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Just to follow up… I found some tiny strings used on an octave guitar. I’m waiting on the diameters to see how small they actually are.
Update… The wire will need to be about 0.0018″ in diameter so I know these will be way bigger. They would need to be drawn down to size. However:
“If it [the hairspring] is off by a mere 0.1 microns, the resulting escapement can deviate by up to three minutes a day.”
Man… 1 micron? Oh well.