  We demonstrate that the detection of shock modulations of the neutrino
spectra from a galactic core-collapse supernova is sufficient to obtain a high
significance determination of the neutrino mass hierarchy if the supernova
event is observed in both a Mton-class water Cherenkov detector and a 100
kton-class liquid argon detector. Neither detailed supernova neutrino flux
modelling nor observation of Earth matter effects is needed for this
determination. As a corollary, a nonzero value of \theta_x will be established.
