I think reading sheet music would be damn hard with a theremin unless you are very well trained at, say, singing directly off the page (sight singing). on a piano, if you need to play a major third, you know that a third is two keys with three keys in between them. On the theremin you have to know what a third SOUNDS like, and that's fairly easy when playing just a third, but when playing it in the context of a song, depending where that third is in the scale and in relation to the other notes going on, could sound very different from another third. Try picking up some sheet music for a song you've never heard, try humming the melody, then go play it on the piano, and unless you are very well trained it's probably going to sound different.
Of course the issue of perfect pitch pops up. very few people can sing a middle C just off the top of their head without a relative pitch to compare. Unlike on any other instrument where a middle C is a particular key, string, fret, etc.
I guess my point is that reading sheet music on theremin is practically useless. You're better off hearing the part played on another instrument or a recording, and learning it by ear.
As far as notation for certain types of vibratos and other colourations, I think that those effects should be left up to the performer. Part of the duty of the performer is not only playing the right notes but interpreting the piece in their own way, playing it the way they think it should be played. That's part of the art of performing music. So again, notation is practically useless for the theremin.
As far as composing for the theremin, my biggest complaint is that it is monophonic. I love to sit around alone with my electric guitar, turn the lights down low, and just play what my mood demands. with polyphony you can get all sorts of different moods, with monophony it is much more difficult. Not impossible, but much more difficult to get a wide variety of textures and feelings.
Speaking of texture, the theremin lacks that too. I mean, sure you can adjust the two tone knobs on the theremin to get different textures, but not while you're playing. I've started using a rather unique distortion pedal with my theremin, and as the volume changes, the texture changes, and there's a certain spot where you can get a very vocal "wha"-like expression. Back when I got my theremin, the warranty card had a spot asking what improvements you'd like to see. I suggested they (Big Briar) come out with an expression pedal, something like a wha-wha pedal, for the theremin. That was nine years ago, still no sign of it. Even just a pedal to control the brightness or Texture knobs on the theremin would be useful. I don't think there's a single other instrument in the world that doesn't produce a varying tone as the volume and pitch change.
I do think that the theremin still has huge potential in the songs of the future, as it is still hardly well known to the masses. I've known about it most of my life, having been a Beach Boys fan since childhood, but when I play my theremin at shows with my band, the majority of the audience are completely new to it. "What the heck was that?" is a question I get frquently, or something to that effect.
As popularity grows, some more Clara Rockmore types should come out of the woodwork and really make the theremin shine, but unlike the guitar or piano, its not an instrument that just anyone can pick up and play a decent tune on in a few days. I like to say that the theremin is probably the easiest instrument in the world to play, but one of the hardest to play well.
The theremin is the ultimate "feel" instrument, right there beside the voice. I find that when I'm not in the right state of mind I just can't play the theremin worth dirt. You need to be in a really calm, focused state to play it well, and I think there's something really deep to this feeling, something vital