BTetrachords and the Cycle of Fifth's
The Major scale can be divided into two halves, one of the first four notes, the other of the last four notes. Each is called a Tetrachord and consists of two tones followed by a semitone.

Lower tetrachord C D E F semitone interval between the notes = 221

Upper Tetrachord G A B C semitone interval between the notes = 221

If we take the upper tetrachord of the C Major i.e. G A B C, and make it the lower tetrachord of a new key and then add a new tetrachord i.e. D E F G, above.

Then follow the convention of the same semitone pattern of '221' you will see that we have to raise the third note of the upper tetrachord, that is the seventh note of the new scale, one semitone, or fret to follow the diatonic or 221 convention.

So the F becomes F# and we have the notes of the G Major scale. This is the beginning of the process.

G -- A -- B - C -- D -- E -- F#- G