It is shown that the framework of Hall magnetohydrodynamics (Hall-MHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfv¿nic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum: the Kolmogorov branch f-5/3, steepening to f-α1, with α1 $simeq$ 3--4 on the high-frequency side and flattening to f-1 on the low-frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD shear Alfv¿n waves. The spectrum of the concomitant whistler-type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of the anisotropy of the turbulence is addressed briefly.