The answer is really quite complicated for people that do not regularly delve too deep into the various theories of our musical arts.
The question is not proper either - Let me, from the outset state that these notes, viz. B#, Cb, E# and Fb do indeed exist.
The basic permise of my answer will be a simple cliché :
"What's in a name? That which we call a rose by any other name would smell as sweet."Thus, the simple answer to these questions is that the note that we refer to as, say, B# is nothing more than a note a half semitone sharper that B and is thus harmonically equivalent to C. Again, Cb is nothing more than a note a half semitone flatter that C and is thus harmonically equivalent to B. Applying this very half halfhearted logic, we conclude that:
B# = C, Cb = B, E# = F and Fb = E
These are referred to as enharmonics.
The distance between the pairs B/C and E/F is a half note. Thus B# means C and E# means F only. Again, Cb mean B and Fb means E only.
There is no space between these two pairs of notes to accommodate an accidental i.e. a sharp or a flat in between them. This is a peculiarity of the chromatic scales.
But why are B/C and E/F semitones?
Please read here. Too long to repeat.
- Which takes us back to answer 2 above.
But there are such notes:
When we construct the C major scale, we have the notes : A B C D E F and G
So for C#major, the notes will be : A# B# C# D# E# F# and G#
And for Cb major the notes will be : Ab Bb Cb Db Eb Fb and Gb
Now imagine writing these notes in staff notation. The C# major will have 7 # signs in its key signature if we use B# and E# and five (2 less) if we use C and F. (Like wise, Cb major will have 7 flats if we use Bb and Eb while it will have 5 if we do not.) Again, if we have to denote, the natural B and F notes in the C# major key where every note is a sharp, we must include the natural sign on top of every such note. Thus we are making the whole staff much more complicated than we can make it if we just drop the # signs and call start calling them by their other non-sharp name. It makes the player's and the composers job a lot less cumbersome and less difficult.
This, in no way erases these names from existence. It does, however, make it very unlikely for one to encounter these notes. It is just convention and convenience that take the upper hand. For some instruments like the violin and the cello, B# and C (and like wise) are not played the same. B# is played only very slightly flatter than C. This is made possible by the lack of frets on these instruments making them not so equally tempered. Thus these notes are identical only for certain instruments like the guitar and the piano.
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