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Melina, thank you for your note. Yes, this chorale is notated A major in the standard Riemeschneider edition, so you are entirely correct. And it could certainly be analyzed entirely in A major, but standard practice of harmonic analysis tells us to write the analysis to show the harmonic material that actually sounds. In this case the sounding harmony of the opening is E Major, as evidenced by the G natural and D# which don't belong to A Major, and the strong cadences on E major chords. The piece then moves to D major and ultimately resolves all that harmonic interest in A major. For me at least, using this method of analysis helps understanding Bach's harmonic genius. I don't think an analysis entirely in A major would explain what's really going on harmonically.
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