[i]I'm probably the only person here who has actually been to Saskatoon.[/i]
Well, apart from Greg Clark.
I believe Fred Mundell's long awaited modular theremin will include a voltage controlled beat frequency oscillator. (AKA a heterodyning, or theremin, oscillator.)
...
In the meantime, if you have an old guitar you don't mind taking a jigsaw to, I did encounter an interesting guitar adaptation a couple of weeks ago.
photo (http://www.flickr.com/photos/8666613@N04/4548658947/sizes/o/)
The pitch-only theremin has a very small field, so that it is only activated when the guitarist sticks out his pinkie and produces rapid exponential chirps (http://en.wikipedia.org/wiki/Chirp) (similar to sound sample in linked page, but faster) in time with his strumming.
Not a terribly interesting effect by itself (IMO) but when we ring-modulated the guitar signal against the theremin signal at my suggestion, WOW!
Bit hard to describe, not like a guitar, not like a theremin, more melodic than you might expect, but - depending on what you want - possibly not as melodic as you'd hope for.
The point is, one way to go would be to use a theremin as the second input to a ring-mod (rather than the internal oscillator that most ring-modulators have) and use it to perturb the sound from another instrument in interesting ways.