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 $a\approx0.076\,\text{fm}$.