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In the scale we just played - the major scale - the distance between the different tones is a whole tone or a semitone. If this is new to you, it may seem a bit strange. There are more things in music theory that do not always seem logical at first glance. Don't worry, as you learn more you will see the logic behind it more and more. The smallest possible distance between two tones is a semitone. The division in the series c d e f g a b c is as follows (H = half/semitone, W = whole tone):

So that is:"whole whole half, whole whole whole half"
There is a whole tone between C and D.
There is a whole tone between D and E.
There is a semitone between E and F.
There is a whole tone between F and G.
There is a whole tone between G and A.
There is a whole tone between A and B.
There is a semitone between B and C.
You could also say that there are two semitones between C and D. Two between D and E, one between E and
F, etc.
On the guitar you can clearly see that there is only a semitone between E and F and between B and C: one
fret is a semitone on the guitar. Two frets is a whole tone.
If you would play this major scale of C on a single string, you can clearly see the distances:

On a piano you can see it even better: there is no black key between E and F and no black key between B and C. The black keys are the tones that are between the root tones (the white keys).

So there are “extra” tones between C and D, between D and E, between F and G, between G and A, and between A and B.
This is where the flats (b) and sharps (#) come in.
The tone between C and D can be seen as a C raised by a semitone, or as a D lowered by a semitone.
If we raise a tone by a semitone, we indicate this with a sharp (#).
For example, the tone between C and D is called C# (C sharp).
If we lower a tone by a semitone, we indicate this with a flat (b).
For example, the tone between C and D is also called Db (D flat).
So the tone between C and D has two names: C sharp (C#) and D flat (Db).
C# and Db sound exactly the same. In music theory, you say that they are “enharmonically” the same.
But why two names for the same tone? We will come to that later, when we talk about scales and keys.