This post is part of the guitar chords from first principles series: it isn’t strictly necessary, but I’ve included it for completeness. Following on from the basic music theory post, we’ll look at why double flats and sharps are needed, and why B#, Cb, E# and Fb exist, so that when you come across them in written music, you won’t go into a panic and freeze in a cold sweat.

There are times when it is more correct to write a note as, for example, Gbb rather than F, or Fx instead of G. Let’s look at why — take the scale of A minor (harmonic minor, to be precise):

A-B-C-D-E-F-G#-A

See how every note letter is used in alphabetical order in the scale? OK, let’s look at Ab minor, where every note is one semitone lower than in A minor:

correct:   Ab-Bb-Cb-Db-Eb-Fb-G-Ab
wrong:     Ab-Bb-B -Db-Eb-E -G-Ab

Here, we see a use for Cb and Fb: if we just used B and E, the sequence would be lost. By using Cb, it’s obviously a minor third. Likewise, Fb is quickly identifiable as being the minor sixth rather than the augmented fifth, which would be written as E natural to maintain the alphabetical sequence.

Now think about the diminished chord, which contains root, minor third, diminished fifth and double-flatted seventh. An Abdim chord would therefore be:

Ab-Cb-Ebb-Gbb

The diminished chord is a stack of minor thirds: each note is a minor third (3 semitones) higher than the last. So on a fixed-note instrument like guitar or piano, the same combination of notes make four different chords. Using strict music theory, though, the notes have different names in each chord:

Ab dim: Ab  Cb  Ebb Gbb
 B dim:     B   D   F   Ab
 D dim:         D   F   Ab  Cb
 F dim:             F   Ab  Cb  Ebb

The same principle applies for double sharps. For example, the fifth note in the scale of B major is F#. A B+ chord (B major triad, but with an augmented fifth) would therefore contain Fx rather than G — even though Fx and G are exactly the same note on the guitar and any other fixed-interval instrument.

Taking this to its logical conclusion, it’s possible to construct an argument for triple-sharps and triple-flats. Take, for example, a piece of music in C# major. The major seventh is B#. Within that key, you’d expect the associated simple chord to be B#dim (B#-D#-F#). However, if you use a B#+ chord during modulation, that would contain the notes B#, Dx and… F### (perhaps F#x?). To quote Mary Poppins, that's going a bit too far, don't you think? Comments welcome.

[Posts in this tutorial series]