An octave is an interval composed of 12 semitones. A semitone is an interval, so they are:
C → C#
, C# → D
, D → D#
, D# → E
, E → F
, F → F#
, F# → G
, G → G#
, G# → A
, A → A#
, A# → B
, B → C
.
In Solfège:
Do → Do#
, Do# → Re
, Re → Re#
, Re# → Mi
, Mi → Fa
, Fa → Fa#
, Fa# → Sol
, Sol → Sol#
, Sol# → La
, La → La#
, La# → Ti
, Ti → Do
.
See how you count the intervals, not the notes? The C#
is not a semitone, it is a semitone above C
.
It's almost correct to say that there are eight notes in an octave. Really, there are eight notes of a major scale within the interval of an octave. This is also true of minor scales, but it's not true of some other types of scale (e.g. pentatonic, blues). The major scale itself only has seven unique notes, but the within an octave, the first gets repeated, so you end up with eight.
So it seems that there's a small error in your count of semitones, and a slight misunderstanding of the relationship between an octave and a scale.