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

"So does the measured or published spectrum of a real instrument have characteristic clues that indicate which peaks are best created by formants and which are best handled by the resonator block? Are you visually sorting out the fixed-frequency content that is specifically NOT harmonically related to the oscillator? Or is the RESON block set largely by ear after the formant peaks are roughed out?"  - pitts8rh

Some violin papers differentiate between the "box" or "air" resonances of the enclosed body, and the remaining resonances of the soundboard, bridge, etc.  The former are lower in frequency and more like formants, the latter higher and more densely spaced, and the decay rates of these two distinct groups are also different, giving a 2 stage decay when combined.  In one paper they use 9 bandpass biquads below 1.4kHz and a waveguide mesh for the resonances above that, but they mention that fewer biquads can still produce a realistic violin sound.  For the D-Lev we're limited to 8 2nd order state variable bandpass formants for the low end, and the resonator provides the top end resonances.  Sometimes I stick the 8th formant up in the resonator range (~3kHz), which can help to brighten things up without getting too "zingy" sounding, as the resonator is apt to do when cranked on.

The resonator has it's own 4th order HPF at its input for these sorts of blending purposes.  Placing the HPF at the input rather than the output obviously helps with overload, and since the system is linear (and if it is used in a linear fashion) it doesn't matter where we place these things.  Varying the harmonic content of the input when synthesizing, say, a drum, can markedly influence the timbre.  The "freq" knob controls the total digital delay, and so the macro spacing of the resonances in the spread, and the variability of the micro spacing can be messed with via the "tap" knob (which controls the ratio of main delay to all-pass delay), the "harm" knob (which controls the all-pass feedback), and to some degree the "reson" knob (which controls global feedback & LFP of it, and the phase of that since it is +/-).

For my analysis, I take the lowest octave and do an FFT over the whole thing with various bin sizes to roughly resolve the lower resonant peaks.  I then look at the FFT of each note in succession, to see if the harmonics "roller coaster" over them and are therefore real (a one octave gliss - a slow motion chirp, actually - would be a much better stimulus to resolve the resonances).  I dial them in to the D-Lev formant bank and do the rest by ear (a miracle hopefully occurs here).  The phase of the crossover point can produce the dip you often see in the spectra (the resonator "xmix" knob is +/-), though this is less "scientific" when using the resonator to also do pseudo-stereo, as both phases are employed and the dip will therefore only exist in one channel.  Simply not placing formants there can also produce a dip of sorts.

Also, violin resonances - and those of many other instruments - tend to be exponentially placed, and the resonator can only do variations on linear spacing.  But using the resonator mainly for the high end seems to work OK, as the ear doesn't seem to be as discerning up there.

Porta Potty

I wonder if I'm obsessing over portability too much.

The original lectern-type Theremin wasn't very portable.  The EW, Subscope, and Theremini are all quite portable.  The EWPro is somewhere in the middle.  Much of the portability is enabled via removable antennae, and being a plate man (for better or for worse) I'm struggling with how to implement that.  But maybe it's not an entirely worthwhile goal?  I mean, of course everyone would prefer to show up at a gig with their 8 oz piccolo in a 6" case tucked under their arm rather than lugging a 300 lb Hammond B3 on a dolly.  But within a single instrument category, portability often negatively impacts playability and quality of sound.  Like almost no one wants to play a highly portable, lightweight (< 30 lbs) digital piano as their main instrument at home, as the keys and sound inevitably kinda suck when compared to lowly upright.  And even instruments which are highly portable in the first place, such as guitar, tend to suffer when pared down to their "travel" variants.

And then there's the case.  You can play quite beautiful and fragile instruments just about anywhere you can take them as long as they are packed well for the travel.  But cases add to the volume and mass, thus ironically negatively impacting the very portability they facilitate.  If your particular instrument can incorporate a travel case as the outside of the instrument, then this penalty can be somewhat mitigated.  But then the audience will be looking at your ugly travel case rather than your beautiful instrument, which might tempt you to get a case for the case to keep it from getting any uglier than it already is, and you perversely wind up schlepping an ugly 100 lb double case Theremin all over town, and who wants that?

And, case or no case, how do you safely transport the stand, power supply, antennae, and other stuff you'll need for a gig?  If the case is built-in then these items either need to fit inside the lid or something - probably making the whole thing quite a bit larger and possibly impacting the basic ergonomics - or be packed separately.

My current thoughts are that if my Theremin (sans accessories) ends up anywhere near the size and weight of an acoustic guitar then it is sufficiently portable, and at that point I should just stop thinking about it (unless someone wants or needs something special). 

I wish wood wasn't so heavy and so capacitive.

I believe mic stand(s) will take most of space and weight.

For an RF analog engineer with no DSP background, a good deal of what I just read from your previous post above sounded like the muted-trumpet "teacher talk" from Charlie Brown .  If I can distill this down it sounds like you:

1)  set the formants for obvious FFT (or realtime spectrum analyzer?) envelope peaks, then
2)  twiddle the RESON knobs until it sounds good. Check?

Actually this morning I was having fun working on the cello preset.  All of this time while playing the D-Lev I've been sitting right next to my old Kurzweil K2500 synth, which is in the same rack as the other processors but has no keyboard hooked up.  I put my little Axiom 25(?) keyboard on top of my monitor speakers, and now I can dial up any of the orchestral instruments to A-B compare with the theremin.  I think it's going to help a lot for maintaining a reference. The instruments aren't necessarily the greatest but in their time they were considered pretty sweet.  Not every note is an individual sample (samples are shared over a few keys) but having a variety of samples over the entire instrument range helps to give a better sense of the timbre.  My first preset mod based on this synthesizer reference has the resonance cranked quite a bit.

It's nice to have everything working again.  The only thing I don't have these days is time to play around with it. 

"I wonder if I'm obsessing over portability too much." - Dewster

IMO, yes.  I know you are drawn to the Tour design for your own theremin (and I still hope to help you with that!), but to get on with things I would find a standard commercially available case that is large enough to contain a conventional (fragile) design with custom cut foam to protect the parts. Like the EW Pro, but hopefully a bit smaller.  Those that need it could buy it at cost; those that don't could live with a zippered padded bag or the cardboard box it came in.

I think it would be interesting to design a "Transformer" travel case that deploys into an operational theremin for a special project, but I can't imagine that it would have much stage appeal, especially if it looked like a a flute case mounted on a stand.  

I would plan for a separate case and concentrate now on what goes inside.

"For an RF analog engineer with no DSP background, a good deal of what I just read from your previous post above sounded like the muted-trumpet "teacher talk" from Charlie Brown ."  - pitts8rh

I resemble that statement!  I'm a weak analog / digital guy with no previous DSP background! ;-)  Like anything, I think a lot of it comes clear once you read a bunch of papers and try a bunch of stuff out.  The "waveguide mesh" is just a fancy, more complicated resonator, with a pedigree in terms of physical modelling (always a handy thing to be able to fall back on reality, however tenuous that grounding actually is) but I'm not casting aspersions or anything, it's a great paper from a fantastic researcher, and I'm sure they didn't have to play around with settings nearly as much as I have to in order to get it to sound OK.

"If I can distill this down it sounds like you:
1)  set the formants for obvious FFT (or realtime spectrum analyzer?) envelope peaks, then
2)  twiddle the RESON knobs until it sounds good. Check?"

Exactly (static FFT in my case).

"Actually this morning I was having fun working on the cello preset.  All of this time while playing the D-Lev I've been sitting right next to my old Kurzweil K2500 synth, which is in the same rack as the other processors but has no keyboard hooked up.  I put my little Axiom 25(?) keyboard on top of my monitor speakers, and now I can dial up any of the orchestral instruments to A-B compare with the theremin.  I think it's going to help a lot for maintaining a reference."

There's nothing like a ready reference for your ears when adjusting these things!  Some of my best violin tweaking took place when one of my wife's students brought her violin over to play during her lesson.  I sometimes tweak when playing along with other fiddles and such in recordings.  They say audio memory is the worst and I'm a believer.

"My first preset mod based on this synthesizer reference has the resonance cranked quite a bit."

The formant "reso" knobs interact with the formant gain (higher reso = higher gain) so there's some back and forth that might have to go on.  Try matching a note in each octave, both spectrally and audibly, sometimes that's the key.

"I would plan for a separate case and concentrate now on what goes inside."

Yah, that's where I'm finding myself.

More Resonance

I think my violin and viola needed more resonance (violin, followed by viola): [MP3].  If you push the resonance too high you get "zinging" sounds and a weird room-like ambiance.

The resonance parameter is the thing that I too have been cranking up, mainly because the Kurzweil string samples have a very strong resonance, and the original theremin cello preset sounds quite flat in comparison.  They also have some built-in ambience that is not a function of the effects block in the synth, so the samples must have been made in a fairly reflective environment. For the cello I've also played with taps and freq as well. And I've set a little reverb on the theremin to help match the acoustic environment of the samples.

The thing I absolutely love about the D-Lev (aside from the customizable pitch and volume fields) is the way that you can start with something like a cello or violin preset and with a few minor changes you can fill up a bank of preset slots with variations, and they all sound great! With my Etherwave and Subscope I would have very narrow windows of settings that sounded decent without going all chipmunky with increasing pitch, but the D-Lev has none of those problems.  I used to think it would be a chore to fill up 99 preset slots, but I could probably do it with just the string variations.  That inharmonic resonator is just incredible.  I'm gushing at the moment, but the last couple of playing sessions have been very productive, not from practice standpoint but for tweaking the sounds.

Anyway, I really need to set up my laptop spectrum analyzer to understand what I'm doing with the oscillators and formants.  No amount of verbal explanation is as effective as having that instant feedback.

I wish I understood more about synthesizing real musical instruments, and I wish I could play better.  Those resonances act like magnifying lenses for your pitch errors.

It's an awesome machine, young man!

"With my Etherwave and Subscope I would have very narrow windows of settings that sounded decent without going all chipmunky with increasing pitch, but the D-Lev has none of those problems."  - pitts8rh

The harsh reality of timbre control via fixed waveform is that just about everything outside of none, odd, or all harmonics (or some combination of these) will meow.  This is why I have almost no desire to experiment with drawing waveforms or anything like that.  Most resonant instruments have fixed resonances (not ones that track the pitch), and it's most straightforward to just state variable filter them into existence.

"That inharmonic resonator is just incredible."

I'm sooo glad I found the paper describing how to build it (though I've altered things a bit in the topology and controls).  If not for the resonator I'd need gobs more formants.  You can kind of see why the Ondes Martinot has a gong antenna with strings and such.

"young man!"

Quick question:

Is there a way of controlling the oscillator's odd harmonic content with pitch?

My cello setup wants more odd at low pitches but at higher pitches it then starts sounding a little woodwindy.