  In this work, we generalise linear magnetohydrodynamic (MHD) stability theory
to include equilibrium pressure anisotropy in the fluid part of the analysis. A
novel 'single-adiabatic' (SA) fluid closure is presented which is complementary
to the usual 'double-adiabatic' (CGL) model and has the advantage of naturally
reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and
CGL, the SA model neglects the anisotropic perturbed pressure and thus loses
non-local fast-particle stabilisation present in the kinetic approach. Another
interesting aspect of this new approach is that the stabilising terms appear
naturally as separate viscous corrections leaving the isotropic SA closure
unchanged. After verifying the self-consistency of the SA model, we re-derive
the projected linear MHD set of equations required for stability analysis of
tokamaks in the MISHKA code. The cylindrical wave equation is derived
analytically as done previously in the spectral theory of MHD and clear
predictions are made for the modification to fast-magnetosonic and slow ion
sound speeds due to equilibrium anisotropy.
