Musical tuning
Musical tuning systems throughout the centuries have tried to find ways of dealing with this problem.  From the 16th century onwards several music theorists wrote long books about the best way to tune keyboard instruments.  They often started by tuning up a fifth and down a fifth so that these notes were perfectly in tune (e.g. C, G and F), then they would continue (tuning the D to the G and B flat to the F) until they met in the middle around F sharp.  Sometimes old organs today are tuned by such a method.  Playing in keys with very few sharps or flats (such as C, G or F) sounds very beautiful, but playing in keys with lots of sharps or flats sounds horribly out of tune.