We investigate the dependence on the applied field of the frequency/wavevector dispersion relations of collective spin waves in arrays of dots, close to a magnetic transition. In particular, we focus on the low frequency “soft” modes in three different cases: end modes in the transition between two different saturated states in ellipses, fundamental mode in the saturated-to-vortex transition in disks, and gyrotropic mode in the vortex-to-saturated transition in disks. Noteworthy, the spin waves with nonzero Bloch wavevector along the direction of the applied field happen to soften earlier than spin waves with a Bloch wavevector along different directions, and this feature is responsible for an asymmetric broadening of the bandwidth along the different lattice directions. This is particularly useful in magnonic/spin-logic device research, if different binary digits are associated to modes with the same cell function but different propagation directions.