I’ve been looking at the antenna shape, and I think it does make a difference. The antenna rod acts as a capacitor, and it’s capacitance to “ground” is going to be proportional to it’s surface area (NOT shape!) so as far as the basic tuning goes, no the shape has no interesting properties there.
But, when you bring your hand near the rod, now things change.
Only the part of the rod that is relatively near you hand, actually “sees” your hand. Difficult to express, but as you get closer, the shape of the rod makes a difference.
A flat plate twoard your hand would seem to give the worst control, and a thin edge, the best. I’m off today, to get the supplies to test an antenna made from airfoiled aluminum tubing. If I’m right, pointing the thin edge at the user will help linearize that last octave as you get close to the antenna, and not affect middle or lower ranges at all.
Rotating the tubing would allow you to adjust this to your preference.
This tubing is available in many aircraft hobby stores, in 3’ lengths, for about $5-$7, under the K+S brand name.
For the Etherwave, you’d have to use a short section of 3/8" round tubing to fit the antenna connector, and then connect that to the airfoiled tubing.
Thinking on the original design, if a larger plate or larger diameter antenna rod would have worked better, that would have been easy to do in 1930. However, if thinner rods work better, you come on a problem, in that thinner rods become more flexible. I don’t think airfoiled tubing was much of an option then. It has almost the rigidity of the larger diameter, but can be made to present a relatively small surface area to the player, in the near field.
Anyway, it’s a theory as yet. I’ll know more this afternoon.