The French Overture had previously been written down in C minor; for the publication of 1735 Bach transposed it to B minor and made slight changes to the musical text, for example in the rhythms of the first movement. The reason for the transposition is not known: one speculation is that the aim was to increase the contrast between the two works. F major is a "flat" key and B minor is a "sharp" key, and the keynotes are related by a tritone, which is the most distant modulation. Another possible motivation is that out of the eight German note names A, B (B♭), C, D, E, F, G, H (B♮), six had already been used as keynotes in the Partitas, thus only F and H remained.[1]
The keys of the Partitas (B-flat major, C minor, A minor, D major, G major, E minor) may seem like an irregular sequence, but in fact they form a sequence of intervals going up and then down by increasing amounts: a second up (B-flat to C), a third down (C to A), a fourth up (A to D), a fifth down (D to G), and finally a sixth up (G to E).[2] The sequence continues into Clavier-Übung II with the Italian Concerto, a seventh down (E to F), and the French Ouverture, an augmented fourth up (F to B-natural). Thus the sequence of customary tonalities for 18th-century keyboard compositions is complete, extending from the first letter of his name (Bach's "home" key, B♭, in German is B) to the last letter of his name (B♮ in German is H).
