Two identical tetrachords · The major scale · Music theory
The major scale divides into two tetrachords, two groups of four notes with the same shape (whole, whole, half), a whole step apart: C–D–E–F and G–A–B–C.
Two identical tetrachords
The major scale divides into two tetrachords, two groups of four notes with the same shape (whole, whole, half), a whole step apart: C–D–E–F and G–A–B–C.
That is why the second tetrachord of a scale is the first of the scale a 5th higher. G–A–B–C opens G major; the next tetrachord, D–E–F–G, needs an F♯ to keep the same shape. That is how each new sharp appears, fifth by fifth.
Going down, the opposite happens: the first tetrachord of a scale is the second of the scale starting a 5th lower. C–D–E–F closes F major, whose first tetrachord, F–G–A–B, needs a B♭. That is how each new flat appears.
An easy chain to remember
Following the chain of tetrachords upward, each scale adds a sharp, and it is always its degree VII: G major adds F♯, D major adds C♯. Downward, each scale adds a flat, and it is always its degree IV: F major adds B♭, B♭ major adds E♭.
This rule lets you work out any key signature without memorizing it, and it is the same logic as the circle of fifths, which comes later.