I don't know much about theremins, and wondered about this: given a constant volume, I would like to know if I can produce the same note with different hand positions or if all notes have a specific/unique combination of hand positions.
In other words: can I correctly deduce the pitch hand position from the sound (frequency) of a note only? What is the degree of uncertainty?
In general, the answer is no. When you turn on a theremin, the first thing you have to do is "tune" it. There will usually be object close enough to trigger the pitch antenna, and less often the volume antenna. Also, you want to pick the place where you want to stand. Once you've got that, you adjust the volume and frequency knobs to that you get the maximum range of both (usually) and it plays the right notes when your hand is in the positions that your muscle memory has developed for those notes.
Depending on your level of experience and the quality of the frequency control, this can be a challenge. Two different possible situations add to the reproducibility of theremin hand positions. First, if you keep a theremin in the same place all the time, never move any objects that are near it, and perhaps mark the place on the floor where you stand, then every day you should be able to put your hand in the same place to get the same pitch. Second, if you are very good at the theremin and you have developed the muscle memory to know where you want your hand to be for each pitch and you are also skilled at adjusting the frequency knob to calibrate it to make it in spec.
Even given one of the above two situations, the calibration points that one theremin player will use that they are used to will not necessarily be the ones that a different player will use. Not only that, your body has an effect on the pitch antenna, and everyone has a different body. I would expect that the hand positions of two different theremin players who have been trained by the same person and who are very good at calibrating their theremins to still vary in distance by 1" - 5" (or 2 - 10 cm) for the same note.
Yes and no. For theramins, pitch is determined by the distance of your hand relative to the rod. The distance is absolute, so if you maintain the exact same distance, you can rotate 360 degrees around the rod without changing.
For this reason, however, this is the extent theramins can provide “alternate fingerings”.
Pitch is controlled by the overall hand (and arm and body) position. You can move the whole hand in and out, or you can use set hand positions plus finger movement. The latter is a useful technique, but many different systems could be devised. For a given pitch, a certain 'amount of body' must be detected by the aerial. There will be many ways of contriving this.
It may be that there's a 'classical' technique, shared by expert theremin players, where you could make deductions from just looking at the hand positions. But I wouldn't rely on every theremin player using it!
