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For example, this ASCII sheet music:
G
trebel--------
|4------------
|-------------
|4--------#G--
clef----------
I know it's terrible, but would the second G be sharp too? And for clarification, we're talking accidentals, not key signatures. I figured that key signatures apply to all octaves, otherwise we'd have a mountain of them...
Accidentals apply to a single bar and a single octave.
Accidentals do not carry over to new bars. A "courtesy" accidental can be used to aid reading and show the tone changed back to the key signature value.
As it stands, the question isn't clear. Two ideas.
If you mean at the beginning, in the key signature, then no, it's not going to be correct. Unless there is already an F♯ and C♯ in that key sig., in which case, it will turn key D/Bm into key A/F♯m, and yes, every G will automatically become G♯.
If you mean in a particular bar, then no, any accidental will affect only the notes on that line/space, and also only for that particular bar. The next barline effectively cancels that accidental.
That's one reason they're called accidentals - they're there temporarily. The ♯ and ♭ in the key sig. are not accidentals - they're there on purpose!
So, any accidental will affect only the note/s it applies to until the end of that bar, unless cancelled earlier, usually with a natural (♮) sign. A sharp on middle C line will not automatically change any other C notes anywhere else in that bar. If they need sharpening, they will need a sharp sign in front of them too.
The sharps and flats in a key signature apply to all pitches of the same pitch class.
If an accidental (a note outside of the key signature) sharp, flat, or natural occurs in a bar, only the notes on that particular line or space in that bar are affected. i.e. an accidental on a G, will not affect the G's an octave above or below.
This is the modern engraving technique.
An older tradition for engraving has a different rule: That the entire pitch class is affected by an accidental. i.e. the G's an octave above and below it in the bar are affected too.
If you really want to be unambiguous, you can write courtesy accidentals: Accidentals (that are already implied) written in parentheses.
There are different answers here about accidentals, because there's no one correct answer. As someone noted in one answer, the modern convention is to assume that accidentals on one pitch only apply to that specific line/space, not to notes an octave above or below in the same bar.
However, this was not always the convention. And different people at different times in history and in different places may have assumed various things. Historically, it was therefore most common to be explicit about what happened to notes in other registers with the same name. If you wanted a G# and marked it sharp, but another note G occurred an octave above later in the bar, it would typically be marked explicitly with either a natural or a sharp (depending on the intent). The natural would not be merely thought of as a "courtesy" accidental, but would generally be required for the sake of clarity.
I still think this latter convention is the least confusing, and I'd recommend using it. Otherwise, unless it's a piece of modern atonal music that has odd accidentals to begin with, there's usually going to be a debate among performers -- "Is this supposed to be natural? I don't know. Maybe it's an editorial mistake and they forgot a sharp. We'll have to look at other parts...."
So, generally speaking, in a modern score with a lot of chromaticism, I'd assume that sharps and flats only correspond to their particular line/space, but honestly that convention cannot be assumed to be universally true (as seen in some other answers here). It's pretty rare to see situations where an accidental is assumed to apply in all octaves, and I think the only place I've seen it is in some really abbreviated types of notation, like lead sheet charts or some loosely edited jazz parts. (And I'm pretty sure even that is rare.)
Yes, the key signature applies to all notes on the staff, regardless of the octave.
In fact, the key signatures are fixed, as in, there is only one "proper" way to notate any key signature. The first accidental should be as high as possible within the staff (so not including the spaces "resting" just outside the lines). If the key signature has sharps, the position alternates going down a fourth then up a fifth. If the key signature has flats, the position alternates going up a fourth then down a fifth. After the first accidental, however, the accidentals can be put on the spaces just outside the staff -- if alternating the "up/down a fourth then down/up a fifth" rule puts the accidental on/above a ledger line, then you break the pattern for that one note.
I have a treble clef and put a sharp on the G part of the G Clef ...
The question implies to me that you are asking about accidentals and not key signs, as it is logical that key signs are affecting all notes (and it would also imply that not only a G would have a sharp following the clef but also the F# and C#):
So I assume the question is referring to accidentals which affect all notes of the same pitch in the same bar. If needed the accidental has to be repeated and added to a G in another octave:
If a note has an accidental and the note is repeated in a different octave within the same measure the accidental is usually repeated, although this convention is far from universal.
