A musician can begin on any note to play a major scale by playing the pattern for a major scale up eight notes and back down to the original note. That is called 'playing one octave' of a major scale.
Each scale is named by the note it starts on. For example, a C scale begins on a C and creates the key of C.
The following sections present advanced concepts which are mathmatically complex. Most musicians learn these concepts over a span of years. Give your brain some time to absorb the logic.
The major scale pattern is made up of:
two tetrachords with a whole step between them, and
a tetrachord is two whole steps and a half step.
A G major scale will need the seventh note of the scale to be sharped, in order to make the pattern. The seventh note is F, so a piece of music written in the key of G will have an F sharp in the key signature.
An F major scale will need to use a flat in order to make the major scale pattern. So a piece of music written in the key of F will have a B flat in the key signature.
The pattern of major scales moves upwards in a sequence called the circle of fifths. To become familiar with all possible key signatures, it is helpful to understand the circle of fifths.
Major scale step pattern
whole whole half (whole) whole whole half
C D E F G A B C C B A G F E D C
F G A B C D E F F E D C B A G F
Key of C: no flats or sharps in key signature
Key of G: F sharp in key signature
Key of F: B flat in key signature
G A B C D E F G G F E D C B A G
Read Music Method teaches students how to play a C Major scale with correct fingering for both hands in contrary motion and much, much more.