Through seveal-week research of theremin, I learn something about theremin:
There is the principle I stumbled across lately is this:
1. If you have a simple LC oscillator (one inductor, series or parallel tank) with the capacitor exposed to the environment via a standard rod “antenna”.
2. If the output of this oscillator is beating against that of a second, fixed oscillator, so that the difference frequency is zero when your hand is some fixed distance away (at the “null point”).
3. Then, no matter what you do to the value of the L, and no matter how you capacitively pad or place capacitors in series with things, as long as the two oscillators are properly nulled you will get the same number of playable octaves (difference frequency) from the arrangement.
The theremin circuit can be simplied into the model as follows:
In altering L and/or C the bulk location of the playing span will likely be higher or lower, but the number of octaves will be the same.
So we seem to be stuck with a certain number of octaves – a certain sensitivity if you will – by using a simple LC as our capacitive sensing oscillator. Where should this span be placed? Human hearing is roughly 35Hz to 16kHz. The geometric mean of this is 715Hz. So, as a very rough first goal, positioning the hand around the midpoint of the playable pitch zone should produce somewhere in the neighborhood of this pitch.
This can be easily checked if one has a single candidate LC oscillator setup on one’s bench by using a frequency counter. Note the frequency with the hand perhaps ~0.8 meter away, then note the frequency with the hand located at 1/2 this distance. To meet the above first goal the difference should be around 700Hz.
Here is a picture of the theoretical pitch response of an LC oscillator set up to do this:
On the Y axis of the graph the value 10 corresponds to ~1kHz, so the limits 5 and 14 here correspond to ~31Hz and ~16kHz respectively, or roughly the human hearing range. The straightest portions of the line represent the most linear playing regions in the pitch space.
There are definitely reasons to alter this response one way or the other, primarily to make playing in the upper or lower registers more linear and therefore easier.