Linking Scales: The Order of Flats
Now let's turn to the flat side. You'll build all the major scales with flats and work out the order of flats.
This time, let's do the reverse. We'll turn the lower tetrachord of the C scale, C-D-E-F, into the upper tetrachord of a new scale. To complete it, add the four degrees that come before it: F-G-A-B.
This tetrachord won't do: it gives “whole, whole, whole” instead of “whole, whole, half.” The B is too far from A, a whole step instead of a half step, and too close to C, so the two tetrachords are no longer separated by a major second but by a minor second. On top of that, F-B forms an augmented fourth instead of a perfect fourth. So the B has to be lowered a chromatic half step with a flat.
The new note is B flat, the subdominant of the new scale. F, the 1st degree, is the tonic, and C, the 5th degree, is the dominant. The tonal notes are F on the 1st degree, Bb on the 4th and C on the 5th.
How the scales link up
| Scale | Flats | New flat (subdominant) |
|---|---|---|
| C major | 0 | |
| F major | 1 | Bb |
| Bb major | 2 | Eb |
| Eb major | 3 | Ab |
| Ab major | 4 | Db |
| Db major | 5 | Gb |
| Gb major | 6 | Cb |
| Cb major | 7 | Fb |
Here again, the table shows you three things:
- Each scale shares its upper tetrachord with the scale before it, which has one flat fewer, and its lower tetrachord with the scale after it, which has one flat more.
- The flat keys follow one another a fifth lower each time.
- Each new flat also appears a fifth below the previous one.
The order of flats
Notice that the order of flats is exactly the reverse of the order of sharps. You can use the phrase “Battle Ends And Down Goes Charles' Father”, and many students also remember the first four as the word “BEAD”.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
|---|---|---|---|---|---|---|---|
| Sharps | F | C | G | D | A | E | B |
| Flats | B | E | A | D | G | C | F |
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
Write out, in order, all the scales that contain flats. For each one, give the tonic, the subdominant, the leading tone, and the number and names of the flats.
Next, we'll see how these flats are written in the key signature, and how to read them.