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From what little I know about MIDI, it's not really suitable for such a task.
That's true. I worked extensively with MIDI,sequencing and SMPTE sync starting in 1986. The MIDI 1.0 spec would let you send note-on and note-off for "notes" designated 0-127. The receiving synth could then apply the note numbers to whatever sound(s) the operator chose.
By nature a Theremin is all 'swoopy' and never has perfect steps between notes (see the chorus on Beach Boy's "Good Vibrations"). MIDI additionally lets you change filters, velocity, and all sorts of computery music things. The MIDI 2.0 standard was introduced at the 2020 Winter NAMM show, but I haven't kept up.
I was around a Theremin once. Since I knew nothing about really playing it, beyond 'this hand is pitch and this hand is volume' all I could do was make strange science fiction noises.
You could define a middle note (c4 or a4) and use pitchbend-like control messages for gliding pitch control.
Much like CV, but in MIDI form. I used that on some occasions with oct/volt equipment and cv-midi interfaces.
Props for the Moog story, by the way. Legend
I used real CV (Control Voltage) once. From memory, that was one volt per octave? Didn't look it up. I used Roland CV from an SH-101 (still have it) to a Jupiter 8 (still have it, the last of the analog monsters, 8 oscillators!! {a MiniMoog has 3} Sync all 8 to one key. You'd better put on a helmet.) The proprietary stuff worked like a charm. CV desired to be what MIDI actually became: The One Interface, To Control Them All. And MIDI really was...
I was more of a MIDIOT, I knew of the cv-MIDI conversions, did not see them.
Again, and as always, the WO provides extreme fringe knowledge from our depth and breadth of experiences. And, Linkin Park videos!
It's 1 volt per octave, correct. Owning a SH101, Minimoog, Jupiter 8 (used for massive Drum'n Bass saw wave bass sounds) and probably some other models from the golden age of analog synthesis is like having legendary status regarding synths (did i say this before already?).
I had a MS20 (Korg) which was also awesome for raw bass sounds, but also bleeps and fx, sported a patch area, but i guess you also know the synth and probably own one. Korg used a different standard (oct/Hz afair) coming from their system100 modulars. I actually owned two of them (EDIT: MS20, not System 100), because i had to sell the first one because i needed the money, bought a second one later, just to sell it years after for the same reason.
We were a small community of music producers (basement class), coming from hiphop DJ and Alternative Rock bands background. Everybody owned some kind of equipment, so we threw it all together in the basement of one of our members' parents. Got in touch with macOS back then, sporting (emagic's) logic as sequencer.
This was when i played around with some legendary analog gear, before we all went digital with samplers and DAW.
Afaik MIDI was mainly useful for saving and restoring data, and man, as i remember these times, i know i did a lot of midi dumps using the younger digital synths (korg 707, roland d50, the midified, less famous Jupiters) until we could afford an Akai sampler with a 3.5" floppy drive...
I have to respect some OpSec as well, but i can tell so much, that we knew a well known geek personally, who was able to repair all the synths, guitars and electronics.
He bought one of my MS20 for getting replacement parts, while he already owned four (!) of them. He never sold a piece or instrument. Never. Visiting his house was like traveling back in synthesis time.
When i gave up making music, two decades later, with an intermittent decade of workaholism in between, i sold my 5 row modular (Doepfer) and put most of the money into Bitcoin and remaining taxes. I used to send CV via my RME audio interface's outputs before i got an eight channel cv/midi interface. It was awesome, making me able to record, edit and play back all the CV using 44,1Hz rate and 8 bit resolution from the DAW.