AETHERPHON, global theremin family

Another thing about long antennas, as you approach, your hand is close to some of the antenna, but far from other parts.  Think of it this way.. Slice the antenna into 1 inch segments, and ar 3' distance measure the distance to your hand.  Not much difference, so the capacitance change per inch of motion is calculated by the effective area of the antenna and hand, distance, and not much else.

Now try again, 6 inches from the antenna. For a few inches length, you get the same distance, but other parts are farther away, and therefore the change in capacitance is smaller per inch than it would be if we used flat plates.  So this has a linearizing effect.

Also, there is a big difference in where the antenna coils are tuned to, but that's another hard one to express.