Linking Scales: The Order of Sharps
In this lesson, you'll build all the major scales with sharps, one after another, and work out the order of sharps.
Let's look for a new key. We'll take the upper tetrachord of the C scale, G-A-B-C, and turn it into the lower tetrachord of another scale.
To complete this scale, add the four degrees that follow: D-E-F-G.
This new tetrachord won't do: instead of “whole, whole, half,” it gives “whole, half, whole.” The F is too close to E, a half step instead of a whole step, and too far from G, a whole step instead of a half step. So it has to be raised a half step with a sharp.
So to form a new scale, we needed a new note: here it's F#, the leading tone of the new scale. G, which was the dominant of C, becomes the tonic, and this is the G scale. D, the 5th degree, is the dominant. The tonal notes are G on the 1st degree, C on the 4th and D on the 5th.
How the scales link up
| Scale | Sharps | New sharp (leading tone) |
|---|---|---|
| C major | 0 | |
| G major | 1 | F# |
| D major | 2 | C# |
| A major | 3 | G# |
| E major | 4 | D# |
| B major | 5 | A# |
| F# major | 6 | E# |
| C# major | 7 | B# |
Look at the table and you'll notice three things:
- Each scale shares its lower tetrachord with the scale before it, which has one sharp fewer, and its upper tetrachord with the scale after it, which has one sharp more.
- The sharp keys follow one another a fifth higher each time.
- Each new sharp also appears a fifth above the previous one.
The order of sharps
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, one after another and in order, all the scales that contain sharps. For each one, give the tonic, the leading tone, and the number and names of the sharps.
Now that you know the order of sharps, the next lesson shows you how they are written at the start of the staff, in the key signature.