Some late baroque-period harpsichords had a selectable A: you could chose ~430, ~410, or ~390. The adjustment came from sliding the keyboards to the left or right based on which A you wanted. Supposedly A = 390 or even lower was used by the French in the renaissance, so you wanted your harpsichord to be able to accurately play historical music.
That's so low, it's more like playing the piece a three semitones lower than an alternate choice for A4.
If the piece was in A, it would be more like playing it in F# (while still using A=440).
(Of course if you did that, the "sweet-spots of 12TET and its off-notes would be different, than if you played with A=360)