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If you wanted to use a pre-constructed pitch only theremin for testing and linearity demonstrations I would use the small $80 pre-built board by Chuck Collins.

With Chucks Theremaniac board you would raise the operating frequency to 900 kHz and it should be able to achieve just over three linear octaves. This is the number Clara Rockmore was most comfortable with. Chuck's pitch only theremin board layout generates a very clean sine wave.

When I originally wound my own oscillator coils with 30 gauge enameled wire as seen in this Ultimate 2b theremin constructed by Dominik, I could not get much more than three linear octaves.

Visit Dominik's webpage and listen to his sound samples in the upper left corner of his page. He is a master theremin builder today and uses built in mechanical spring reverbs for a nice affect.


Observation:

I upgraded my Ultimate 2b pitch oscillators from 30 gauge wire on an air core coil to 22 gauge wire on a ferrite core in my later RS Illusion theremin design. Using two heavy gauge 100 uh choke/coils per oscillator, to my surprise, it expanded the pitch field out to just over five linear octaves, without any other circuit change. A five octave linear spread over a 18" to 20" pitch field distance is an ideal number for arm reach and playing distance.

My guess is the heaver 22 gauge enamel coated wire on a ferrite core improved the circuit Q factor considerably which in turn delivered more current into the tuned antenna. Here is a close up view of my RS Illusion theremin board showing my pitch oscillator split coils which generate 5 linear octaves. heavy gauge.

The oscillator split coils I use in my RS Illusion theremin are not shielded and so I must place the pitch and fixed oscillators farther apart. This is why my two oscillators are on separate boards. The two oscillators interacting within close proximity to one another can cause unwanted wave shapes or distortion in the audio, sometimes good but most of the time very bad.

1. From observation I believe ideal theremin linearity is a direct response to the use of high Q oscillators and a Low Q Antenna.

2. The amount of energy available to the pitch antenna determines the number of linear octaves. In a Lev Antenna pitch field there are no non-linear octaves just more or less octaves. Normally this is 3 to 7 octaves.

Here is one of several interesting letters I received from a dear friend of Lev's. It hints at how he had trouble finding parts in his later years of experimenting in Moscow. Lev Sergeyevich is not often thought of as experimenting with transistor circuits and ferrite coils but without doubt he did. He experimented until his death in 1993.

Below are some important behaviors worth mentioning.

Note 1: Fine tuning for the Null point on a transistorized heterodyne theremin can be accomplished by slightly varying the circuit current using a variable resistor on the emitter or base of the oscillators of  a bi-polar transistor. This is manipulating the junction capacitance of the transistor similar to a variactor diode which controls the oscillator frequency. 

Note 2: Variable caps should be avoided in a theremins pitch or fixed oscillator to avoid extra temperature drift issues caused from room temperature fluctuations.

Note 3: In a transistorized theremin it is important to use two oscillator transistors that come from the same manufactures batch # so they have very similar characteristics. Most thermal drift develops from the mismatch here. To minimize thermal drift you want the two oscillator transistors to behave like identical twins.

Note 4: There "are not" extra non linear octaves in the perfectly linear pitch field, the linear octaves exist between the Null point and the pitch antenna. The pitch field spreads out wider adjusting the pitch tuning knob as usual but it still remains linear. In the phrase "three linear octaves", linear means they line up in a relationship like piano keys on a musical scale. The notes or intervals are all the same width right up next to the antenna.

Linearity gives you precision note control of the theremin. I adjust my Theremin to play one octave lower with my hand closed which gives me a predictable one octave higher jump snapping my fingers open. One octave of notes is held in the fingers of my hand. Here is an old sound sample from my tube theremin Linearity Test.mp3 (200k)

Master those seven and play with the same accuracy anywhere in the theremin playing field. Similar to the Carolina Eyck method. Your pitch adjuster allows you to narrow or widen the octave width to match the size of your hand for accurate aerial fingering.