I went through more topics in the forum, just to get more familiar with the matter. I saved the most relevant posts, and I think it may be a nice reference to have them all in one place, so I'll copy-paste them below, with links to the relative topic.
Hope it's useful to others too.
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http://www.thereminworld.com/Forums/T/27550/is-the-theremin-supposed-to-be-linear-etherwave
The actual version of the Etherwave Standard (if well tuned) is designed to have a almost linear range of 4 1/2 octaves, 2 1/2 above and 2 below middle C.
The problem is that pitch tuning and some other effects also affect the linearity. In order to obtain an optimal result (only valid for the Etherwave standard, other models have to be broken in a different way):
a) Do not try to play melodies in the first four weeks. You will most probably learn bad habits which will be hard to overcome later. Make only interval exercises in order to get familiar with the theremins physics.
b) Switch the theremin on but let the amplifier still off. Let the theremin warm up for about 15min so that the oscillators may stabilize. Have a coffee and a cigarillo.
c) Position yourself in front of the theremin, not in the middle, but facing the wooden part on the left of the control panel and step back as much as possible on this axis until you are able to reach the pitch rod only with an almost fully extended arm.
d) Coarse pitch tuning: adjust the pitch knob so that the theremin produces no sound when you have you right hand near your body.
e) Move your closed right hand near the pitch rod until you hear C4 (middle c). Open your right hand towards the pitch rod without moving the arm until you hear C5. This should correspond to an octave width of about 3" to 3.5".
f) Repeat the previous step with C5 and C6 as a verification.
g) Store this "default octave width" in your muscle memory. Repeat this some times with other tones and their octave in the C4 to C6 range. After some days of practicing this, we may continue and extend the pitch range:
h) Fine pitch tuning: Make an octave jump this time starting on C4 with the open hand and hear where you land. Above C3? Turn the pitch knob slightly clockwise. Below C3? Turn the pitch knob slightly counterclockwise. Repeat the jumps C5 -> C4 and C4 -> C3 and the fine pitch tuning until you get an equal octave space.
i) If you are familiar with this procedure of "octave equalization" between C5/C4 and C4/C3, make the same with C5/C4, C4/C3 and C3/C2. The lower you come, the more even slightest turns on the pitch knob will make effect. Adjust fine-tune it until you have really three equal octaves. The fourth one, C5 to C6 will then fit automatically.
Steps b, c, d and i should be repeated each time you want to play. Besides the warm-up phase, you will learn to tune your instrument then in a few seconds.
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http://www.thereminworld.com/Forums/T/33305/can-someone-give-me-an-idiot-proof-tutorial-on-how-best-to-do-an-internal-tuning-of-etherwave-standard
Here's the "Amos" technique for tuning the volume circuit:
Set the volume knob on the control panel to 3 o'clock. Stand as far to the right (pitch side) of the unit as possible, so you are away from the volume antenna. With the unit powered on and hooked up to amplification, reach over with the trimmer tool and start turning L11 through its range. Somewhere in the middle, you should hear a sound start to be audible, reach a maximum loudness, and then die off again. Turn the lug back to the point where the sound is loudest. This should put it in the correct range, to where the sound is silent when your hand approaches the antenna and them becomes louder as you draw away; additionally the Volume knob should be set correctly such that it controls not the actual volume but rather the hardness or softness of the volume curve; meaning how quickly the sound reaches maximum loudness as you draw your hand away. At the clockwise extreme it should have a brighter, sharper attack and at counterclockwise the volume should increase smoothly and slowly as you draw your hand away from the volume antenna.
Tuning the pitch circuit is really an art in itself. Roughly speaking, L5 controls the "top end" or the highest pitch you hear when you are touching the pitch antenna, and L6 controls the range, or how far from the antenna the zero point (zero beat, or silence) is located. I perform the tuning using a special wooden cabinet top with holes drilled above the variable inductors, because the presence or absence of the top influences the adjustments. It is more difficult when you have to perform the tuning with the cabinet top completely removed, and then listen to it again with the top in place to see if the tuning is still correct. Generally I find the top seems to influence the pitch downwards from what you hear with the top removed; if so in tuning it helps to "tune high" by a bit and then set the top in place to see if it falls into range. Here is my procedure.
First, listen to see if the pitch goes higher or lower as you draw your hand away from the pitch antenna. If it goes higher, adjust L5 so that the pitch descends through the zero point and then starts rising again; now it should be in the right direction. The next step is to grasp the pitch antenna and adjust L5 so that the frequency you hear is in the neighborhood of 3.8 kHz. L5 and L6 interact, so there will be a decent amount of back-and-forth between the two adjustments. Once you have the top end around 3.8 kHz, move your hand away and see where the zero point is located. It will likely be too close (too short a scale range); to adjust, stand at arm's length from the pitch antenna and reach over from the left to adjust L6. You want to adjust it so that the zero point is about an arm's length from the pitch antenna. Generally this involves turning the lug in L6 in the same direction as you adjusted L5 to get the top end.
NOTE: if the top is off the unit, you actually want to hold your right hand just about at the front edge of the wooden cabinet (~3 inches away from the pitch antenna) and adjust L6 until zero beat falls where your hand is, only 3 inches from the antenna. In my experience, this translates to about an arm's length when the top is put back on. The top kind of "stretches" the pitch field response by a large factor, which is part of why this whole tuning business is so difficult.
The first time you dial in zero beat, it will probably drive the top end higher than you wanted it to be, so go back to grasping the pitch antenna and turn L5 in the appropriate direction to get back in the neighborhood of 3.8kHz. Notice which direction it went (higher or lower) as a result of setting L6; and overshoot in the appropriate (opposite) direction to cut down on the number of times you have to go back and forth between the two adjustments.
keep track of any adjustments that you make. Add a little tape flag to the top end of your tuning tool (and only use a plastic hex tool, not metal) so that you can see the rotations that you make and so that you can reinsert the tool in the correct orientation if you must alternate between inductors. Make a sketch of your starting positions and record each change so that you leave a trail of bread crumbs to get back to where you were if necessary.
I've updated and annotated the schematic to match the 11-211J version of the main board, but if yours is a different version it will probably be close enough. You can download it from here. (Errata: C21 should be 4.7uF like C22)
If you are just trying to recenter the pitch range then L6 is probably the inductor to start with. This controls the frequency of the "fixed" oscillator, which is the one varied with the pitch knob. A minor tweak of this will usually get the zero beat recentered on the knob, although you will have to keep slipping the cover into place to really check where you are as it affects the frequencies quite a bit.
L5 adjusts the variable oscillator (the one whose frequency is influenced by the player) and this is trickier because this oscillator frequency has to be optimized with the actual resonance frequency of your particular board and antenna (the components have tolerances) . The bendable wire running above the grounded patch of aluminum foil is there to give the user a small adjustment without involving adjustment of L5 as long as it is still properly calibrated. If L5 hasn't been touched, try to leave it alone unless tuning L6 doesn't do what you need.
And finally, remember that the cover must be in place for the final evaluation, and in fact the screws will affect things a little as well. But don't replace the screws every time that you want to slip the cover back on to roughly check your tuning - you'll wear out the holes. It can be a tedious process but as you proceed you will probably find that you will learn how far off the tuning should be with the cover off for it to be correct with the cover on. I beat the system by building an identical "tuning cover" complete with embedded screws and access holes over the inductors. But even that isn't a complete solution, because different wood affects the tuning a bit.
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http://www.thereminworld.com/Forums/T/26425/does-it-matter-if-you-tune-the-etherwave-std-pitch-pots-way-in-or-way-out
You have to imagine that L5 and L6 are not pots but coils. Adjusting the slugs allows to vary their inductance by +/-10% which makes vary the frequency by +/-4.8% or +/-14kHz.
Since you hear only the frequency difference between both oscillators, there seems to be no difference between the different slug positions, but there is, since the working point of the variable oscillator has also an impact on pitch range and linearity:
The more the inductance of L5 is high (clockwise), the more the higher octaves are slightly compressed compared to the middle octave C4 to C5.
The more the inductance of L5 is high (clockwise) AND the antenna wire is far away from the aluminum foil ground plate the higher the maximum audible frequency (top of the pitch range).
The more the inductance of L5 is high (clockwise) the more the oscillator becomes unstable and more dependent from the ambient temperature. Sometimes it will even not start (no audible sound) until you touch the pitch rod for a moment, especially if the ambient temperature is low. Or the frequency will sometimes jump when you play in the lowest register.
So the first tuning principle should be to keep the inductance of L5 as low (counterclockwise) as possible and just as high as needed in order to obtain the desired highest audible frequency after having bent the wire in the right way. But be aware that the linearity will get worse with each halftone that you add.
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http://www.thereminworld.com/Forums/T/28808/adjusting-etherwave-for-pitch-linearity
You may smoothen the volume response by turning the volume knob counterclockwise. If that is not sufficient, you should slightly increase the frequency of the volume oscillator. This is done by adjusting L11. If it's the old model with the "normal" slug turn it 1/12 turn wise counterclockwise. If it's the newer variant with the hexagonal slug turn clockwise.
Close the cover after each tuning step, let the instrument warm up for a few minutes and turn the volume knob to its center (12 o'clock) position. You are done when you obtain maximum volume with your hand around 6"/15cm above the volume loop. Then check the operation of the volume knob without a hand near the volume loop by turning it slowly counterclockwise. The max volume should go down when you are around 9 O'clock. On the other side beyond 3 o'clock, the volume response should be snappy again. Then you are able to adjust it perfectly to the desired behavior within these positions.
Tuning the pitch side for best range and linearity has already been discussed in public here on TW. In one of the ESPE01 topics you will find a conversation between Thomas Grillo, Wilco Botermans and me, containing lots of practical hints from experienced "tuners" which give far better results than Moog's original tuning method.
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http://www.thereminworld.com/Forums/T/27704/is-this-how-it-should-be-tuned
Q:
Actually, today I did the tuning all over again. I made notes for myself to be able to repeat the procedure if needed. Please check if you agree 
1. Remove wooden cover. (This will alter the apparent tuning, but I compensate for it as described below.)
2. Set the Pitch control to its center position.
3. Hold antenna with one hand, and adjust L6 with the other hand until zero beat is reached.
4. Rotate L6 clockwise until the audio frequency rises from zero to approximately 4.2 kHz.
5. Let go of antenna, and pull hand away slowly until it's about 9 cm from the antenna (as far as the rightmost edge of the front panel of the instrument is from the antenna). Does the audio frequency then go down continuously to zero or some very low frequency?
6a. If yes, tuning is finished.
6b. If zero beat is reached before 9 cm, and frequency starts rising again, rotate L5 counterclockwise and start again from step 3.
6c. If zero beat is not reached at all up to 9 cm from the antenna, rotate L5 clockwise and start again from step 3.
7. Replace wooden cover. This "stretches" the intervals so that zero beat will now be reached a lot further away from the antenna than 9 cm as used above.
With this tuning method I was able to get the result I wanted.
NOTE: Step 4 differs from what the manual is saying! This makes me wonder. If I do as in the manual, i.e. rotate L6 COUNTERCLOCKWISE after finding zero beat, my tuning ends up being reversed so that pulling my hand away from the antenna will RAISE the frequency (with no zero beat in between)! (Is this a typo in the manual?)
Also, I found today that the 3 kHz recommended in the manual isn't high enough. When I use 4.2 kHz instead, I get an usable range of up to C at approx. 2.1 kHz, which I can play with my fingers still a couple of cm from the antenna, and the upper octaves aren't so compressed anymore. If I tune for 3 kHz as described in the manual, I find that I must keep my fingers very (read: inconveniently) close to the antenna to reach C at 2.1 kHz.
Thierry:
The absolute position of L5 affects range and linearity That's why I always tell people to not to touch at it!!!).The 1 or 2 top octaves remain still somewhat compressed by design, absolute linearity is not possible with the E-Standard.
The tuning method described in the manual is very basic, but it has the advantage that it will however work.
With this basic method you may get a 90% result in 10% of the time compared with more sophisticated methods which is not too bad.
When you tune it for about 3kHz when holding the pitch antenna, you match the range of older Etherwave theremins which had other linearization coils and thus were designed to have a playable range of only 2.5 octaves above middle C ~1.620kHz.
Tuning it for 4 to even 5kHz (the latter gives still a little headroom above C ~2.160kHz up to Eb or E) is ok with newer production runs where the windings of the linearization coils are divided by three in order to reduce parasitic capacitance.
Do not go higher although it seems possible with this method, you risk that a too high resonance current through the linearization coils will virtually shorten the oscillator's tank circuit and overheat the transistors to death, especially when there is a low antenna capacitance, i.e. when you walk away some meters from the instrument.
There is no typo in the manual, it just hadn't been updated when the adjustable coils (L5, L6 and L11) where changed since 2003/2004:
Older Etherwaves have Japanese coils whose cores can be turned with a normal (plastic) screwdriver and which react in the classical way: Turning clockwise increased the inductance and the frequency got lower.
Newer Etherwaves have Chinese coils whose cores require a hexagonal tool and whose reaction is reversed: Turning clockwise decreases the inductance and thus raises the frequency.
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http://thereminworld.com/forums/T/33204/seasonal-tuning-changes
Make sure you have a good earth-ground, more important than many realize.
There are two methods of re-tuning by not taking the cover off.
#1 - Send it to Thierry as the only one I trust in theremin repairs.
#2 - Use a gimmick wire like seen in the picture. This only works in one direction so you may get lucky. It is 50/50 that it will get better or worse. Dangle an eight inch looped wire at the base. Add or Trim to meet your need if it works.
Never touch L5 unless you have a scope, you will mess up pitch field linearity if not tuned to just above the antenna circuit.
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http://www.thereminworld.com/Forums/T/28555/etherwave-standard-module-installation
Hi, first thing I do prior to install, is to tune the instrument. Then I pull the board, do the install, and then I let the instrument warm up fully, then put the tuning lid on (has holes over inductor adjustments). Once she's warmed up for half an hour, I do the "quick retune", and then I roll up the sleeves, and get to work going back and forth between the L5 and L6. I'll start with L5 by giving it enough turns to go up an octave, then I go back to L6, and bring in zero beat, but back to L5, and up an octave again, and back to L6 for zero beat. I'll repeat this back-and-forth several times, with each time resulting in a higher pitch until I get at least a C or D in the correct octave range, and do a final zero beat adjustment. No scope used, just my ear. Before I started getting patient and doing the back-and-forth, I used to take L5 up into the nearly inaudible range, and then tried to get zero beat, but that resulted in even more work, so I settled on patiently doing the above method. There's also another method that works which involves touching the pitch rod and tuning for very high frequency, and then getting zero beat later.
Thierry:
Your "wet thumb" approach (without oscilloscope) is perfect for the Etherwave theremins, at least as long as you adjust for the highest tone at ~4kHz, which is 4 octaves above middle C (~260Hz). In that case you should hear a tone between the E and F above (~5kHz) when you touch the pitch antenna with one finger. Trying to go beyond that will lead to massive stability problems. Bending the wire a far as possible from the aluminum foil will not only make "high" tuning easier, it will also increase the tone spacing of the highest octave.
When I started tuning theremins (I practiced that on my own instrument), I killed the transistors of the variable pitch oscillator twice. Then I started checking for resonance currents and power dissipation keeping within reasonable limits. That way I found out with the years that your procedure will perfectly allow to remain in the safe area.
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