In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the
tangent bifurcation of the band edge modes (q=0,π) of nonlinear Hamiltonian
lattices made of N coupled oscillators. Introducing the concept of {\em
partial isochronism} which characterises the way the frequency of a mode,
ω, depends on its energy, ϵ, we generalize these results and
show how the bifurcation energies of these modes are intimately connected to
their degree of isochronism. In particular we prove that in a lattice of
coupled purely isochronous oscillators (ω(ϵ) strictly constant),
the in-phase mode (q=0) never undergoes a tangent bifurcation whereas the
out-of-phase mode (q=π) does, provided the strength of the nonlinearity in
the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger
equation governing the slow modulations of small-amplitude band edge modes and
show that its nonlinear exponent is proportional to the degree of isochronism
of the corresponding orbits. This equation may be seen as a link between the
tangent bifurcation of band edge modes and the possible emergence of localized
modes such as discrete breathers.Comment: 23 pages, 1 figur