By the way, most of the vintage lathes are worm drive.
Furthermore, DC motors have zero torque at constant speed.@dover These two statements are false. I own a Scully lathe which is typical of what was used to make many older recordings. Its not worm drive. It employs a 1/8th horsepower syncronous motor which drives an anti-vibration coupling which then drives a transmission (which allows for shifting from 33 to 45 rpm). The transmission employs bevel gears in an oil bath but no worm drive. Its output is a shaft which drives another vibration isolation coupling; that in turn drives the platter directly, which rests on a set of carefully machined bearings (which require frequent attention).
DC motors have torque even at constant speed, so long as there is a load. This link might be helpful:
https://www.motioncontroltips.com/torque-equation/
However its a bit of a misnomer to equate a servo controlled multi-pole motor with a simple DC motor, and its also worthy of note that AC motors have a similar property of lockup being the point of highest torque output (as I'm sure you know quite well). I'm guessing that what might have been conflated/misconstrued in your comment above is the fact that when a motor has no load, its **current draw** is its lowest. But I think you'll find that how much torque it has is another matter altogether! Certainly a motor at constant speed will be making torque...
Its one thing to 'scope the waveform that is driving the servo operation, its quite another to see how the system responds to that waveform. I very much doubt that the platter speed variation can be represented by a triangle wave!