EM Theremin - Headphone noise

Is it normal that the headphone cable somekind of acts like an antenna? the pitch varies when i move my hands to the cable...

Naturally it's normal! It's not because it acts like an antenna, but like another grounded element in the field because the cable's shielding is connected to the internal ground of the theremin.

To minimize the side effects of that, take headphones with a long cable (5m or 15ft), let it go from the theremin's output down to the floor, then between your legs and BEHIND your back. Thus your body will act as a shield between the cable and the pitch antenna. And no extra will move in the pitch field.

You should know that playing on headphones is NOT ideal with theremins. They are much more stable and have a better sound when connected to a good amplifier which is grounded through the mains cable.