Relative keys
This lesson shows you how to find the relative key of any scale, and which intervals occur in each mode.
You have seen that a minor scale without a leading tone contains the same tones as a major scale on a different tonic, and that the 7th degree of the minor scale is raised a half step, or semitone in British English, to remove the ambiguity. To describe the relationship between these two scales, one major and one minor, we call them relative scales, or relative keys.
Every major scale therefore has a relative minor, and it is in turn the relative major of that minor scale.
The minor third rule
Here is the rule to remember. The minor scale lies a minor third below its relative major, and the major scale lies a minor third above its relative minor. In other words:
- a major scale has as its tonic the mediant of its relative minor;
- a minor scale has as its tonic the submediant of its relative major.
The key signature is shared by both scales. The accidental that raises the 7th degree of the minor scale is never part of the key signature, because it is chromatic: it is always written as an accidental in the music.
Building the relative minor of a major key
- Raise the dominant of the major scale a chromatic half step, so that it becomes a leading tone, or leading note in British English;
- Take as the tonic the note a minor third below the major tonic.
Building the relative major of a minor key
- Lower the leading tone of the minor scale a chromatic half step, so that it becomes a dominant;
- Take as the tonic the note a minor third above the minor tonic.
Table of relative keys
| Key signature | Major key | Relative minor | Leading tone of the minor |
|---|---|---|---|
| no sharps or flats | C | A | G# |
| 1 sharp | G | E | D# |
| 2 sharps | D | B | A# |
| 3 sharps | A | F# | E# |
| 4 sharps | E | C# | B# |
| 5 sharps | B | G# | F## |
| 6 sharps | F# | D# | C## |
| 7 sharps | C# | A# | G## |
| 1 flat | F | D | C# |
| 2 flats | B♭ | G | F# |
| 3 flats | E♭ | C | B♮ |
| 4 flats | A♭ | F | E♮ |
| 5 flats | D♭ | B♭ | A♮ |
| 6 flats | G♭ | E♭ | D♮ |
| 7 flats | C♭ | A♭ | G♮ |
Clockwise: add a sharp (up a fifth). Counterclockwise: add a flat (down a fifth). At the bottom, enharmonic keys join the two branches.
- Key signature
- no sharps or flats
- Relative
- A minor, a minor third below; leading tone G♯ added as an accidental
- Closely related keys
- A minor, F major, G major, D minor, E minor
- Landmark
- the model scale, no accidentals
Intervals in the major and minor scales
To complete our study of the two modes, let's look at the intervals you get by building, on each degree, an interval that uses only notes of the scale. For minor, we use the harmonic form, the one Danhauser studies. Each cell gives the number of such intervals and the degrees they are built on.
| Interval | Major scale | Minor scale |
|---|---|---|
| Minor second | 2 (degrees 3, 7) | 3 (degrees 2, 5, 7) |
| Major second | 5 (1, 2, 4, 5, 6) | 3 (1, 3, 4) |
| Augmented second | 0 | 1 (6) |
| Minor third | 4 (2, 3, 6, 7) | 4 (1, 2, 4, 7) |
| Major third | 3 (1, 4, 5) | 3 (3, 5, 6) |
| Diminished fourth | 0 | 1 (7) |
| Perfect fourth | 6 (1, 2, 3, 5, 6, 7) | 4 (1, 2, 3, 5) |
| Augmented fourth | 1 (4) | 2 (4, 6) |
| Diminished fifth | 1 (7) | 2 (2, 7) |
| Perfect fifth | 6 (1, 2, 3, 4, 5, 6) | 4 (1, 4, 5, 6) |
| Augmented fifth | 0 | 1 (3) |
| Minor sixth | 3 (3, 6, 7) | 3 (1, 5, 7) |
| Major sixth | 4 (1, 2, 4, 5) | 4 (2, 3, 4, 6) |
| Diminished seventh | 0 | 1 (7) |
| Minor seventh | 5 (2, 3, 5, 6, 7) | 3 (2, 4, 5) |
| Major seventh | 2 (1, 4) | 3 (1, 3, 6) |
| Perfect octave | 7 | 7 |
Finally, the following intervals occur in neither the major nor the minor mode: they can only arise from chromatic notes. They are the diminished third, the augmented third, the diminished sixth, the augmented sixth, the diminished octave, the augmented octave, and all doubly diminished and doubly augmented intervals.
Name the major and minor keys (harmonic minor) that contain each of these intervals: E♭-G, D#-F#, B-E, G-C#, B-A♭, E-B, C-A♭, C-E♭. (Danhauser also suggests copying the table of relative keys, writing only the flat major keys and the sharp minor keys, then filling in the rest from memory.)
Now that you know how relative keys work, the next lesson shows you how to tell which of the two a piece is actually in.