Dave H asks:
How many notes of a twelve tone equal tempered scale
should I be able to play by sliding my knuckles before I need to move my arm to reach the next note?
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Depending on the size and dexterity of your pitch hand, a major third or a fourth.
The most important thing to consider, however, is where you must aim for the next note you are required to play. Let's say you are playing the following notes in ASCENDING ORDER on the theremin: C, D, E, C.
Using a Rockmore style aerial fingering approach, you may be able to play your first three notes (C, D, and E) with simple knuckle extensions without changing your hand or arm position, but since you must go from your E up to the C above it, you should play your E with a closed hand which will necessitate a change of hand position for your E, even though it is only a third above the note you started on. With practice this will become quite natural and you won't have to think about it.
Beware of techniques that require thrusts of the wrist or extension of the fingers toward the pitch antenna. Many people, including some who actively promote these methods, have had all sorts of carpal tunnel and other stress injury problems as a direct result of these kinds of approaches. If you choose to experiment with any of these methods, stop if you feel any sort of pain or irritation. There is a lot of tension involved with playing in this way, and you can often hear it in the music.
The secret of good technique, regardless of the instrument you play, is RELAXATION. The best way to play, is to use the method that requires the least amount of effort to achieve the desired effect.
As you point out, tuning affects linearity (spacing of the notes). Tune so that when you stand about 20 inches from the pitch antenna, with your arms at your side, there no sound (null).
Unfortunately, the self-taught thereminist is often also the judge of his or her own success with the instrument. We end up being student, teacher and examiner rolled into one, and that just doesn't work.