GordonC asks:"What does "theremin" mean in the context of this assignment? Does it mean "any proximity controlled musical device" or specifically the sort of instrument that thereminists use?"
I think that expanding the scope of the Theremin to include "any proximity controlled musical device" would be an error.. I do not regard Epsilon as a Theremin, but perhaps could say it was a Theremin related instrument.
Could an instrument which used some mechanism other than capacitance (optical or ultrasonics, for example) and behaved like a Theremin (had pitch and volume antennas) be rightfully called a Theremin?.. ie - If one had an instrument which looked like an EW, played like an EW, and sounded like an EW, but had completely different technology, be a Theremin? hmmm.. I dont know!
If the scope of the assignment includes any means of generating notes by proximity sensing, then a polyphonic "Theremin" is not only possible, but easy..
One could buy 12 PSoC proximity evaluation boards, use the PSoCs MDACs as VCA's, Have a single pitch antenna running at HF, with a HF reference and D-Latch 'mixer', build a top octave generator using HC74193 programmable dividers*, feed the 12 top octave signals (after simple RC filtering) to the 12 proximity boards (input to the MDAC), Sum (mix) the 12 MDAC output signals to get your polyphonic output. The volume for each 'key' would be determined by proximity to the key, and the master pitch determined by proximity to the pitch antenna.. It would be like having a keyboard with the pitch bender wired to a "Theremin" CV out..
You will need to place the 'keys' reasonably far apart, and have the sensitivity quite low, to have any chance of making it playable.. might need some clever key arrangement so that musically pleasant combinations are more likely when sensing fields overlap.
*this is a clumsy way of generating a top octave - I used it before top octave ICs were available - then they were manufactured making life for electronic organ builders much easier.. Then these ICs were discontinued, and the replacements could not handle wide range frequency input (I do not know if there are any TOS ICs still made).. I have a few of these rare IC's somewhere, and if you chose this route I could send you one to simplify things - you need all the help you can get! :)
I have just realised that you dont need a TOS.. The PSoC has sufficient resourses to allow each sensor to generate its own semitone reference from the pitch oscillator input - I will advise you on this if you need help.
Which is the other way to do this - build a polyphonic analogue (or even MIDI) synth, and take a pitch controlling output to it from a proximity sensor.
Whichever way you do it - 1 month? I will still eat my hat!