Let's Design and Build a (mostly) Digital Theremin!

Anca!

An absolutely mesmerizing piece arranged and played by Anca Bold Martin (who is no slouch at video editing either!):

Heterodyning Timbre?

I've been asked about the mechanisms behind heterodyning timbre, but I'm no expert, and it feels like a rather elusive subject.  I wasn't sure whether to ask this on the analog or digital thread, but since I'm more involved with synthesizing the effect than the actual cause of it I'll post it here.  Because timbre generation is completely disconnected from fields generation in the D-Lev, I've never had the need to formally sit down and try to figure this all out in simulation / spreadsheet fashion.  But it's a good question, and if I ever write a book I'll need to delve into it more deeply.

I've analyzed the audio of several analog Theremins and noticed that on most there is a suppression of a region of the harmonics that behaves somewhat like an imperfectly tracking notch filter.  For example, Rob Schwimmer's Moog Melodia when playing a D4 at 293 Hz the 4th harmonic at 1173 Hz is suppressed (as well as the second harmonic a bit).  But when playing an F5 at 679 Hz the 3rd harmonic at 2090 Hz is suppressed.  I'm pretty sure this is due to the frequency ratios and waveforms presented to the mixer, and how the mixer mangles them.  When playing very low notes there is no harmonic dip, but there seems to be a downward drooping cut-off around 2kHz.  The question is: what exactly causes these features, and how does the math work?

Other than the above rather subtle effect, the coupling of the oscillators in the bass region can provide much more timbre variation with pitch, which is why oscillator buffering (i.e. YAEWSBM and the like) is a meowing timbre killer, and why the EPro timbre is so static (IMO).  And of course there is the upper heterodyne image rejection low pass filter, as well as audio filter & tone control circuits generally suppressing the brightness.

Timbre variation with pitch is important to add variety, but IMO timbre variation with volume is more important.  The Theremins that tend to get described as "expressive" have this, indeed virtually all musical instruments share this rather expected and therefore important feature.

I believe, non-ideal (non-sine) VFO and FFO, multiplied by non-ideal mixer cause all the effects.

"I believe, non-ideal (non-sine) VFO and FFO, multiplied by non-ideal mixer cause all the effects."  - Buggins

I agree, but what mechanism exactly causes the notch?  And how might one predict where it will end up for given VFO & FFO frequencies?

Filter Order

The other day I was trying to produce a preset of a particular analog Theremin, and it needed more nuanced filtering than the D-Lev could produce in a straightforward fashion.  These types of presets don't require the noise generator, so much like the pitch preview section having modes that turn it into a 4th oscillator, I decided to optionally co-opt the noise EQ (bass and treble controls) and multi-mode filter (2nd & 4th order low/band/high pass and notch) for the oscillator section.  To make it a fairly natural seeming thing, the switch in of the oscillator takes place when the noise is fully switched out, i.e. when the nois knob on the NOISE page is 0.  

It all worked out quite simply, just 3 additional lines of assembly, mainly because both multi-mode filters and the noise source and EQ are all handled by a single thread (4).  In this mode the processing gauntlet is: 

  Osc => EQ => Filter => EQ => Filter => Formant bank => Resonator => out

The two multi-mode filters each have independent volume and pitch modulation of the cutoff frequency, as do the 4 pairs of formant (bandpass) filters.  Each EQ is a pair of 2nd order filters, so the total order can add up to 4 + 4 + 4 + 8 = 20, and the resonator can provide a bunch more.  You can get a lot done with that much filtering under the hood!  Afterward the mod I was able to dial in the preset rather easily. 

All You Need Is Q?

RC oscillators are sensitive to direct variation in C, whereas LC oscillators are sensitive to sqrt(C).  Sensitivity by itself is good for digital resolution, but there's instability to be considered too, and depending on the characteristics you may be able to trade one for the other to some degree via averaging.  I've been doing web searches for "high stability RC oscillator" etc. with no real luck.  One thing that seems pretty common to stability is Q or quality factor, e.g. atomic clocks have an astronomical Q, crystal oscillator Q is in the millions, LC oscillator Q with a good coil can be in the hundreds.  Q here refers to how many cycles the oscillating system will keep going without external stimulus, how long it takes to run down - the longer the better the intrinsic timekeeper it is, which makes sense.

So it seems to me that a high stability RC oscillator could be made with a capacitor and some form of active inductor, itself formed around a capacitor, such as a gyrator or second order filter.  It wouldn't be like a real coil in the sense that it wouldn't support a voltage gain that exceeds the supply voltage.  Really high Q might be difficult, and it would most likely have more noise than a real coil due to the resistors and active components that make it up.  But it wouldn't be susceptible to external magnetic fields, and it would be fairly trivial to make it do relatively large inductance values.  It's this last feature that is most appealing to me, as obtaining coils for Theremins is getting harder all the time.

Katica!

Franz Schubert's Ave Maria on Roger's P3:

Grégoire!

With Soprano Dima Bawab performing Pergolesi’s Stabat Mater Dolorosa:

Beautiful !

I recognize the Grand théâtre de la place du Ralliement in Angers (France) and the cathedral Saint-Maurice behind. 

Is this strange theremin a D-Lev ?
And what is the accompanying instrument ?

Edit : got my answers from Gregoire's YouTube channel

https://www.youtube.com/watch?v=kxbHf7pnraM

"Is this strange theremin a D-Lev ?"  - André

Yes, he extended the pitch box with a longer ribbon cable.  Someone needs to make him a proper case - he is requesting this in the YT text, but I'm unfortunately not so good at making pretty stage enclosures.