@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 it also turns out that a simple 80:1 gearing gets you 45 rpm from a 60 Hz synchronous motor
-F