The 1Hz to 20Hz doesn't need to be a high-fidelity sine wave, but a reasonable facsimile (although I'll be using only the positive alternation). I've been experimenting with a 4-bit R2R ladder and filtering with surprisingly good results, and I think the DAC on the 16F1827 with a sine lookup table should be fine.
The higher freqs will be just audible tones, low-pass filtered to knock off the corners.
The positive alternations of the 1Hz - 20Hz will serve as an amplitude envelope for the higher freqs. I tried simply turning them on and off at a 1Hz - 20Hz rate, in a tone-burst fashion, but it produces an objectionable "popping" audio artifact. I think the envelope will solve that.
Your DDS approach is very interesting, but I wouldn't have a clue how to implement it, and I fear it would make a bigger project out of it. I'll keep it in the back of my mind.
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