  Recently, formulas for the mixing matrices of quarks and leptons have been
put forward. My contribution here describes the relevant foundational and
technical aspects which have led to those results. The work has been carried
out in the framework of the microscopic model. The most general ansatz for the
interactions among tetrons leads to a Hamiltonian H involving
Dzyaloshinskii-Moriya (DM), Heisenberg and torsional isospin forces.
Diagonalization of the Hamiltonian provides for 24 eigenvalues which are
identified as the quark and lepton masses. While the masses of the third and
second family arise from DM and Heisenberg type of isospin interactions, light
family masses are related to torsional interactions among tetrons. Neutrino
masses turn out to be special in that they are given in terms of tiny isospin
non-conserving DM, Heisenberg and torsional couplings. The approach not only
leads to masses, but also allows to calculate the quark and lepton eigenstates,
an issue, which is important for the determination of the CKM and PMNS mixing
matrices. The almost exact isospin conservation of the system dictates the form
of the lepton states and makes them independent of all the couplings in H. Much
in contrast, there is a strong dependence of the quark states on the coupling
strengths, and a promising hierarchy between the quark family mixings shows up.
