@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 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 synchronous motors are only able to run at integer fractions of the supply frequency, so at 50 Hz you get 3000 RPM on a two-pole motor, or 1500 on a four-pole machine, or 1000 on a six-pole one...
and at 60 Hz you get 3600, 1800, 1200, 900, and so on
-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.
@Felthry Yeah, there's some little differences you get between 50 Hz and 60 Hz power supplies and now I wonder if listeners in different electrical zones just got used to songs sounding a tiny bit different. The way that there (used to?) be a little PAL speedup to US-made TV shows.
There's shows I watched in Singapore with theme songs that just sound *sluggish* when I hear them now.