If so, it would be quite nasty for keyboardists, who must decypher figured bass and play
the notes in real-time. With an “ambiguous” slash, they would have to decide on sight
whether to increase or lower the tone!
There are probably different schools that coexist. According to Wikipedia: (Figured bass - Wikipedia):
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A backslash raises the note (in the French system, we never use this notation).
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“More rarely, a “forward” slash through a number indicates that a pitch is to be lowered by a semitone”.
With these two rules, a slash (without forward or backward indication) could indeed mean a modified interval in either way as you mention.
Wikipedia mentions that the “+” means “augmented” pitch, but in the French system, the “+” rather means that the “sensible” note is present in the chord. In some cases, the two definitions coincide (e.g., +4) but in other cases not (+6, +7).
Back to the forward slash notation: /5 means a three-note chord B-D-F (in C major).
My guess is that one only uses slash when the sensible note is present in the chord but, for some other reason, it is impossible to write a +. A proof for this is that the two other inversions of this chord have a +:
- chord D-F-B is written “+6 over 3”
- chord F-B-D is written “6 over +4”