  We present a phenomenological theory of the low energy moir\'e minibands of
Dirac electrons in graphene placed on an almost commensurate hexagonal underlay
with a unit cell pproximately three times larger than that of graphene.A slight
incommensurability results in a periodically modulated intervalley scattering
for electrons in graphene. In contrast to the perfectly commensurate Kekul\'e
distortion of graphene, such supperlattice perturbation leaves the zero energy
Dirac cones intact, but is able to open a band gap at the edge of the first
moir\'e subbband, asymmetrically in the conduction and valence bands.
