WARNING: This post is not for those whose primary interest is playing the slow music of long dead composers (admittedly my original goal, but I kind of had a paradigm shift after hearing Gordon's music so I'm diverging in two directions now).
It's clear that the full potential of the Theremini is not unlocked until you start applying various kinds of MIDI control as virtually every parameter is controllable and you also can access a number of waveforms and other control features you can't from the front panel or app. (Perhaps Moog will unlock some of this hidden potential in future app and firmware updates, but through MIDI you can do things now you just can't in any other way on the Theremini).
Let's remember the Theremini is a Theremin on the front end and a wavetable-based synthesizer on the back end. It's controller was meant to be the antennas, so Moog does not support (at least yet) the ability to send MIDI note data. You can not play it through MIDI like a normal synth from a sequencer or notation program. However, what Moog did do is allow the user to control transposition from -64 to +63 semitones. Well guess what? You can use this feature to play the Thermeini like a synth - with one big difference. If you "program it to play a melody", the antennas are still active and have their normal control. This can create what I call a second order melodic effect or perhaps you could think of it as not frequency modulation but melodic modulation.
OK, let's start with how you can use your trusty MIDI sequencer to play the Theremini. The concept is that we'll place a fixed object in the pitch field (I used a mic stand) to play a constant note. Then you can create a MIDI file of notes to play. The MIDI notes themselves have absolutely no effect on pitch. Pitch is being generated by the pitch antenna on the Theremini. So in the sequencer, I can create a set of repeated pitches on whatever rhythm I like. In this case I used the pitch content (but not from MIDI notes) from Bach's Cello Prelude #1 in G Major (though I was not at all concerned about what key I was going to wind up in). The base key was totally based on whatever pitch that mic stand was playing.
Here's the trick. In the sequencer I create a MIDI continuous controller lane (on CC102 = Theremini Transposition) and I tagged a flat CC102 value for the duration of each note coinciding on the NOTE On message. Because MIDI goes from 0..127 and the transposition maps -64..+63 semitones, I started my base key on CC102=64. This puts me starting at a point where I have lots of transposition headroom above and below the starting pitch. So if CC102=64 maps to a G, then 65 would be a G#, 66 an A, 63 an F#, 62 an F, etc. Then I did the hard part of putting in a CC102 value by hand in the sequencer for each of the notes of the piece (arrgh!). Because the Theremini was set to play a constant note, when I played back the sequencer, the transposition changes change pitch as desired. The pitch is really still the same on the Theremini antenna, but the digital transpose function creates the change in pitch that basically allows me to play the piece.
I can also create a controller lane for volume and add a dynamic shape to the piece. And if I wanted to I could add a shape to control filter resonance, change in patch, whatever I like if I want to create really nice dynamic changes in sound. The only drawback is repeated notes because there is no envelope I can set for each note (as Gordon pointed out). So if say CC=66 gets repeated three times because Bach repeated notes, the Thermeini is really still playing the original pitch and transposition is not changing for that time frame - hence you get a held tone, not a repeated tone. I would have to go in and bring the volume down to 0 before the end of the note and then back up again for the next note to simulate a repeated note. But that's not my intent here.
So here's the result - using the "North Pole" patch and some reverb of various kinds in addition to adding a Waves octave doubler.
Theremini Playing Bach through Sequencer
Now, you should be asking: "What in the world does any of this have to do with theremins or Theremin World as you have only treated the Theremini like a synthesizer and you could have done it much better if you just used a Little Phatty (or synth du jour) that processes MIDI note data". And there's the rub. I never actually intended to play the piece as is. Sorry Herr Bach!
I'm now going to lose that mic stand as it was only there so I could easily test that I programmed the right notes. Now when I play back my sequencer and as that Bach piece spews out, I can play the theremin as intended and all those transpositions will take on a new meaning as they shift to the pitch I'm really playing. But I won't be playing notes based on my normal use of that pitch and volume antenna. The "notes" that will be played will actually be the Bach transpositions applied to the current pitch. As I alter pitch I will in essence be modulating that Bach piece in various ways. Bach in this case becomes the sound source.
Theremini Melodic Modulation on Bach
Now of course I don't have to use Bach as the transposition material (actually more original not to). I could draw in numerous CC102 transposition shapes in the sequencer to create a world of different glides, slides, (and as Gordon points arpeggios) etc. Also my transpositions here are all moving slowly to match the notes, but because this is continuous MIDI controller data I can create all kinds of very quickly changing transpositions on single notes that will totally change the sound of the original. Also I can dynamically control pitch correction and create all kinds of interesting microtonally shifting patterns as I play.
So for those that are interested in coaxing more potential out of the Theremini, read the end of the manual where they discuss the MIDI parameters and have some fun!