Why is there both a sharp and a natural sign in parentheses before this note?

On Andre Gedalge's Traite de la Fugue book, there are these examples, where before the F note, there is both a natural and a sharp sign, both of which are in different parentheses.

Which one do I choose? And why did the author include both of them?

(there is no key signature)

• This is the Greek translation, so is it possible it's a mistake? – Shevliaskovic Oct 17 '18 at 11:20
• What is represented by the separate systems? Different solutions for the same task? Obviously the parentheses can't be courtesy accidentals, and the only alternative I can imagine is choose either one, or alternate between all of them. If this is somehow related to a minor scale, it might be the difference between standard and harmonic minor, but example 3 looks quite chromatic. – guidot Oct 17 '18 at 11:37
• What is the context of this example? – Richard Oct 17 '18 at 11:53
• @Richard there really isn't any context. These are just examples of Subjects with their answers (the answers are on the right, not shown on the pic) – Shevliaskovic Oct 17 '18 at 11:58
• Check the header. Flat?! – Tim Oct 17 '18 at 12:54

Since these are sample fugue subjects, here is my take:

Because these are all examples of motion from scale-degree 5 up to scale-degree 1 in the key of C, they seem to be showing that, in choosing a lower neighbor to G, you can have either F or F♯. Since using F♯ in no way alters the local tonality, you are welcome to use either option.

One reason why this is important to show is that, since these subjects begin with scale-degree 5, they require tonal answers (not real answers). This lower-neighbor motion from the G will result in the same tonal answer, which (I'm guessing) is one rationale for having the examples presented in this way.

In some other fugal circumstances—like if these were countersubjects or some other extra contrapuntal material—you may want to shy away from using F♯ if you want to make it extra clear you're in tonic and not moving to the dominant.

This is usually done when a double sharp gets lowered back to a sharp.

Like for instance, when you are in a# melodic minor and the Leading Tone note gets raised from the G# in the key signature up to a Gx, now when the descending natural minor form is used now this Gx needs to go back to a G#, so one of the forms of notation for this would be a natural sign followed by a sharp sign.

You also get the notation where just a single sharp is used, but this is ever so slightly ambiguous. I do prefer the notation with the natural sign.

• But there are no previous bars, so as to imply something like that and there isn't a key signature either – Shevliaskovic Oct 17 '18 at 12:00
• It could be an excerpt of a piece where this happened and the formatting was kept. – Neil Meyer Oct 17 '18 at 12:03
• This certainly is the normal use of such a sign, although it appears there wasn't an Fx to cancel. +1. – Tim Oct 17 '18 at 12:32
• No, then they would have been together in the same parentheses. Together with the fact that there is no previous bar I see no reason to invent a preceding double sharp. It’s highly unlikely this is an excerpt since it’s part of a list of examples of moving from dominant to tonic. Even if it were an excerpt, Baroque fugue has zero instances of where it makes sense to write f double sharp just a bar before such a clear c major. – 11684 Oct 17 '18 at 16:03
• I prefer the notation with only a sharp sign. I generally think we would be better off if courtesy accidentals were never written. This kind of stuff is basically boilerplate – it's only needed because musicians expect that a removal of an accidental comes with a courtesy, thus they'll get confused when none is there, thus orchestrators will write courtesies, thus musicians expect that a removal comes with a courtesy... (But +1, since this is indeed commonly done.) – leftaroundabout Oct 17 '18 at 17:09