This discussion of transpositions, keyboard compasses and the presence of chromatic bass notes has been an interesting one.

As it happens, I am currently working on BWV 1015, sonata for violin and obbligato harpsichord in A Major. It is thought to have been composed in Cothen in 1717-1723 (AFAIK).

In the third movement, the final cadence is Phrygian and the last note in the left hand is a low C#, while the right hand plays a high C# (C#'''). (The violin plays e''.) I cannot help but feel that Bach is thinking: "well, I've got these notes and I'm damn well going to use them!"

Of course it is far easier, and cheaper, to experiment with keyboard ranges in harpsichord building than in organ building. And harpsichord builders presumably had just a single customer to satisfy, rather than the municipal councils, congregations and church authorities which organ builders had to deal with (just think of the politics around the temperament of the Alkmaar Schnitger). So my guess is that Bach's writing for the harpsichord does reflect actual instruments which he knew - including of course the double-manual harpsichords which he occasionally specifies.

The intended instruments for some of the organ works are a great mystery. I take the point that there was no tradition of performing pre-composed repertoire in the church service. However it is interesting that Bach's organ works are always playable by two hands and two feet (albeit sometimes with great difficulty); this is no accident - he took great care in this regard.

 

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