IPA characters in Computer Modern Roman

To input IPA characters in LaTeX, I can either use the tipa package which typesets them in the Computer Modern font, or I can input them directly using XeLaTeX or LuaLaTeX, provided I specify a Unicode font with fontspec, for example Doulos SIL. If I skip the last step and use the default font, the IPA specific characters don't appear. Why? Given the existence of tipa one would assume that there are glyphs for all IPA characters in the Computer Modern Roman font.

These two examples both produce the intended output. With tipa:

\documentclass{article}
\usepackage{tipa}
\begin{document}
\textipa{aI p\super{h}i: eI}
\end{document}


and with another font (and XeLaTeX):

\documentclass{article}
\usepackage{fontspec}
\setmainfont{Doulos SIL}
\begin{document}
aɪ pʰiː eɪ
\end{document}


However, this does not work even when using XeLaTeX:

\documentclass{article}
\begin{document}
aɪ pʰiː eɪ
\end{document}


My question is really asking what one can do to input IPA characters without tipa, but still using the default font.

• The TIPA font is a separate font with a separate encoding (T3). So they are not "part of Computer Modern" but instead a font designed to match Computer Modern. As Ulrike's answer shows, if you load the OpenType version of CM, then IPA symbols are included in it, but these are not TIPA symbols (unless they were converted from the TIPA fonts.) Sep 4 '17 at 18:42

The default font is not computer modern but latin modern. With computer modern it works:

\documentclass{article}
\usepackage{fontspec}
\setmainfont{CMU Serif}
\begin{document}
aɪ pʰiː eɪ
\end{document}


• When I try this, I get the error message that The font "CMU Serif" cannot be found. I tried googling it but I didn't find anything helpful. Sep 4 '17 at 18:49
• It is in my texlive in fonts/opentype/public/cm-unicode/cmunrm.otf Sep 4 '17 at 18:57
• I use MiKTeX, but I just had to download the (font?) package cm-unicode. Sep 4 '17 at 19:06