Experiment with power grid may throw off your electric clock

Yes it will, but I'm not sure anyone will notice. (Your link above gave me a "404" error, but still I read about it at http://www.newser.com/article/d9o2fu...ric-clock.html)

I got the impression that there would be a slow drifting of frequency that would not be corrected. If so, then we might not be able to perceive the pitch change. If the changes were more abrupt then that would be more noticeable.

I briefly worked in a remote mining town that got all of their electricity from diesel generators in a large powerhouse. Every time one of the electric shovels in the open pit mine scooped up a large load, the towns lights would dim slightly. One day a roving company arrived to display/sell the latest Hi-Fi gear in the towns gymnasium. I had to laugh when all the record players slowed down and sped up in sync with the electric shovels load. Quartz-locked turntables were already common back then (1980) and I couldn't understand why they weren't featuring them as a selling point.

Since this appears to affect motors that expect 60 cycles per second, won't it affect turntables, etc?

It will only affect those with synchronous motors slaved to the mains. Most direct drives and higher end TTs which use their own generator will not be affected.

There is very little equipment, including electric clocks, that sync themselves to the power frequency anymore....quartz oscillators are preferred.