I am trying to construct a new symbol: a circle with a vertical bar through it. The following MWE sorta works but doesn't look quite right.

\documentclass[12pt]{amsart}
\newcommand{\bcirc}{\mathrel{\ooalign{$\circ$\cr\hidewidth\hbox{$|\mkern 1.9mu$}\cr}}}
\begin{document}
New symbol $x \bcirc_3 y$ works.
Also huge version {\huge$x \bcirc_2 y$} works fine.
In displaymath, compare:
\begin{align*}
x \bcirc_1 y &= \pi_{w \bcirc_2 z} , \\
x \circ_1 y &= \pi_{w \circ_2 z} .
\end{align*}
\end{document}
- Spacing to the right of the new symbol seems slightly too large I think?
- More importantly, this symbol does not resize when used as a subscript. Any tips/modifications I need to make to the definition?
This is based on an answer to this other tex.SE question.

\mathpalettemight be perfect here, as in the solution you linked. By the way, is the unbalancedness intended? – Manuel Jan 22 '15 at 15:31\usepackage{tipa,amsmath,graphicx} \def\bcirc{\scalebox{.7}{\text{\sffamily\textphi}}}– Fran Jan 22 '15 at 21:30