  In this paper, we construct two infinite families of tight sets with
parameters $(q^{2r-2}-1)$ and $(q^{2r-1}-q^{2r-2})$, respectively, in the
Hermitian polar space $\mathcal{H}(2r-1,q^2)$ for any $r\ge 2$ and any prime
power $q$. Both families admit $(q-1).\PGL(r,q^2).2.2e$ as the full
automorphism group, where $q=p^e$, $p$ is a prime, and $e$ a positive integer.
