Doing stuff like this in the 8-bit era was never particularly hard. The difficulty was doing this and then anything else, because you basically need the entire CPU just for audio synthesis. For games, there was a very real trade-off between calculating video, game state, and sound, and sound often took the back seat.

It's also why everything looked and sounded better on 8-bit computers that had hardware support for graphic sprites or sound generation, even if they had a less powerful CPU. And it's the untold story behind why 16-bit graphics looked so much better: it wasn't about the CPU as much as it was about having a dedicated video card / chipset with its own memory, a sound card that handled polyphonic sound and MIDI synthesis, etc.