[coldtea]

360Hz?

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)

[pclmulqdq]

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.