The foundation of Western music theory is the major scale. Knowledge of the major scale in all keys enables construction of all chords and all other scales when applying the correct formulae.

By name, there are fifteen major scales: one (C major) without accidentals (sharps or flats), seven with sharps and seven with flats. Because there are three enharmonic equivalent scales (G# = Ab, C# = Db, F# = Gb) there are twelve major scales by sound (15 minus 3 equals 12) coinciding with the twelve notes of the chromatic scale.

The formula for the major scale is 2 ½ 3 ½ steps, i.e. W W H W W W H. (W = Wholestep, H = Halfstep)

Major Scales with Sharps (#)

Here are the steps, in order, for constructing the major scales with sharps (#).

Go up a perfect fifth.
Retain the sharps (#) from the previous scale.
Add a sharp (#) to the seventh note

We will start on the note C of the music alphabet (A B C D E F G) which gives us the C major scale which has no accidentals, i.e. sharps (#) or flats (b):

C D E F G A B C

Following the three steps listed above gives G as the starting note for the next major scale. We retain the sharps, which are none in this case, then add a sharp to the seventh note of the current scale under construction, giving us the note F#. Hence the G major scale has the notes:

G A B C D E F# G

The next scale will be D major, having an F# (from the previous scale) and a C# (the new # on the seventh note).

The D major scale has the notes D E F# G A B C# D

The A major scale has the notes A B C# D E F# G# A

The E major scale has the notes E F# G# A B C# D# E

The B major scale has the notes B C# D# E F# G# A# B

The F# major scale has the notes F# G # A# B C# D# E# F#

The C# major scale has the notes C# D# E# F# G# A# B# C#

Major Scales with Flats (b)

Here are the steps, in order, for constructing the major scales with flats (b).

Go up a perfect fourth.
Retain the flats (b) from the previous scale.
Add a flat (b) to the fourth note.

We will start on the note C of the music alphabet (A B C D E F G) which gives us the C major scale which has no accidentals, i.e. sharps (#) or flats (b):

C D E F G A B C

Following the three steps listed above gives F as the starting note for the next major scale. We retain the flats, which are none in this case, then add a flat to the fourth note of the current scale under construction, giving us the note Bb. Hence the F major scale has the notes:

F G A Bb C D E F

The next scale will be Bb major, having a Bb (from the previous scale) and an Eb (the new b on the fourth note).

The Bb major scale has the notes Bb C D Eb F G A Bb

The Eb major scale has the notes Eb F G Ab Bb C D Eb

The Ab major scale has the notes Ab Bb C Db Eb G Ab

The Db major scale has the notes Db Eb F Gb Ab Bb C Db

The Gb major scale has the notes Gb Ab Bb Cb Db Eb F Gb

The Cb major scale has the notes Cb Db Eb Fb Gb Ab Bb Cb