I am supposed to play an F#, but there is no sharp sign to suggest it [duplicate]

Question

Given this piece of music:

A learning app tells me to play an F# as the 2nd and 3rd note. My concern is that there is no sharp symbol on the 1st space. I figured there is a sharp on the line corresponding to a higher F# (the leftmost symbol), but that's a different note...

Luckily, the piece doesn't have that higher F#. If it had, would I be supposed to play both higher in pitch? Or only the higher one (the lower one would just an F)?

Also I read you can't put more than 7 symbols (either flats or sharps) in the key signature. It doesn't make sense since there are more lines and spaces combined (including or not ledger lines).

Could you please explain it? Thanks.

Answer 1

In music, there's a notion that we call octave equivalence. It basically states that, in certain conditions, any instance of a given pitch, no matter what the octave, is viewed as equivalent to all other instances of that pitch.

I say this because key signatures assume octave equivalence. Thus, even though the left-most sharp in the key signature is for a higher F♯, it applies to all instance of F, not just the one on the top line of the treble staff (or the second highest line of the bass staff). Therefore, the second and third pitches of this excerpt are to be played as F♯. They would only be played as F♮s if a new key signature got right of the F♯s or if a ♮ was placed into the music directly.

You can have more than seven symbols in the key signature, but these extra symbols aren't necessary to apply to all pitches. Instead, they are the result of so-called "theoretical key signatures" that require extra accidentals. See Where do the double accidentals go in "theoretical" key signatures?