Fascinating subject!
The original Theremin , still used occasionally as a musical instrument, had two similar oscillators running at a few hundred kHz.
Both were free-running but one (A) was attached to an antenna such that the capacitance of a nearby object affected it's frequency. The other (B) was similar, but shielded to eliminate that effect, and was carefully tuned by a variable capacitance at start-up to be at exactly the same frequency as the first( without a nearby influence).
The two were multiplied together ( RF people call this mixing) and the difference frequency in the audio range extracted by a low pass filter, amplified, and fed to loudspeakers.
This was done back in the 1920's! with, of course, valves.
Drift was a serious problem, and the device had to be turned on and left for several hours with a stable power source and constant room temperature, with regular careful retuning until just before the performance...
I think you could make a modern version working on this principle with an arduino providing an auto-tune feature.
If anyone's interested I'll give it some serious thought - but I'm a bit busy with another project just now.
Give me a few days.........
regards
Allan.