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It's not by chance 60fps. It was chosen because power grid in USA is 60Hz, so it was easy and cheap way to synchronize frames without having additional timing hardware. As for 59.97, that was a 0.1% slowdown introduced when color TV was added to prevent cross-talk in chroma channels. Weird solution but it worked out fine. Today there's no reason for sync anything with power grid but 60 is still a very convenient number as it's easily divisible by many others.
Funny effect, though - many cheap electronics (think coffee makers and microwave ovens) use the line frequency as a time base. Taking a 60Hz or 50Hz appliance and plugging it into the other causes the clock to be off.
Yup.
Huh, now that is interesting - our microwave's clock continually edges forward until it's a few minutes out from the oven clock right next to it. I wonder if that's why. I'm in the UK and as far as I know, all our appliances are too, but maybe not?
That's probably just fluctuations in the line frequency and the method for keeping time varying between the two (one might use a crystal that drifts). Being on the "wrong" frequency will have it shift by hours every day. I had a (US/60Hz origin) microwave in my apartment in Bonaire (50Hz) last year that never seemed to have the right time, and when I did the math I realized it was the frequency - it was behind by ~4 extra hours every day (50/60 x 24 hours).
Oh ok, it's usually a few minutes over the course of a week or so, so I guess it's not that! :-)
Yeah, that's just a shitty (or out of spec) time base. My Seiko watch gains 1-2 minutes a day, but it's completely mechanical so it depends on temperature and winding/mechanism tension for accuracy. There are electronic timing circuits which are resistance and capacity based, and as the resistance and capacitance of the system drift (time/age and temperature) they also drift. A crystal, made to vibrate at high frequency (piezoelectrically, iirc), will provide a much more stable time base and be accurate to seconds over many days' time.
Interesting aside - time keeping is how ships at sea used to determine where they were in the ocean. Latitude can be found from the stars, but longitude can't so it needs a time reference standard. The book, Longitude tells the story of the search and the competing methods for determining location prior to the invention of crystal/electronic time bases and modern GPS. I won't say that the storytelling is particularly gripping, but the actual path to discovery is fascinating.