Hello there, i_rina,
Thanks for your support. Unfortunately, these suggestions did not resolve the issue.
It appears that the new Music program that replaced iTunes will not allow screensaver and sleep modes when the program is open and active. For many years, I was able to have music play, even after the screensaver and eventual sleep mode started. I have music playing all night while I sleep and my computer is in my bedroom. I do not want the screen on all the time anyway, as it is still likely to burn out the monitor at a faster rate. In the end, it's just annoying that this can't be controlled by the user anymore...unless there's a workaround, which I can't figure out yet.
Let me know if there's something else. When I quit the process (as outlined in one of the links you included for me), it just quits the program, which stops the music, of course. This is not the sought after solution.
Thanks again for your help. I really do appreciate the effort on this community board!
Regards,
Michael