For me as a non-English native speaker it was a big task to write down all that and I think I should share that here so that others will also make use of it:
[i]diagnosing theremin problems is like diagnosing old analog RF circuits. That means that you have to verify the operation of each stage and tune it. So an oscilloscope with a minimum bandwidth of 5MHz, a frequency counter and a multimeter are required. As soon as you find that a signal is missing or tuning is not possible by going through the instructions below, stop and repair the circuit part on which you are actually working or come back to me with more detailed information, telling me at which point you do not get the wanted signal or cannot do the needed adjustment.
a) Turn all control knobs on the front panel into mid position (12 o'clock), make sure to work on a wooden table and that all metal parts (tools, cables etc.) are as far away as possible from the antennas.
b) Check if all three oscillators (fixed pitch, variable pitch, volume) are working.
- fixed pitch oscillator around Q1: Check with an oscilloscope that there is a signal of about 460kHz and at least 0.5Vpp at Pin 1 of the demodulator IC1 (MC1496)
- variable pitch oscillator around Q2: identical check at Pin 10 of the demodulator IC
- volume oscillator around Q3: identical check at the base of Q4
c) If all oscillators are working, make sure that the beat frequency is in the audible range.
- Check the frequency at Pin 1 of the demodulator with a precision frequency counter and write it down
- Check the frequency at Pin 10 of the demodulator with a precision frequency counter and adjust the white coil T2 near Q2 until f(Pin10)=f(Pin1)-800Hz
d) Then make sure that the volume CV circuit is working.
- Check the frequency at the base of Q4 with a precision frequency counter and adjust the white coil T3 near Q3 until f(bQ4)<=f(Pin1)-7kHz
- Adjust the black coil T4 near Q4 until you get 1.7V at Pin3 of IC2 (LM358) while all metallic parts, tools, hands, multimeter cables etc. are far away from the volume loop!
- Make sure that the voltage at Pin3 of IC2 decreases when you approach your hand at less than 10cm / 4 inches from the volume loop
- Adjust the nearby potentiometer to get 4.3V at Pin1 of IC2 while the voltage at Pin3 is 1.4V
e) Check the AF section.
- Recheck the frequency at Pins 1 and 10 of IC1 and make sure that there is a difference of about 500Hz - 1kHz
- Check with an oscilloscope at Pin12 of IC1 if this difference frequency of about 500Hz - 1kHz appears with at least 250mVpp
- Same check at Pins 5,6 and 7 of IC2 and at the audio output.
f) Fine-Tune the white coil T2 and eventually the "environment" knob on the back side in order to obtain an optimal pitch response.[/i]
I added in my reply that as soon as there would be a problem when going systematically through these instructions, one should stop and recontact me (or post here) telling what is not possible at which point, allowing a deeper analysis of the problem.
Happy diagnosing!