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Over the past few hundred years, Western Europeans gradually figured out an alternative system to harmonics-based tuning, called 12-tone equal temperament (12-TET for short). It’s the system that the entire Western world uses today. The idea behind 12-TET is to have everything be pretty much in tune, which you accomplish by having everything be a little bit out of tune. Is this a worthwhile compromise? Let’s do the math and find out. Contrary to