In Part I, we saw that the key signature in modern music notation supports 15 major keys although only 12 are usable at a time if one wishes to avoid enharmonic scales. Here are the 15 with the 12 that Bach used in the major key preludes and fugues of his Well-Tempered Clavier in bold.
C# F# B E A D G C F Bb Eb Ab Db Gb Cb
Note that C#, F# and B are no more preferable than Db, Gb or Cb. A choice of 12 of the 15 will always include E, A, D, G, C, F, Bb, Eb, Ab but 8 combinations exists for choosing C# versus Db, F# versus Gb and B versus Cb. Mind you, one would probably be unlikely to choose Gb over F# if they had not also chosen Db over C#. That would mean having a 4-flat and a 6-flat but no 5-flat. So, in practice, a composer choosing 12 major keys from the 15 possible would probably choose either C#-Ab (as did Bach), F#-Db, B-Gb or E-Cb.
But we are still missing some enharmonic alternatives. Each of the seven letter names can appear with a sharp or flat (or nothing) and that gives us 21 note names:
Ab A A# Bb B B# Cb C C# Db D D# Eb E E# Fb F F# Gb G G#
In particular the following are not from amongst our major key candidates:
G# D# A# E# B# Fb
If we have a look at our minor key signatures, the following are missing:
E# B# Fb Cb Gb Db
These are acceptable note names, they just can't be (major and minor, respectively) keys. Why not? Well a clue is in the fact that we've already seen the keys that have up to 7 sharps or 7 flats. Given there are 7 distinct note names in an octave, we've run out of notes we can make sharp or flat!
C# major, for example, already sharpens all 7 letter names. What would G# do?
The C# major scale has the following notes:
C# D# E# F# G# A# B# C#
Note that even though there are alternative enharmonic spellings of these notes when considered in isolation, in the context of the C# major scale they must be spelt as above.
This is because only one note can use each letter name. Furthermore, even though the notion of a double-flat or double-sharp is available for individual chromatic notes in a piece, the diatonic notes of a scale are restricted to natural, flat or sharp.
We'll explore these two conventions more in Part III.
The original post was in the category: music_theory but I'm still in the process of migrating categories over.
The original post had 4 comments I'm in the process of migrating over.