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Some musicians don’t want to accommodate to 12-TET, insisting instead that we should continue to use pure intervals derived from harmonics the way God and Pythagoras intended. Harmonics-based tuning systems are collectively known as just intonation systems. This is a poetically apt term, because it implies fairness. By contrast, the implicit message of 12-TET is that life isn’t fair. Just intonation systems give you some lovely pure intervals, but you can’t change keys unless you retune all your instruments. In other world cultures, this is not necessarily a problem. Hindustani classical music uses just intonation over an omnipresent drone, so everything is always in the same “key.”
In the 16th century, Chinese and Dutch musicians independently came up with an alternative system to harmonics-based tuning, called 12-tone equal temperament, or 12-TET. 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.