Enharmonic keys
This lesson explains how 15 scales come down to just 12 tones, and how that closes the circle of fifths.
Two scales are called enharmonic scales, or enharmonic keys, when their corresponding degrees are enharmonic equivalents, as you saw in the lesson on enharmonics in Part Two. Take C# major and D♭ major, for example: every note of one is the enharmonic equivalent of the corresponding note of the other.
Why it matters: 15 scales for 12 tones
There are 15 major scales, and as many minor ones: 1 with no sharps or flats, 7 with sharps in the key signature and 7 with flats. But the chromatic scale really contains only 12 tones, and therefore 12 starting points. Thanks to enharmonics, each of these tones can be the shared tonic of two scales that are enharmonic with each other. In each mode, three pairs overlap:
| Sharp key | Flat key | Sharps and flats in total |
|---|---|---|
| B major (5 sharps) | C♭ major (7 flats) | 12 |
| F# major (6 sharps) | G♭ major (6 flats) | 12 |
| C# major (7 sharps) | D♭ major (5 flats) | 12 |
| G# minor (5 sharps) | A♭ minor (7 flats) | 12 |
| D# minor (6 sharps) | E♭ minor (6 flats) | 12 |
| A# minor (7 sharps) | B♭ minor (5 flats) | 12 |
Two branches that meet
Now arrange the keys in two branches starting from C: the sharp branch (G, D, A, E, B, F#, C#) and the flat branch (F, B♭, E♭, A♭, D♭, G♭, C♭). Bend the two branches toward each other, and they meet where F# and G♭ are enharmonic equivalents. As they cross, further equivalences appear: C# meets D♭, C♭ meets B, and so on. The result is the circle of fifths.
So, starting from C through the order of sharps, you come back to it through the order of flats. Every step forward in the order of sharps is a step backward in the order of flats, and vice versa.
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
What it is good for
Enharmonic scales can stand in for each other. This lets you avoid keys with too many sharps or flats and makes reading easier. More broadly, enharmonics are the keystone of the modern tonal system: they are the link that joins the order of sharps to the order of flats. Through them the keys interlock, and, setting out from the same point along two opposite roads, they return to their starting point just when they seem farthest from it.
Copy the table of relative major and minor keys and, next to each key, write its enharmonic equivalent.
With every key now in its place on the circle, the next lesson shows you how music travels from one key to another.