Accidentals

The notes ..  A B C D E F G A B ... are not equally spaced. There are historical reasons for this.

The Semitone is the smallest note interval that can be represented accurately on a stave.

Two semitones make a whole tone.

Going from:

A to B is one tone.

B to C is a semitone.

C to D is one tone.

D to E is one tone.

E to F is a semitone.

F to G is one tone.

G to A is one tone.

There is no obvious reason (nowadays) for this strange state of affairs except that keyboard players will notice that the lines and spaces represent the white notes of their keyboard.

So when we go from B to C, we move from a line to the next space or a space to the next line and since this is the smallest interval, a semitone, all is well.

But when we go from, say, D to E (line to next space or space to next line), there is a whole tone difference. How do we represent the note a semitone above D and a semitone below E.

Like this:

The  # (Sharp) sign, just before the second note (D) means that the note D# (D Sharp) should be played. This is one semitone above the note D. Depending on the instrument you play, this will mean different things as far as sounding this note.

The b (Flat) sign, just before the third note (E) means that the note Eb (E Flat) should be played. this is one semitone below the note E.

Again, depending on the instrument you play, this will mean different things.

Db and E# are not identical for all sorts of reasons, but are often sounded the same (on a keyboard they are the same note) and are considered to be enharmonic equivalents.

What happens when there is only a semitone between two notes?

Here we have B, B#, Cb and C. B to B# is the same as B to C, thus, for all practical purposes, B# and C are the same note.

Similiarly, Cb and B are the same note. thus, going from B# to Cb is the same as going from C to B, down a semitone.