In the staff, would one write enharmonic notes with # or b? Does it matter which you'd use and why?
For example: In the key of C Major, would it be better to write this passage with an A#, as it is, or Bb?
In short, what rules govern this issue?
There are a few general rules.
The reason for these enharmonics is the number of key signatures they are naturally found in. C# is found in 6 key signatures, while Db is only found in four. So, C# is the primary name for that enharmonic. D# is found in four, while Eb is found in 6. You can find a complete list here.
However, if one accidental makes a passage a lot easier to read, prefer that one over the one specified in these rules. For example, E D# E would be preferred to E Eb E♮.
Basically, these are general guidelines and have plenty of exceptions.
In addition to American Luke's answer. Each key has its own key signature, as in, Gmaj. =F# only. Gmin. has Bb and Eb. So, using your example, in key of F#, the A notes would already be sharpened by virtue of the key signature, which will contain a sharp sign on the A space (treble clef).
An important factor is that once you've started a tune using one or the other, it USUALLY makes sense (and is often easier to read) if you continue to use the same. However, technically this is not always the case. Take the tune in,say, G maj. using one # all through. To use a chord of Cmin., the E will need to be flattened, 'cos that's exactly what has happened to it. It wasn't a D that was sharpened, so in a 'sharp' key, one would have to use a flat for that note.
Another point to help you is that in ANY key, there will be a note (from its scale) for EACH letter of the musical alphabet. Thus, in spelling, for example, Bb, the notes would be Bb, C, D, Eb, F, G, A, Bb. Thus, the Eb couldn't possibly be D# as there is already a D there.Otherwise, writing on the stave would become a mess with naturals cancelling bs and #s all over.
As the OP's question has now gone on a different tilt, here is a new answer...
Taking your point of writing a C note in the key of F# : A## (or Ax) would give the enharmonic B, so wouldn't work.Cb is unnecessary, as this would make B also. The way to show C is to write C natural (can't find the qwerty key for this !), as it is a C note that you want played.If the note came from, say, an augmented 4th interval such as F# to B,augmented, the note would be shown as B#. Hope this answers the 'new' question.
Truth is, it doesn't really matter... but in general, you should write it so it is easily understood. Some helpful tips for making it easy to understand are:
If you are going up, it's easier to read a sharp (C up to D# instead of C up to Eb)
If you are going down, it's easier to read a flat (C down to Bb instead of C down to A#)
Use accidentals of the same key (key of G uses sharps, key of F uses flats)
Avoid mixing sharps and flats together (A# with Gb is awkward to read)
No unison enharmonics (don't write a B# and a C♮ in the same measure)
No reversed enharmonics (don't write a B# and a Cb in the same measure)
No inversed enharmonics (don't write a Cb and a C♮ in the same measure)
No contradicting accidentals (don't write Db and D# in the same measure)
Use the least amount of accidentals (reading A#, B, A# is easier than reading Bb, Cb, Bb)
Put every note on a letter if you can (Instead of writing C, B, Bb, G, Gb, F, Eb, C; it's better to write it as C, B, A#, G, F#, E#, D#, C because each note is assigned to a letter)
Follow music theory if it applies (sharps for augmented steps, flats for diminished steps)