Exchange spring magnets, consisting of a [Co(0.5 nm)/Pd(1 nm)](5) multilayer with perpendicular magnetic anisotropy and a Co20Fe60B20 film with easy plane anisotropy, of variable thickness t(CFB), are investigated using Brillouin light scattering. On reducing t(CFB) in the range 0.8-2.3 nm, the spin-wave frequency gap displays a remarkable increase from nearly 4-48 GHz, reflecting the corresponding rapid growth of the tilting angle of the magnetization with respect to the film normal. These findings are interpreted using a one-dimensional model in which each atomic layer is assumed to be uniformly magnetized, subjected to an effective out-of-plane or easy-plane anisotropy depending on the layer position in the stack, and exchange coupled to its two nearest neighbour atomic layers. With respect to previously investigated [Co/Pd]-NiFe hybrid magnets, a largest frequency tunability, restricted to a narrower range of the soft layer thickness, is observed.