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 approximately 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 superlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moir\'e subband, asymmetrically in the conduction and valence bands.