Keys, scales and numbers
Practice it: Numbers
A key is a set of seven notes, and numbers name the notes and chords inside it. Learn them and a song in G is the same song in A, played two frets higher.
The major scale
A major scale picks seven of the twelve notes with a fixed pattern of steps: whole, whole, half, whole, whole, whole, half. A whole step is two frets and a half step is one. Starting on G: G A B C D E F♯ G.
Keys and scale degrees
A song in G major uses the notes of the G major scale. Number them from the root: G is 1, A is 2, B is 3, C is 4, D is 5, E is 6 and F♯ is 7. "Play the 4 in G" means play C.
Chords built in thirds
Stack every other note of the scale on each degree and you get the key's chords: G B D on G, A C E on A. The gap from the root to the middle note decides the chord. Four frets (a major third) makes a major chord, three frets (a minor third) makes a minor chord. When the top note is six frets above the root, the chord is diminished.
The chords of a major key
Every major key follows one pattern. Capital numerals are major chords, lower case are minor, and ° marks the diminished chord. In G:
| Number | Chord | Notes |
|---|---|---|
| I | G | G B D |
| ii | Am | A C E |
| iii | Bm | B D F♯ |
| IV | C | C E G |
| V | D | D F♯ A |
| vi | Em | E G B |
| vii° | F♯dim | F♯ A C |
Natural minor
E natural minor uses the notes of G major, starting on E. Its chords run i ii° III iv v VI VII, numbered from E:
| Number | Chord | Notes |
|---|---|---|
| i | Em | E G B |
| ii° | F♯dim | F♯ A C |
| III | G | G B D |
| iv | Am | A C E |
| v | Bm | B D F♯ |
| VI | C | C E G |
| VII | D | D F♯ A |
Modes
D Dorian uses the notes of C major starting on D, so its chords are C major's chords numbered from D: its IV is G major. The other church modes work the same way. Harmonic minor raises natural minor's 7th, and melodic minor raises its 6th and 7th, which changes some of their chords. Seventh chords stack one more third on each triad. The numerals count each mode's own notes, so D Dorian's III is F, its third note, with no flat sign.
| Mode | Chords | Seventh chords |
|---|---|---|
| Major (Ionian) | I ii iii IV V vi vii° | Imaj7 ii7 iii7 IVmaj7 V7 vi7 viiø7 |
| Dorian | i ii III IV v vi° VII | i7 ii7 IIImaj7 IV7 v7 viø7 VIImaj7 |
| Phrygian | i II III iv v° VI vii | i7 IImaj7 III7 iv7 vø7 VImaj7 vii7 |
| Lydian | I II iii iv° V vi vii | Imaj7 II7 iii7 ivø7 Vmaj7 vi7 vii7 |
| Mixolydian | I ii iii° IV v vi VII | I7 ii7 iiiø7 IVmaj7 v7 vi7 VIImaj7 |
| Natural minor (Aeolian) | i ii° III iv v VI VII | i7 iiø7 IIImaj7 iv7 v7 VImaj7 VII7 |
| Locrian | i° II iii iv V VI vii | iø7 IImaj7 iii7 iv7 Vmaj7 VI7 vii7 |
| Harmonic minor | i ii° III+ iv V VI vii° | i(maj7) iiø7 III+maj7 iv7 V7 VImaj7 vii°7 |
| Melodic minor | i ii III+ IV V vi° vii° | i(maj7) ii7 III+maj7 IV7 V7 viø7 viiø7 |
Chord tones
A chord's notes are its root, 3rd and 5th, plus the 7th in a seventh chord. In G the V chord is D major, D F♯ A, so its 3rd is F♯. Landing on chord tones on purpose is how a solo follows the chords.
Substitutions
A substitute chord stands in for the V7 or leads into another chord of the key. Numbers asks about four of them, in major and natural minor keys. A minor key borrows its V7 from harmonic minor: G7 in C minor. The examples are in C major.
Tritone sub
The tritone sub swaps the V7 for the dominant 7th on the key's ♭2. G7 is G B D F. D♭7, a tritone away, is D♭ F A♭ C♭ (B). They share B (C♭) and F, the tritone that wants to resolve: B rises to C and F falls to E. Its root slides down a half step to C, so D♭7 resolves where G7 does.
How to play it: D♭7
Diminished sub
The diminished sub plays a dim7 on the leading tone, which is the V7's 3rd. Bdim7 is B D F A♭. G7♭9 is G B D F A♭, so Bdim7 is G7♭9 without its root. Each of its notes is a minor 3rd above the last, so Bdim7, Ddim7, Fdim7, and A♭dim7 are the same four notes, and a dim7 shape repeats every three frets.
How to play it: Bdim7
Secondary dominants
A secondary dominant is the V7 of another chord in the key. In C they're A7 to Dm, B7 to Em, C7 to F, D7 to G, and E7 to Am. A7 is A C♯ E G, the dominant 7th a perfect 5th above D. A7 pulls to Dm the way G7 pulls to C, and its C♯ comes from outside the key.
How to play it: A7
Backdoor dominant
The backdoor dominant reaches the I from a whole step below. Numbers asks for it in major keys. B♭7 is B♭ D F A♭, the ♭VII7 borrowed from C minor. Its A♭ falls to G and its F falls to E, while B♭ steps up to C.
How to play it: B♭7
Why numbers
- I IV V is G C D in G and A D E in A. Learn the numbers once and every key works.
- Bands call changes in numbers: "go to the 4".
- Progressions sound alike because their numbers match: I V vi IV runs under hundreds of pop songs.
How to practice
Start Numbers in G, C and D, answering with the root. When those are quick, switch to chord tones, then add keys and natural minor. After that, add modes one at a time, name seventh chords, and try the substitutions.