossia}
\setmainlanguage{english}
\setotherlanguage{greek}

\usepackage{unicode-math}
\setmainfont{EB Garamond}
\setmathfont{Cambria Math}[Scale=MatchLowercase] % optional

\begin{document}
This is math mode: $\tau\acute{\varepsilon}\mu\nu\omega$. 

This is text mode:\ \textlang{greek}{τέμνω}.
\end{document}

Answer 2

You could use CMU serif instead of Latin Modern for the greek.

\documentclass{article}
\usepackage{polyglossia}
\setmainlanguage{english}
\setotherlanguage{greek}
\newfontfamily\greekfont{CMU Serif}[Script=Greek]
\begin{document}
This is polyglossia \textlang{greek}{τέμνω}.
\end{document}