The major scale formula is whole step, whole step, half step, whole step, whole step, whole step, half step, or W–W–H–W–W–W–H. Applied to C, it gives C, D, E, F, G, A, B, C, and the same pattern builds a major scale from any starting note.
What is the major scale formula?
The major scale formula is the pattern of whole steps and half steps that builds a major scale from any starting note: whole, whole, half, whole, whole, whole, half, usually written W–W–H–W–W–W–H. A whole step is two semitones and a half step is one semitone, so the formula describes the exact distances between the seven notes of the scale. Start on any note, follow the pattern, and you get a major scale; start on C and you get C, D, E, F, G, A, B, C, the scale with no sharps and no flats. The formula matters because it is the foundation of all Western harmony. The major scale is the scale that every other scale is compared with: its intervals are all major or perfect, its chords are the diatonic chords of the key, and its modes are the other scales you meet most often. If you know the major scale formula, you can work out the notes of any major key, build any major chord, and understand why a piece of music sounds the way it does. Without it, you are memorising note lists; with it, you are doing music theory.
How the major scale formula works
Apply the pattern step by step from the root. Start on G: a whole step up from G is A, another whole step is B, a half step is C, a whole step is D, another whole step is E, another whole step is F#, and a half step back to G. The result is G, A, B, C, D, E, F#, G, the G major scale, with one sharp, F#. The half steps fall between the 3rd and 4th degrees and between the 7th and 8th degrees, which is why the major scale has its characteristic shape: two whole steps, a half step, three whole steps, and a half step. The same pattern works in flat keys too. Start on F: a whole step is G, another whole step is A, a half step is Bb, a whole step is C, another whole step is D, another whole step is E, and a half step back to F. The result is F, G, A, Bb, C, D, E, F, the F major scale, with one flat. In the sharp-only system used by ChordFlow, Bb is spelled A#, so the scale appears as F, G, A, A#, C, D, E, F, but the intervals are identical. The G major scale and the F major scale show the pattern in two keys, and the scale finder builds a major scale from any root.
Worked example — D major. Start on D and follow W–W–H–W–W–W–H. A whole step from D is E, another whole step is F#, a half step is G, a whole step is A, another whole step is B, another whole step is C#, and a half step returns to D. The D major scale is D, E, F#, G, A, B, C#, D, with two sharps, F# and C#. Check the half steps: F# to G is one semitone, and C# to D is one semitone, exactly where the formula puts them. The D major guitar chord is built from the 1st, 3rd and 5th degrees of this scale, and the key of D major shows the chords it produces.
How to practise the major scale formula
Practise the formula by building scales from scratch, not by copying note lists, so the pattern becomes a skill you can use in any key.
- Pick a random root note, write out its major scale using the W–W–H–W–W–W–H pattern, and check your answer against the scale finder.
- Play the C major scale on your instrument ascending and descending, and say the interval pattern aloud as you play: whole, whole, half, whole, whole, whole, half.
- Build the major scales of G, D, A and E in turn, noticing that each new scale adds one sharp, following the circle of fifths.
- On piano, play a major scale with your right hand while your left hand plays the root note, then move the whole pattern up a semitone and rebuild it.
- Use the scale degree calculator to check which degree of the scale each note belongs to as you practise.
Common mistakes
- Putting the half steps in the wrong place — The half steps in a major scale fall between the 3rd and 4th degrees and between the 7th and 8th degrees. Putting them anywhere else gives a different scale, not a major scale, so check those two gaps first.
- Forgetting the sharps in sharp keys — D major needs F# and C#, A major needs F#, C# and G#, and E major needs four sharps. Playing the natural notes instead gives you the wrong scale and the wrong chords.
- Memorising note lists instead of the formula — Knowing that C major has no sharps does not help you in F# major. Learn the W–W–H–W–W–W–H pattern, and you can build the scale on any root, including the ones you have never played before.
Quick reference
This table lists the major scale in six keys, so you can see the W–W–H–W–W–W–H pattern producing a different set of notes from each starting point. The sharp keys add one sharp at a time, following the circle of fifths, and the flat key, F major, has one flat, which appears as A# in the sharp-only spelling used across ChordFlow.
| Key | Major scale notes | Sharps or flats |
|---|---|---|
| C major | C – D – E – F – G – A – B | None |
| G major | G – A – B – C – D – E – F# | 1 sharp: F# |
| D major | D – E – F# – G – A – B – C# | 2 sharps: F#, C# |
| A major | A – B – C# – D – E – F# – G# | 3 sharps: F#, C#, G# |
| E major | E – F# – G# – A – B – C# – D# | 4 sharps: F#, C#, G#, D# |
| F major | F – G – A – A# – C – D – E | 1 flat: Bb (A#) |
Work through the table by building each scale yourself from the formula, starting from the root and counting whole and half steps, and check your answers against the rows. When you can build all six without looking, try the same exercise for B major, which has five sharps, and for Bb major, which has two flats.
Frequently asked questions
What is the major scale formula?
The major scale formula is the pattern of whole steps and half steps that builds a major scale: W–W–H–W–W–W–H, or whole, whole, half, whole, whole, whole, half. Applied to C it gives C, D, E, F, G, A, B, C.
How many sharps are in the D major scale?
Two: F# and C#. The D major scale is D, E, F#, G, A, B, C#, D, and the sharps fall on the 3rd and 7th degrees, following the W–W–H–W–W–W–H pattern from D.
Why does the major scale have half steps in those places?
Because the pattern of whole and half steps is what gives the major scale its sound: the half step between the 3rd and 4th degrees and the half step between the 7th and 8th degrees create the leading-note pull toward the tonic, which is the defining character of the major scale.
Can I build a major scale from any note?
Yes. The W–W–H–W–W–W–H pattern works from any of the twelve notes, including sharp and flat roots. Some results are easier to spell than others, but the interval pattern never changes.
What is the difference between a major scale and a major chord?
A major scale has seven notes and a major chord has three, but the chord is built from the scale: the major triad is the 1st, 3rd and 5th degrees of the major scale, so the scale contains the chord and the chord comes from the scale.