Capital Roman numerals depict major and lower case depict minor.Playing this from the dots, to me now sounds like Amin. moving through C dom.7th to Dmin. If this is what the composer intended, the A# needs to be Bb, the flattened 7th of C.
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TimOct 11 '13 at 18:15

You were right, it was actually vi. Is it ambiguous now?
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JovitoOct 11 '13 at 18:20

4 Answers
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Most accidentals should be of the type found in the key signature. For example, in G Major, use G# -- not Ab. In F# major, use A# instead of Bb.

If the accidental is in a chromatic scale, use sharps ascending and flats descending

In any other scale, use the accidental that typically goes with the scale. For example, Bb and Eb in a Bb major scale instead of A# and D#.

In a chord, use the normal accidentals so it is recognizable. For example, Eb in a Cm chord instead of D#. In the example from the question, prefer A#. An A# dim chord is usually spelled A# C E. A Bb dim chord is usually spelled Bb Dbb Fb, which is a lot more unusual than an A# dim chord.A musician will bore easily recognize A# dim.

Of the enharmonics, prefer C#, Eb, F#, Ab, and Bb when no other rules apply. For example, in C major, prefer F# instead of Gb. This is assuming no other rules apply and neither accidental is easier to read than the other.

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.

Great answer here - just want to add (at the risk of confusing someone) it's also important to keep in mind the nature of the instrument you're writing for (saxes are more used to seeing sharps / brass are more used to seeing flats.) A very small but important point.
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jjmusicnotesOct 11 '13 at 0:35

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Also, if you're writing music more on the edges of tonality, you want to avoid mixing flats and sharps within the same chord or measure. Stick to one type and it'll be easier for the player to read.
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NReilingh♦Oct 11 '13 at 3:17

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Great answer. The basic philosophy is that you want to use the one that will be easiest for the musician to read. These rules should help you get there.
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Ben MillerOct 11 '13 at 3:43

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@Tim - because of the transposition, saxes, though pitched in Bb and Eb, tend to be put into sharp keys - especially Eb saxes. Brass players are comfortable reading flats from the band world where Bb, Eb, and Ab are the "standard" band keys; even Db is quite comfortable as well. If you want to hear something scary, ask a beginning band to play in E major.
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jjmusicnotesOct 11 '13 at 14:07

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Another thing to note is on chromatic instruments which have parts associated with particular pitches (e.g. organ pipes and reeds, piano strings, actuating levers, etc.) it is common to always use the "sharp" forms of pitches to identify them. For example, if the bottom note on a pipe organ rank is C, the fourth pipe from the bottom would be described as D# (rather than Eb).
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supercatOct 18 '13 at 17:05

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.