We present dynamical scaling relations for a homogeneous and representative sample of ∼500 massive galaxies, selected only by stellar mass (>1010 M⊙) and redshift (0.025 < z < 0.05) as part of the ongoing GALEX Arecibo SDSS Survey. We compare baryonic Tully–Fisher (BTF) and Faber–Jackson (BFJ) relations for this sample, and investigate how galaxies scatter around the best fits obtained for pruned subsets of disc-dominated and bulge-dominated systems. The BFJ relation is significantly less scattered than the BTF when the relations are applied to their maximum samples (for the BTF, only galaxies with H i detections), and is not affected by the inclination problems that plague the BTF. Disc-dominated, gas-rich galaxies systematically deviate from the BFJ relation defined by the spheroids. We demonstrate that by applying a simple correction to the stellar velocity dispersions that depends only on the concentration index of the galaxy, we are able to bring discs and spheroids on to the same dynamical relation – in other words, we obtain a generalized BFJ relation that holds for all the galaxies in our sample, regardless of morphology, inclination or gas content, and has a scatter smaller than 0.1 dex. We compare the velocity–size relation for the three dynamical indicators used in this work, i.e. rotational velocity, observed and concentration-corrected stellar dispersion. We find that discs and spheroids are offset in the stellar dispersion–size relation, and that the offset is removed when corrected dispersions are used instead. The generalized BFJ relation represents a fundamental correlation between the global dark matter and baryonic content of galaxies, which is obeyed by all (massive) systems regardless of morphology.