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== Background ==
By the end of this page, it may seem like 12-TET is clearly the best choice as well as the simplest to derive. Yet historically, it seems like it was one of the last tuning systems to be developed (outside of China), with [[#Pythagorean Tuning|Pythatgorean Pythagorean Tuning]], [[#Meantone Temperament|Meantone Temperament]], [[#Just Intonation|Just Intonation]] and [[#Well Temperament|Well Temperament]] all being adopted before 12-TET. Here we explore why these tunings were developed in such order.
Pythagorean tuning was developed in ancient Greece (~500 B.C.?), long before any common understandings of music and human perception of sound had been established. Pythagoras noted that pitches using small integer ratios produced harmonious sounds. He used the perfect fifth's 3:2 ratio to derive the entire chromatic scale by traversing the circle of fifths. This produces dissonant 3rds and at least one fifth that sounds quite out-of-tune, but this conformed with how ancient Greece composed and listened to music. There were no big orchestras filling rich harmonies - only a few reed and string instruments in addition to vocalists. Instruments had quite limited ranges compared to modern instruments such as a grand piano.