Well Tempered
In a 1974 article (Hafner, Everett, "The Forty-Eight Revisited in Thirty-One",
Well Tempered Notes, November 1974, Motorola Scalatron Inc) Everett Hafner makes the fascinating observation that
each prelude and fugue in Bach's Well-Tempered Clavier, Book I, requires only twelve notes in a chain of meantone
fifths, and that the tuning for this chain may be defined in a completely regular way. Hafner's rule is that for
each key signature, we start the chain a tone (two fifths) below the major tonic associated to that signature.
Hence, for instance, C minor or E flat major, with key signature of three flats, starts the chain at D flat, a
tone below E flat.
Below is Bach's Well Tempered Clavier, Book I, in Everett's tuning, with 1/4-comma meantone as the choice of meantone. Bach seems to have preferred sharper thirds as a general rule, but there would seem to be no reason to do so in this instance.
P&F1 P&F2 P&F3 P&F4 P&F5 P&F6 P&F7 P&F8 P&F9 P&F10 P&F11 P&F12
For Book II, we find that some preludes and fugues do, and some do not, allow tuning according to Everett's rule.
Some that do can be found below:
Others work nicely with twelve notes of meantone, but only if the notes are chosen differently than what Everett's
rule gives: