  Let $\Omega\subset\mathbb R^{n+1}$ be open and let $E\subset \partial\Omega$
with $0<H^s(E)<\infty$, for some $s\in(n,n+1)$, satisfy a local capacity
density condition. In this paper it is shown that the harmonic measure cannot
be mutually absolutely continuous with $H^s$ on $E$. This answers a question of
Azzam and Mourgoglou, who had proved the same result under the additional
assumption that $\Omega$ is a uniform domain.
