Are tonal (sharp, flat and natural) key signatures octave specific? [duplicate]

Question

I recently bought a piano for learning (by myself at the moment) and apart from doing basic exercises, I decided to start learning a piece to get a grip on music sheet reading as I go.

On the sheet I'm trying to play there are 2 sharp key signatures at the start of the line: higher C and higher F (pardon me if terms are not accurate). What caught my attention is that in this piece at higher octave C and F do not sound right without a sharp.

With that in mind, I am wondering if tonal signatures are specific to octave they are written on. For instance, in my case if higher C and F have sharp signatures, would every C and F in the section be a sharp or just the ones on the lines sharp signatures are written on?

Sheet I am trying to play in case my descriptions are hard to read.

Answer 1

Accidentals in a key signature always apply to any octave you play in.

The human ear hears the same note in neighbouring octaves as almost identical (in fact, many people have a hard time distinguishing them at all). People sing along to a tune in a higher or lower octave with no qualms, and often without noticing. Some instruments, e.g. kettle drums, emit sound that is in fact hard to assign to a particular octave even if you measure it with precision instruments. In brief, it would be majorly unexpected and awkward if an accidental applied only to exactly one particular tone, therefore the rule has always been that it applies to all octaves indifferently.

The specific way the accidentals are arranged on the modern five-line system is merely a convention. It's nice to have because it lets experienced players recognize a key at a single glance, but it's irrelevant to this principle. In fact, when notated in the bass clef many accidentals go in different places, and that makes no difference either.

(Note that individual accidentals inserted into the middle of a piece can in principle break this rule, but it's very rare to combine e.g. an f with an f sharp, and you'll probably go years without ever encountering such an advanced chord.)

Answer 2

Most scales are assumed to be octave-repeating, due to the way that we hear a similarity between notes that are an octave apart (the reason for this being that with many instruments, any note contains harmonic partials at the frequencies of all the overtones of a note an octave below).

This includes the diatonic scale, which is the scale that standard notation assumes and that key signatures are relevant to, and this is why key signatures are read as applying to all octaves.

Incidentally, there do exist scales which are not octave repeating, e.g. http://en.wikipedia.org/wiki/Bohlen%E2%80%93Pierce_scale.

Answer 3

In principle key signatures apply to all octaves, while individual accidentals apply only to the octave, where they appear. Sometimes score editors are helpful by repeating individual accidentals (courtesy or cautionary accidentals); if these are not especially marked (smaller print, parentheses) it makes the rule more diffcult to recognize for the inexperienced.

In the strict sense, even an accidental in small print (e.g. within an ornamentation) applies to all notes up to the end of the bar.

I revised my answer according to Eduards comment, but even if I found the information, that individual accidentals on in the octave where they occur in every reference I encountered, I received nothing but astonishment from every professional musician I asked. So I would summarize:

While individual accidentals theoretically apply only to the specific octave, this can't be relied upon: few people (including sheet editors) are aware of the rule, so in case of doubt, use what sounds more appropriate.