  We present the status of an ongoing project aimed at the inclusion of
isospin-breaking corrections arising from the non-degeneracy of the light quark
masses and electromagnetic interactions in calculations of the low-lying octet
and decuplet baryon masses. Our ultimate goal is to perform a precision
determination of the lattice scale including isospin-breaking effects. We apply
the perturbative formalism to isospin-symmetric $N_f=2+1$ CLS ensembles. We
show results on baryon masses up to leading order in isospin-breaking
corrections on two ensembles with $m_\pi\approx290\,\text{MeV}$ and
$m_\pi\approx215\,\text{MeV}$ at a lattice spacing of
$a\approx0.076\,\text{fm}$.
