@Dud le Bricoleur built another copy of this, which reminded me of this thread and that strange power supply connection, and after skimming through some 70s opamp literature I think I’ve figured it out.
Here’s the Iabc input on the CA3080:
The Iabc input (pin 5) controls the current through the differential input pair that handles the input signals (pins 2 & 3), via a transistor connected to the negative supply rail (pin 4). Note that this means that Iabc is held one diode drop above the negative rail, so if you feed it through a passive resistor you have to dimension things for CV + 10.6 V 11.3 V to get the right current (for a ±12 V supply, that is, adjust accordingly for other supplies).
Most designs work around this issue by using an active current source to drive Iabc; either a transistor configured as a common base amplifier (see e.g. the Henry BD++) or better an opamp + transistor (see e.g. Electric Druid’s vintage VCA). This lets you ignore that 11.3 V difference and think only in terms of current, but it adds some external components, and if you’re sneaky you can save one whole transistor by using one that’s already there:
By putting Iabc in the feedback loop, the incoming Icv current (CV / the input resistor) has nowhere to go other than through pin 5 (Iabc), and for that to happen the opamp needs to pull pin 4 down roughly two diode drops (D2 + internal circuitry).
Of course, the output stage uses the same supply rail but since the output is current-driven that’s not a problem as long as you drive into ground or higher (e.g. the current to voltage converter with a virtual ground used here).
You can use the same trick with the LM13700 but it has two diode drops to the rail so you need to add one more diode in series with D2 to have some margin, and of course both halves use the same supply, so you’re probably better off using an external transistor so you can use the second amplifier for something else…
(if anyone wonders about the D1 in the original schematics, it’s there to protect against reverse CV polarity).