We explore the radial (p-mode) stability of stars across a wide range of mass (0.2 < M < 50 M⊙), composition (0 < X < 0.7, Z = 0.001, 0.02), effective temperature, and luminosity. We identify the instability boundaries associated with low- to high-order radial oscillations (0 ⩽ n ⩽ 13). The instability boundaries are a strong function of both composition and radial order (n). The classical blue edge shifts to higher effective temperature and luminosity with decreasing hydrogen abundance. High-order modes are more easily excited and small islands of high radial-order instability develop, some of which correspond with real stars. Driving in all cases is by the classical κ-mechanism and, at high luminosity-to-mass ratio, strange-mode instability. We identify regions of parameter space where new classes of pulsating variable have recently or may, in future, be discovered. The majority of these are associated with reduced hydrogen abundance in the envelope.