basic experiments

A further thought to theremin as a voice. 

Normally, a theremin has -after heterodyning and demodulation- no formants. Playing a deeper or higher tone - the  time signal form is always similar, only the duration of the time periods changes. Due to a.f. filtering some phase distortions occur, but thats all of effect. 

The more ripples are within one time period the more intensive and amplitude-different overtones higher order you get. This is the key to the timbre creations. If one would interpret the harmonics maxima here as formants, the theremin had sliding formants along the pitch.

Using the derived formant-frequency formula above: In analogy to the voice of humans, these behavior would be only reachable by changing the speed of sound in air. 

The theremin comparison with human vocal voice is therefore reasonable, if we imagine the pitch high of the voice would be varied like helium speech.   

The screenshot below shows the effects of formants in a waterfall diagram. Here fixed pitch with manually varying multiple resonance maxima by a filter circuit.
 

JPascal, I've noticed that a lot of vocal researchers compensate for the harmonic rolloff of the excitation ("tilt the spectra up").  This normalizes their calculations, and it makes it so the relative levels of the formants can be read directly from the spectral humps.  It also makes some of their papers difficult to get real data from!

That is a new aspect for building a theremin: one unit only influences the timbre (tones with their harmonics in fixed ratios) and a second independent one is for formant sliding.

An interesting online tutorial about some basics of music I found in the german website http://www.lehrklaenge.de by Markus Gorski.  There are charts with time signals of instruments like this:

I am wondering if such curves can be created with theremin. 

Some experiments later. Yes, a heterodyning theremin can produce a sound similar to the above curves. And the theremin can transpose this sound in lower and higher pitches than a transverse flute for example.

The theremin can be horribly low in the frequency, deeper than the greatest tube of an organ. Here please find a vizualisation about the behavior of my experimental stuff below 100 Hz. Now it is clear, why this is called waterfall diagram...

The effect of the "sliding formants" in case of theremin versus fixed formants of classical musical instruments is visible. 

The year ends and I think about the new one. My "basic experiments" on analog theremin are largely complete. All the ingredients for a prototype are there now and I know what to do with it. A lot of time often goes into the optimization processes of the individual modules and I now have to decide on a whole configuration. The remaining challenge is to implement volume control in such a way that all the useful features and a 80 dB dynamic range are available by hand movement only.

Some specifications (goals!):
1. Less is more: Minimum parts, if ever possible. No ICs.
2. High quality: high inductive air coils, no (turnable or fixed) ferrit core coils in pitch oscillator circuits
3. Low frequency temperature drift, short time and long time (1 percent within10 to 40 centigrade)
4. 20 Hz to 2000 Hz
5. Full linearity, playable with opened / closed hand method
6. Battery operation; grounding via amplifier.

Five knobs are necessary:
1. Volume output
2. Volume calibration
3. Pitch calibration
4. Pitch timbre preselection (5)
5. Timbre continuously
optionally:
6. Formants selection pattern (5)

Now I'm dealing with a gestural ADSR unit including velocity effect. This means that if the hand moves slowly enough, the volume follows as is known. The faster the movement, the more a short attack amplitude grows up. 

I think, a proper benchmark for such a unit is Dominik's subscope. By dynamic variation (slow, initial very fast) with the volume hand a suitable ADSR result is obtained as shown here: snippets from a published youtube video, here the audio track recorded with audacity program. It is clear: A simple triggering of the signal cannot do so. 

You can learn a lot by watching Dominik's video and by doing the audio analysis like you are doing. 

I found Theremin envelope generation to be one of the toughest nuts to crack, particularly if you want to be able to "trigger" it at various distances.  It's not a trivial problem to solve.