The notes B# and E# (or Cb and Fb) don’t seem to exist on a piano or in music in general. Why is that?
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They do exist. E# is just the same note as F, just like C# and Db are two names for the same note.
Now if you just want to point out one note on its own, there’s no reason to use E# over F. However, if you want to use the F# major scale, for example, you’d call its notes F#-G#-A#-B-C#-D#-E#-F# so every letter is still represented once in the scale. This makes notation easier, as you can just mark both the E and F as sharp at the beginning of the staff and then write an E whenever you’re playing a natural F and an F whenever you’re playing an F#. Otherwise you would have to switch back and forth with sharp and natural signs all the time.
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