Just like math, there is a good analogy with sets, that we all learned in school at some stage. only, there is no ambiguity, not any other note or an octave higher or lower. ![]() ![]() The above note, middle C corresponds to the middle C key on the keyboard. ![]() I know it is kind of stating the obvious, but the fact that you asked the question makes me think that you think middle c could be written in more than one place, an octave above or below and map to the same key, which is not the case ( apart from the conventions pointed out using notations like 8va and such. FWIW, I suppose another way to look at it which is clear from the diagrams above posted by Morodiene is that there is a unique one to one correspondence of each key/note on the keyboard to a unique place on the staff.
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