This paper produces a good result: http://large.stanford.edu/courses/2007/ph210/otey2/. If you game is OK sounding synthetic, I've had good results simulating a string plucked off center, decay each harmonic proportional to the frequency, then adding reverb.
A sound font or VST plug-in with appropriate licenses may be another route, but I can't speak to how difficult that would be to work with. It's on my to-do list.
I wish comparisons like this would include unicode coverage. I have code that uses the symbols, arrows, etc. to avoid needing image assets. Or some non-English text that need accented characters or the CJK glyphs.
The Cypress PSoC might be of interest. It's a combination FPGA and microcontroller, the low-end demo boards with USB programming get as low as ~$10.
Though most of what you can do with the FPGA would be covered by built-in timer/capture modules or the PICO PIO modules on other chips (though IIRC, some of the boards have analog support in the FPGA if you wanted to do real-time audio processing). I have not found a particular hobbyist use for them, only know it from my father teaching some computer engineering courses and picking since he could use the same board for digital logic and microcontroller programming.
A sound font or VST plug-in with appropriate licenses may be another route, but I can't speak to how difficult that would be to work with. It's on my to-do list.