  Let $R$ be a ring and $T \in {\rm Mod-}R$ be a (non-classical) tilting module
of finite projective dimension. Let $\mathcal T=({\mathcal T}^{\leq0},
{\mathcal T}^{\geq0})$ be the $t$-structure on $D(R)$ generated by $T$ and
${\mathcal D}=({\mathcal D}^{\leq0}, {\mathcal D}^{\geq0})$ be the natural
$t$-structure. We show that the pair $(\mathcal D, \mathcal T)$ is right
filterable in the sense of [FMT14], that is, for any $i\in\mathbb Z$ the
intersection ${\mathcal D}^{\geq i}\cap {\mathcal T}^{\geq 0}$ is the co-aisle
of a $t$-structure. As a consequence, the heart of $\mathcal T$ is derived
equivalent to ${\rm Mod-}R$.
