Lessons · Beginner
The Major Scale - Formula, Degrees and How to Build It
The whole-and-half-step formula behind every major scale, the names of its degrees, and how to spell it from any note.
The major scale is the reference point for almost all Western music theory. Intervals are named by comparing them to it, chords are numbered by its degrees, and the other scales and modes are usually described as "the major scale with a few changes". Learn how it is built once, and you can write it out from any starting note in seconds.
The formula: W-W-H-W-W-W-H
A major scale has seven different notes plus the octave. The distances between neighbouring notes follow one fixed pattern of whole steps (W, 2 semitones) and half steps (H, 1 semitone):
W – W – H – W – W – W – H
In C major, which uses only the white keys of the piano, you can see the pattern directly:
| From | To | Step |
|---|---|---|
| C | D | W |
| D | E | W |
| E | F | H |
| F | G | W |
| G | A | W |
| A | B | W |
| B | C | H |
The half steps fall between degrees 3–4 and 7–8. That is exactly where the piano has no black key between white keys (E–F and B–C), which is why C major needs no sharps or flats.
C – D – E – F – G – A – B
Measured from the tonic in semitones, the notes are 0 – 2 – 4 – 5 – 7 – 9 – 11 – 12. As intervals: major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, octave. Every interval from the tonic is major or perfect, which is where the name "major scale" comes from.
Tetrachords: two identical halves
Split the major scale into two groups of four notes, called tetrachords:
- Lower tetrachord: C D E F = W – W – H
- Upper tetrachord: G A B C = W – W – H
Both halves have the same shape, and they are joined by a whole step (F to G). So the major scale is really one small pattern played twice: (W W H) + W + (W W H).
This explains a beautiful connection. The upper tetrachord of C major (G A B C) is the lower tetrachord of G major. To complete G major you add a new upper tetrachord starting on D: D E F# G. That F# is the one sharp in G major. Keep doing this and you walk clockwise around the circle of fifths, adding one sharp each time.
Scale degrees and their names
Each note of the scale has a number (its degree), a traditional name, and a solfège syllable (movable do).
| Degree | Name | Solfège | In C major | Role |
|---|---|---|---|---|
| 1 | Tonic | do | C | home, point of rest |
| 2 | Supertonic | re | D | step above the tonic |
| 3 | Mediant | mi | E | halfway from tonic to dominant; decides major or minor |
| 4 | Subdominant | fa | F | a fifth below the tonic; tends to fall to 3 |
| 5 | Dominant | sol | G | strongest pull back to the tonic |
| 6 | Submediant | la | A | tonic of the relative minor |
| 7 | Leading tone (leading note) | ti | B | a half step below the tonic; pulls up to 8 |
| 8 | Tonic (octave) | do | C | home again |
The names make sense once you see the pattern: the dominant is a fifth above the tonic, the subdominant is a fifth below. The mediant sits halfway up to the dominant, the submediant halfway down to the subdominant.
Degrees are often written with a caret, like ^1, ^5, ^7. Chords built on each degree use Roman numerals (I, ii, iii, IV, V, vi, vii°); see Diatonic harmony.
Building a major scale on any note
Two rules guarantee a correctly spelled scale every time:
- Use every letter name once, in order. Starting on D, the letters are D E F G A B C D, no skipping and no repeating.
- Adjust each letter with a sharp or flat so the steps follow W – W – H – W – W – W – H.
Example: D major
Letters: D E F G A B C D.
- D to E: whole step. Good.
- E to F: only a half step, but we need a whole step, so raise F to F#.
- F# to G: half step. Good.
- G to A, A to B: whole steps. Good.
- B to C: half step, but we need a whole step, so raise C to C#.
- C# to D: half step. Good.
Result: D E F# G A B C# D, with two sharps.
Example: Eb major
Letters: E F G A B C D E, starting from Eb.
- Eb to F: whole step. Good.
- F to G: whole step. Good.
- G to A: we need a half step, so lower A to Ab.
- Ab to B: we need a whole step, so B becomes Bb.
- Bb to C, C to D: whole steps. Good.
- D to Eb: half step. Good.
Result: Eb F G Ab Bb C D Eb, with three flats.
All twelve major scales
Arranged around the circle of fifths, each scale differs from its neighbour by one note.
| Key | Notes | Sharps / flats |
|---|---|---|
| C | C D E F G A B | none |
| G | G A B C D E F# | 1 sharp |
| D | D E F# G A B C# | 2 sharps |
| A | A B C# D E F# G# | 3 sharps |
| E | E F# G# A B C# D# | 4 sharps |
| B | B C# D# E F# G# A# | 5 sharps |
| F# | F# G# A# B C# D# E# | 6 sharps |
| Db | Db Eb F Gb Ab Bb C | 5 flats |
| Ab | Ab Bb C Db Eb F G | 4 flats |
| Eb | Eb F G Ab Bb C D | 3 flats |
| Bb | Bb C D Eb F G A | 2 flats |
| F | F G A Bb C D E | 1 flat |
F# major is written with E#, not F, because the scale needs one E and one F. Its enharmonic twin Gb major is spelled Gb Ab Bb Cb Db Eb F.
The major scale on the guitar
On a single string, the formula is literally a fret pattern: 2 – 2 – 1 – 2 – 2 – 2 – 1 frets. Across the neck, the same scale forms a set of connected shapes. Here is G major across the first twelve frets:
Look for the root notes (degree 1) first, then learn one position around them before connecting positions.
The major scale on the bass
The bass is tuned E A D G, like the four lowest guitar strings an octave lower, so the same W-W-H-W-W-W-H formula becomes one compact hand shape. Put finger 2 on the root G (string 4, fret 3) and use one finger per fret between frets 2 and 5: the whole octave fits without shifting.
Because the shape is movable, starting it on string 4, fret 5 gives A major, and on string 3, fret 3 gives C major. Notice that degrees 3-4 (B–C) and 7-8 (F#–G) are always neighbouring frets: the two half steps of the formula.
For more fingerings and how to connect them, see scales and modes on the bass and the major scale positions exercise.
Practice
- Write out the W-W-H-W-W-W-H formula from memory, then play it on a single string starting from any fret.
- Spell the major scales of A, Bb, E and Ab using the two rules, then check them against the table.
- Name the dominant, subdominant and leading tone of G, F, D and Eb major.
- Split D major and Bb major into tetrachords and check that each half is W-W-H.
- Play one octave of C, G and F major slowly with a metronome, saying the degree numbers out loud.
Next steps:
- Worksheets: Scale spelling 1 and Scale spelling 2.
- Guitar: Major scale positions. Bass: Bass major scale.
- Explore any key in the scale explorer and print the scale formulas chart.
- Lessons: Minor scales, Key signatures, Modes and Diatonic harmony.
- See a single key in detail: G major or the D major scale.