Rare Musical Keys and Unused Key Signatures

From the Complex to the Musically Absurd

A close up shot of a musical sheet
Karl Tapales / Getty Images

There are a few keynotes, namely B#, E#, and ​Fb, which seem to be missing from the circle of fifths. But, just like on the piano keyboard, these notes are really just C, F, and E in disguise.

So, there is essentially no need for these keynotes; and if they were used, their key signatures would include double accidentals, rendering them too complicated for practical use. B# major, for example, contains seven accidentals – five of which are double-sharps (x) – while it’s just a more complicated way of writing the accidental-free C major scale:

  • C        D        E        F       G        A        B
  • B#     Cx      Dx      E#     Fx      Gx      Ax

How Many Unused Scales Exist?

The circle of fifths shows only the working scales. But, if we expand on its pattern, we can see that it’s actually more of an infinite spiral, so there’s no end to the possibilities of musical scales. One could write a song in the key of B quadruple-flat if one were properly motivated (or sufficiently bored).

Thankfully, a key signature only needs to be as complex as seven accidentals. After that, double-sharps or double-flats come into play. Take a look at the order of the sharp key signatures (working key signatures are in bold):

(C) - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# - Fx - Cx (etc.)

G# major would be after the 7-sharped C# major, and it would also be the first scale to contain a double-sharp:

  • G-Sharp Major:         G#   A#   B#   C#    D#   E#   F##
    (enharmonic with)
  • A-Flat Major:             Ab    Bb    C     Db    Eb     F      G​

Try It Yourself: The key of C-flat major is the last active scale with flats. Try to find which key would come next, and which note in its scale would have a double-flat.

The ‘Missing’ Scales

Most notes act as keynotes for both major and minor key signatures, but some only label one or the other; three keynotes aren’t seen at all – here’s a simple breakdown:

  • Not Seen As Major:    G#   A#   D#
  • Not Seen As Minor:    Cb   Gb   Db
  • Not A Working Key:    Fb   E#   B#

To learn which keys exist, and which exist only in the minds of bored music theorists, consult the easy-to-read outline of the keynotes.