. Another way of doing timing stuff would be a microcontroller of some sort, but those generally also have set clock frequencies that are pretty much entirely independent of current and voltage
All microcontrollers I know of have either crystals or RC resonators to get them going. In both cases the supply voltage doesn't matter, it just has to be enough and not too much.

Does anyone know anything about Technics turntables? The one in my avatar has a strobe light that you can use to adjust the platter speed, but I don't know if it syncs off the mains or not, and I also don't know if the mains frequency changing would cause the turntable speed to change.