The density maximum of water dominates the thermodynamics of the system under ambient conditions, is strongly P-dependent, and disappears at a crossover pressure P(cross) approximately 1.8 kbar. We study this variable across a wide area of the T-P phase diagram. We consider old and new data of both the isothermal compressibility K(T)(T, P), the pressure constant specific heat C(P)(T) and the coefficient of thermal expansion alpha(P) (T, P). We observe that K(T)(T) shows a minimum at T* approximately 315 +/- 5 K for all of the studied pressures, whereas, at the same temperature, C(P)(T) has the minimal variation as a function of P in the interval 1 bar-4 kbar. We find the behavior of alpha(P) also to be surprising: all the alpha(P)(T) curves measured at different P cross at T*. The experimental data show a "singular and universal expansivity point" at T* approximately 315 K and alpha(P)(T*) = 0.44 10(-3) K(-1). Unlike other water singularities, we find this temperature to be thermodynamically consistent in the relationship connecting the three response functions. By considering also the P-T behavior of the self-diffusion coefficient D(S) and of the NMR proton chemical shift delta we have the information that at T* the water local order points out, with decreasing T, the crossover from a normal fluid to the anomalous and complex liquid characterized by the many anomalies.