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I'm checking BWV 1004 for a project I'm working on. I sometimes see that Anna Magdalena Bach wrote some veeeery strange flats. For example...

Bars 113 and 114 from Chanonne. Bar 113 has on the bass voice: F# G F♮, she writes F# G Fb, then on bars 113-144, highest voice has: D C# | C♮ B♮. She writes D C# | Cb B♮ (which is plain wrong by reading with our current rules).

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So I guess that sometimes she means b to "cancel" a previous # and leave it as a ♮? But I find that in some other cases she uses a ♮ to cancel previous #s. Take bar 47: G# A E F G♮ (not that she had to write the ♮, anyway... from what I can gather, JSBach and her wrote all accidentals except on repeated sounds and so if she hadn't written the ♮ that means that she would have wanted a G♮ to play anyway because that's the key signature).

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Any general rule that can be applied to figure this out?

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Yes, this seems to have been Bach's (and his family's) practice in the early part of his career. Schweitzer mentions it in his book 'Bach' (1911). I don't think anyone's come up with a plausible reason for the inconsistency. From the two examples given I might hazard that there was one rule for structural harmony notes, another for decorative ones in passage-work?

https://books.google.co.uk/books?id=A9K-1_t873kC&pg=PA386&dq=Anna+Magdalena+Bach+sharp+for+natural&hl=en&sa=X&ved=0ahUKEwjOy-_D4OHZAhUaOsAKHeoQCiUQ6AEIPzAE#v=onepage&q=Anna%20Magdalena%20Bach%20sharp%20for%20natural&f=false

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