I finally found that old doorbell I wanted to perhaps use. It's a really old fashioned one with a solenoid hitting metal plates for the sound.
It's design is simple yet clever. A little double sided hammer sits in the middle with a spring and solenoid around it. When the doorbell is pressed, the solenoid activates and slams it into the shorter metal plate, making a "ding" sound. When the button is released, the solenoid deactivates and the now compressed spring swings it into the longer metal plate on the other side, creating a "dong" sound.
An interesting solution to put the delay between the two notes in a "ding-dong!" sound. Now, how to exploit that...
I could, perhaps, try using PWM to put the hammer in a position where it could slam either of the metal plates just as hard. changing the duty cycle to 100% would play a ding, and putting it to 0% plays a dong. After 50ms or so it would return to whatever PWM value results to it sitting in equilibrium. I'm not sure how well this plan might work, but it's worth a try. It's not that far off from how drums currently work, which is a 50ms long LOW-HIGH-LOW pulse.
Getting it to be useful in a song is another problem. It isn't really percussion, and it can only play 2 notes. I could set it up so whenever those notes play in a certain channel, it would play the note instead of a floppy drive, or alongside a floppy drive. For some reason, I'd imagine the classic Super Mario theme wouldn't sound too bad if some of the notes were played by a doorbell. I'm not musically talented enough to tell you what notes in the song match, and therefore would be replaced by the doorbell's notes, but that's my control software's job, not mine :D