  We show that for uniform domains $\Omega\subseteq \mathbb{R}^{d+1}$ whose
boundaries satisfy a certain nondegeneracy condition that harmonic measure
cannot be mutually absolutely continuous with respect to $\alpha$-dimensional
Hausdorff measure unless $\alpha\leq d$. We employ a lemma that shows that at
almost every nondegenerate point, we may find a tangent measure of harmonic
measure whose support is the boundary of yet another uniform domain whose
harmonic measure resembles the tangent measure.
