I can reproduce the messed up CMS music in DOSBox by booting real DOS, depending on cycles. It sounds mostly OK at 1000 cycles, breaks up a bit at the default 3000 cycles, and gets progressively worse as cycles increase.
A major influence on the uneven music playing appears to be polling for keystrokes with the DOS direct console input function, which has a fair amount of code overhead associated with it (several hundred instructions executed just to report no keystroke is available). DOSBox's emulation of DOS is mostly unaffected because there is very little code overhead with the function being handled internally.
I made a workaround program that replaces the DOS function call with BIOS functions. In DOSBox with booted MS-DOS 5 the workaround keeps the music playing smooth as cycles increase, but some notes still get iffy when cycles are pushed too high. Run the program instead of PRINCE.EXE to start the game (e.g. "popkb gblast"). It hasn't been tested on real systems yet, so no guarantees.