Funny you mention this, I have spent the last few days trying to find out what is the current state with theremins, thinking that it would be fun to play a bit with one of those.
Aren't the waves they output close to an asymmetric sine? I presume that adding legato mode and loads of vibrato and reverb you could get close with any synth.
There are loads of circuits available and many toy boxes. I think that the main problem going completely DIY is to get the right coils. For kits, I narrowed the options to two: the Moog Etherwave:
http://www.moogmusic.com/products/ether ... n-standard
and the Paia Theremax:
http://www.paia.com/theremax.asp
The Moog one appears to be quite popular, yet £350 or so just for a bit of experimental fun is too much for me.
The Theremax kit is quite interesting, not sure if Paia is still in business?
Most of the Arduino based ones do not seem to be emulations of the real thing, but just a VCO controlled by different means without the 2nd (articulation) antenna (so they continuously output sound). Fun to build, but musically useless.
Something super cool I found was an arduino project of a midi controller similar to the Ondes Martenot to control soft synths. It is surprisingly simple. Moving the pointer controls mechanically a 10-turn pot which is then the arduino boards translates into midi pitch bend data and a switch with a piezo transducer to provide the note articulation.
http://www.scoop.it/t/arduino-geeks/p/2 ... oller-2012
Edit: some typos.