Possibly the simplest way to picture the story is
(a) in subsonic flow the CP typically is somewhere near 0.25MAC
(b) for supersonic flow read 0.50MAC
(c) transonically the situation with shockwaves is rather dynamic.
Overall, if the CG remains constant, as the CP moves aft .. albeit not necessarily steadily, there will be an increasing nosedown couple leading to a nosedown pitching moment.
Depending on the design of the aircraft, what is happening on the tailplane so far as shocks, and pressures are concerned might be having a significant effect as well ...