Apologies if I'm being patronizing, as I do not know your level of background / knowledge.
What you *could* do is to control a Digital-to-Analog Converter (DAC) and synthesize an arbitrary waveform that you then feed to an amplifier. This is (basically) the same way your PC / laptop or MP3 player generates not only 'pure tones' but also play the whole gamut of music and sounds that we play through them these days:
http://en.wikipedia.org/wiki/Digital-to-analog_converter
However, since you're more interested in playing individual notes, you may be interested in waveform generator ICs, or better yet, sinewave generators (these would produce 'pure' tones probably quite similar to what you hear from most tuners). For instance, the Fairchild ML2035 is SPI-settable: you simply tell it which frequency to produce, and it outputs that frequency!
http://media.digikey.com/pdf/Data Sheets/Fairchild PDFs/ML2035.pdf
...Unfortunately, they don't seem to make it anymore, and none of the major players seem to have it in stock (as seen at
www.findchips.com) Maxim doesn't make/sell the MAX038 family anymore either, which was a far more robust IC. You may be able to find one of these if you look hard enough (or Digikey or Mouser may actually be able to quote you for some of these) Not sure if this shows the ascendancy of DACs or what, but they seem to be a dying breed these days!
About the only one of these I CAN find is the Exar ICL8038, from one vendor (though I didn't look terribly hard):
http://www.jdr.com/interact/item.asp?itemno=ICL8038CCPD
Good luck!
EDIT: This page also summarizes the three ICs I mentioned:
http://www.siliconfareast.com/waveform-gen.htm