I have just found Thierry's posting
here (http://www.thereminworld.com/forum.asp?cmd=p&T=4277&F=1)
Thierry discusses the matter comprehensively - the bottom line being that, although the B3 will work from a DC supply >= 9V, to get stable operation you need >= 14V to allow headroom for the 78L12 regulator.
Which would be better.. inverter or 12V DC from battery? .. If I had to place a bet, I would go with 12V DC.
Best (as Thierry suggests) is two 9V batteries in series.. Or one could use a battery holder / holders which takes 12 rechargable 1.5V cells (C,AA, whatever) in series, which would give 14.4V when cells are at 1.2V each, or 18V if they are 1.5V each... (rechargable "1.5V" NiMh cells are usually less than 1.5V even if fully charged).
... Or, as TeslaTheremin says, if playing outside, why not go 'green' - one of the solar photo-electric panels designed to top-up a car battery should give enough power to drive the Theremin, even in moderate lighting.. Rig up a bunch of NiMh cells, couple of diodes and a resistor to control charging and discharging paths, and you could probably be playing all day and night(or at least until the battery in your amplifier ran out.. and this is another possible source from which you may be able to power your Theremin..)
(quite important to think about the supply for any amp you order! little point in having a battery Theremin if you need mains to run your amp!) I have this amp - DJ-Tech Visa 80 Light (http://www.djtechpro.com/product_detail.asp?category_id=46&sub_id=88&product_id=227)