It's like it's off key or something. It's not godawful to listen to but it's not quite the nostalgia I was looking for since it's a little off. Any ideas what I can try to change it?

Privateer 1 or 2?

Either way maybe you want OPL FM which most soundcards used at the time and maybe the game is configured to use General Midi or some other output.
To change it you must open the soundsetup program and pick the soundcard you want.
The shortcut should be supplied with the game (I hope).