@Felthry Hand-cranked records of time found around 70-80 rpm made for decent fidelity. When records got standardized there was a common 3600 rpm motor on the market, and a 46:1 gear that was common, and that gives you 78.26 rpm and there, that's a standard.
I don't know how 33 1/3 got picked for the next speed, but suppose there was some similar common motor/gearing pair available.
@Austin_Dern it'd be a 108:1 gearing on a similar synchronous motor to get 33⅓ exactly
and 108 is conveniently easy to break down into multiple gear stages, you could even go five stages with 2:1, 2:1, 3:1, 3:1, 3:1 though i imagine something like 9:1, 12:1 or 3:1, 36:1 would have been more likely if they did that
-F
@Austin_Dern oh 33⅓ also works out nicely at 50 Hz, since the same motor on 50 Hz power would give you 3000 rpm, and you can gear that down to 33⅓ rpm with a 90:1 gearing
-F
@Austin_Dern to control the speed of a synchronous motor, you have to change the frequency of the supply voltage, which certainly can't be done with 1940s tech though it's easy today
other types of motor don't work for this because their speed is variable; induction motors and DC motors both slow down when they have more load on them and you can't control the load
-F
@Felthry Yeah, there'd really be no practical way to make a 'universal' record player that kept to a constant speed, not unless you also swapped out a gear inside. Probably easier to just accept stuff sounds a little different on different sides of the Atlantic.