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ABSTRACT We present a comprehensive study about the phenomenological implications of the theory describing Galactic cosmic ray scattering on to magnetosonic and Alfvénic fluctuations in the GeV−PeV domain. We compute a set of diffusion coefficients from first principles, for different values of the Alfvénic Mach number and other relevant parameters associated with both the Galactic halo and the extended disc, taking into account the different damping mechanisms of turbulent fluctuations acting in these environments. We confirm that the scattering rate associated with Alfvénic turbulence is highly suppressed if the anisotropy of the cascade is taken into account. On the other hand, we highlight that magnetosonic modes play a dominant role in Galactic confinement of cosmic rays up to PeV energies. We implement the diffusion coefficients in the numerical framework of the dragon code, and simulate the equilibrium spectrum of different primary and secondary cosmic ray species. We show that, for reasonable choices of the parameters under consideration, all primary and secondary fluxes at high energy (above a rigidity of $\simeq 200 \, \mathrm{GV}$) are correctly reproduced within our framework, in both normalization and slope.