(This answer copied from another Theremax thread)
The volume antenna affected the pitch depending on the setting on coil L4.
This procedure worked for me:
After tuning the pitch oscillators, before you remove the VCA jumper, go ahead and turn the adjustment on L4 and you may find a place where L4 interacts with the pitch oscillator. Adjust L4 to a position where the pitch is stable as you move your hand to and from the volume antenna. Then, remove the jumper and tune L3 to achieve your desired volume response.
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Also, might be worth your while to go to Forums/Theremin Construction/Theremax ... The problem you are describing has happenned to others and I have been able to reproduce the problem on mine. Also, PAIA's website has some troubleshooting info (written by Scott) that discusses this issue. Hang in there -- the Theremax is not the easiest kit to build however most problems are due to the tuning of the coils, damage to the coils from overheating during soldering, cold/weak solder joints, and improperly polarized components.
So get out your schematic, your magnifying glass, and hang in there. The Theremax has a clear tone and you will enjoy it once you get it working.