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MaxQ complains: he (Howard Goodall) had sold me a pup with his statement that J.S. Bach's "The Well-Tempered Clavier" was largely responsible for our "equal temperament" system
It certainly led the way. Before any of the temperament schemes the just intonation system, which was based on the harmonic tuning, would not have allowed for the playing of any key on a keyboard instrument such as a a harpsichord or, later, a piano. In a well temperament the various keys *do have different qualities, the thirds and fifths are all slightly different. If Mozart had tried to write his music in just intonation the romp around the circle of fifths I described above, rather than leading to increased and then decreased discordance (and it wasn't really *bad, just a little off color) would have ended in a train wreck when he came back home.
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