Particles occupy mass levels within three geometric sequences that descend from the Planck Mass. Every third level in each sequence is a superlevel of type 1. Every fifth level in each sequence is a superlevel of type 2. The charged leptons in partnership with pseudoscalar mesons are arranged symmetrically about closely coincident superlevels of type 1. The quarks, in weak isospin doublets, are arranged symmetrically about closely coincident superlevels of type 2. A symmetrical pattern of three-sequence coincident superlevels of type 1 extends over many orders of magnitude. The electron and the up quark both participate in partnerships with pseudoscalar mesons that are arranged symmetrically about the centre of the pattern. The model admits of the partnership of an electron neutrino of mass of 10.9 meV with a scalar of mass ~2x10^7 GeV, and of the partnership of a 15.9 keV fermion, conjectured to be the sterile right-handed electron neutrino, with a scalar of mass ~16 GeV.