IIRC, those were used to produce the eerie sound effects in the plethora of 'B' sci-fi films from the 60's.

Actually, the instrument your thinking of is the Theremin. It is also the instrument used in the Beach Boy's "Good Vibrations" that sounds like a singing voice.

I don't know how they are getting the discharges from a Tesla coil to make musical notes. The electrical pulses are high voltage/low amp "sparks" that don't have any musical sound of their own. It sounds like a preprogrammed arpeggiator and the electrical pulses are being used simply as a trigger. With each trigger the next note in line sounds. This is just a guess.