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This often leads to some "tweaking" of the tuning in real performances, away from equal temperament.

Here, “well-tempered” refers to Bach’s enthusiastic — and then quite edgy — pursuit of an “equal temperament,” a tuning that would allow all of the keys to be played.

In its simplest terms, just intonation means that the ratios between notes are whole numbers, rather than the irrational ratios that divide the octave in the familiar framework of equal temperament.

But it also loses in the process a richness, making me wonder what might have happened were it played in a more acoustically natural equal temperament.

He had tuned his harpsichord not to the relatively smooth, equal temperament of modern times, he explained, but to a “severe” mean-tone temperament used in the early 17th century.