"note locations were nearly the same for both antennas. " - Gary
Once again, I think it likely that the geometry of capacitive fields may be giving different apparent results for different situations.. I think that Rich'es playing style and biasing may make the effect of a longer antenna more significant - Your fixed position box at the bottom of the antenna probably has less effect.
A longer antenna will give more angular capacitive coupling to the players arm, whereas a shorter antenna's capacitive coupling will prediminate more on the horizontal hand-antenna axis.
IMO, this usually gives better linearity for longer antennas - capacitance change as the hand approaches the antenna is somewhat less abrupt because there is a greater angular component which changes with a different law to the straight inverse-square law one would get if the hand was aproaching a plate.. Also, I think longer antennas could improve sensitivity in the far field. I am not able to formulate any maths equasions for any of this, my maths skills aint up to that, so I may be talkning out my arse...
BUT - If there is any validity in the above, then I suspect that moving the hand / arm at the bottom end of the antenna (where the arm is closer to bulk ground capacitance and therefore has less coupling significance) then the improvement in linearity is greatly reduced.
I suspect that best linearity improvement (if it exists) would be obtained if the hand / arm was moved horizontally towards the centre of the antenna. I have drawn scale diagrams and tried to determine the effects of length and position with simple maths, and I think the best results would be with an antenna of twice the total length of the outstretched arm, with the arm moving on a horizontal plane to the centre of this antenna.. The best antenna to implement linearity would be a archery bow shape with the 'string side' facing the player..
Alternatively, one could just design the theremins electronics to give usable linearity... IMO, its not primarily linearity that makes the toy impossible to play, worrying about theremini linearity is really straining at the gnat while swallowing a camel! .. ;-)
Fred.