Bach’s correspondence shows that he was notoriously finicky when it came to keyboard tuning. One reason for this was that older tuning methods—called “mean-tone” tunings—tended to leave the more difficult and lesser-used keys out of tune. Modern “equal temperament,” however, slightly compromises the mathematical perfection of the intervals in order to make all of the keys equivalent. Bach’s strategic use of all 24 major and minor keys (even the really weird ones, like C# major), would thus sound more in tune on an equal-tempered instrument. However, while Bach’s term “well-tempered” probably referred to something more like modern temperament, it probably wasn’t quite all the way there yet! Tiny variations continued to give different keys slightly different sounds. These were noticed and appreciated by listeners, including Bach himself!