In my distant past, I used to teach music in college (ear training, theory & composition) and it occurs to me that the theremin is a perfect tool for aiding in training the ear. Every college and even high school should have at least one as a means to help students match pitch and develop their sense of relative pitch. Many students have a hard time hearing they are singing in tune. The theremin provides an excellent medium for translating ones voice into an external instrument. In fact, after playing with it now for a month I can't think of another instrument that comes as close to simulating the art of singing as the theremin. When playing you really do get the feel that you are singing. (If Moog works out the kinks in that Theremini - that would really be a perfect tool as it's inexpensive and portable and for this application, sounding or playing exactly like a theremin is not really the most important consideration).
I'm going to talk to a professor friend (who is a world renown expert in aural theory and musical pedagogy) about this (we co-authored an Anthology of Sight-Singing used in colleges today). I'm very interested in seeing if we can put together a little experiment to see how well my theory here holds water. I'm sure I'm not the first to think of this. Have to do a bit more research.
I do see the theremin as a training tool in other areas. This one is interesting.
http://engineering.missouri.edu/2013/01/teaching-tool-instrumental-in-revamped-introduction-course/
In a related topic, I've been thinking: Is it better to have perfect pitch or a good sense of relative pitch when playing the theremin - or is it irrelevant. I'd be interested hearing people's views on that. Since I don't have perfect pitch my view could be skewed (thinking people with perfect pitch may actually have a harder time as actual pitch moves each time you calibrate the darned thing).