"I agree that, particularly in the far field, perfect linearity is likely an impossibly elusive thing." - Dewster
First, I suppose, the word "perfect" needs to be looked at briefly - "perfection" is never obtainable - so I am talking about measurable error when I talk about "perfection" - or error which impacts in any way on playability..
And here I think "elusive" is too weak a word. If one takes any given situation, and examines the capacitive "components" which influence linearity, it is (IMO) clear that a given instrument can only approach "perfect linearity" for one precise configuration - as in, all parameters which affect linearity (grounded objects, atmospherics - humidity, temperature, and anything which affects the dielectrics - AND the players body position WRT the theremin and other objects - to name just the most important) must be identical.
It is my view (based on slaving for perfection for years, and eventually going back to basics and looking at real world capacitive influences - things like the effect of the arm, angular capacitances to the antenna and ground etc) - that I was seeking unobtanium.
IMO, not only is "perfection" unobtainable in the real world, but linearity errors will always be at a level which will actually have SOME impact on playability.
This does not, IMO, mean that designing for best possible linearity is pointless - One can get damn good linearity, and perhaps inclusion of a user linearity adjustment control would go some way to correcting gross environment-induced linearity errors..
But some linearity errors will always be with us, "perfection" is a myth. And I believe that the "preview" feedback mechanism gives us the needed means to "manualy" correct for the minor linearity errors we cannot get rid of.
Fred.
ps - my interest in linearity was not originally with the theremin in mind.. my other business is in capacitive sensors for industrial application - There is a market for a long range sensor with ACTUAL linear output (as in, gives 10V at 1m, 9V at 90cm, 5V at 50cm, 1V at 10cm..) - There is more money in industry than from theremins - And I design custom sensors for clients..
There is no problem making short-range sensors for controlled applications / environments - I have made (well, actually designed - the client usually makes them - even the prototypes - as they tend to be tiny SMD units) capacitive joysticks and motor rotation decoders and compression sensors having a range up to 10cm and linear to better than 0.01mm..
But as soon as one introduces any "untargeted" capacitive "bulk" anywhere in the range of the sensor, the precise linearity is lost - Linearity correction is performed by applying computation (either analogue or digital) to the sensor output - This computation must work on rules which are based on its inputs.. If the input capacitances vary due to "unseen influences" which cannot be factored into the processing, well - the old term "Garbage in, Garbage out" applies.
With long range capacitive sensors (and theremins) there is just too much "garbage in" to get a "perfect" output. With theremins this is an inconvienience - but for a vehicle guidance system (for example), its a non-starter!
