A Few Simple Synths from Jan Ostman
Each of these four directories can be moved into your Arduino sketch directory, compiled, and flashed. They're all serial-port adaptations of some synthesizer cores that Jan Ostman wrote, and they make fantastic jumping-off points for your own experimentation.
I wrote an article on Hackaday to go with them. Go there for samples and instructions. Or just flash the code and hook up to the Arduino with a good serial terminal at 9600 baud.
In the long run, it'd be neat to modify and modularize these to make an easier-to-modify AVR-based synthesis library. If you're interested in such a project, fork away and get in touch.