  The isomeric and $\beta$-decay properties of neutron-rich $^{53-57}$Sc and
$^{53,54}$Ca nuclei near neutron number $N$=32 are reported, and the low-energy
level schemes of $^{53,54,56}$Sc and $^{53-57}$Ti are presented. The low-energy
level structures of the $_{21}$Sc isotopes are discussed in terms of the
coupling of the valence $1f_{7/2}$ proton to states in the corresponding
$_{20}$Ca cores. Implications with respect to the robustness of the $N$=32
subshell closure are discussed, as well as the repercussions for a possible
$N$=34 subshell closure.
