This is loosely based on this circuit:
http://www.555-timer-circuits.com/toy-organ.htmlBy loosely, I mostly refer to making a mistake in design and also not using the correct components, just what I had to experiment with.
That means, most of the notes are off and none is really in tune.
I never used a PCB design tool, and then I rushed this design to take advantage of a coupon, as the PCB cost me $2 shipped. I didn't connect everything well, costing me one button and resistor (it could probably be fixed with some wires but is not that important).
With that in mind, I'm amazed that it even works at all. With the right component values, even the tune might be slightly better.
So, the result is not great at all, but it works!

(the sticky stuff is mostly glue, and not flux, to try to insulate things from fingers).
Here's a short snippet of it recorded using a microphone, then filtering with a tool called Ignite. The filtering is mostly adding some reverb, the out of tune sound is intact.
http://picosong.com/wsymx/(If you do have a listen, don't expect an enjoyable experience, only 4 buttons are slightly in tune relative to each other, others are mostly useless)
As a potential redesign, perhaps keeping a piece of the board that connects the 555 timer itself, and then having each note have its own trimmer pot and button might be a good choice. They can be added on a protoboard which would connect to the main board to shape the resistance. That would allow independent tuning of each tone. There's also the fact that these things are much more easier to do with something like Arduinos. There's also the fact that using these PCB push buttons, even if everything was in perfect tune, playing would not be easy. But it's good to keep in mind that this circuit is just for fun, and not any actual playing.