A symbol, placed before a notehead on staff-notation, or placed after a nominal in text, which indicates a change in pitch of one chromatic semitone higher than that of the plain nominal. The sharp is a specific type of accidental.
A note with a sharp is also one diatonic semitone lower than the plain nominal just above it, i.e., A#:B is a diatonic semitone.
The sharp sign (and the natural sign as well) evolved out of the "square-b" notation which was used to indicate the higher version of the note "B" which appears in the diezeugmenon tetrachord of the greater perfect system.
In a general sense, "sharp" simply means higher in pitch by some amount (which may be defined or undefined); often used in this (undefined) sense when one instrument is out-of-tune with another.
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