  We construct novel black strings that are neither time-translation invariant,
nor axisymmetric, nor translationally invariant in the string direction, but
nevertheless have a helical Killing vector field. These solutions branch from
the superradiant instability of $D=6$ Myers-Perry black strings with equal
angular momenta. We coin these solutions as {\it black resonator strings} and
we find that they have more entropy than Myers-Perry black strings for the
energies and angular momenta where both solutions coexist. We also construct
Kaluza-Klein geons, which share the symmetries of black resonator strings, but
are horizonless. Unlike in other superradiant systems, Kaluza-Klein geons are
not the horizonless limit of black resonator strings and are instead entirely
separate solutions.
