James Tauber

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The Naming of Musical Notes, Part II

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.

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Comments (4)

Rachel Cross on Sept. 28, 2005:

Hiya James: might I add that which key signature you choose also depends on where and in what context it occurs? Also if it is the main key of the piece (ie in earlier than some C20 music, the tonic) the related keys that you're using through the piece will affect which signature you choose to use. I always thought that easier=preferable=least number of notation ie least number of sharps/flats. Last note (heh heh) is that I was unaware of a convention about not using double sharps/flats in scale writing as an exercise (i.e. scales on their own rather than in a composition). At school and Uni we always used doubles, because you have to to write out the whole range (I know this is a bit circular, just keep reading); leading me to suppose that in Perth at least theory makers use doubles (in scale writing). Oh and also AMEB Musicianship exam writers and markers. Also RCM, London in the 1970s (when my piano teacher trained there!). Just thought of something else, I prefer C# minor to D flat minor because E major is a hell of a lot easier to think about than F flat major. I see your point though, theoretically you could just about write anything as just about anything!! RC :-)

James Tauber on Sept. 28, 2005:

I was very careful to call it a "convention" for the reason that there is nothing "wrong" as such with having a notion of a G# major scale. It is possible to write out the scale using double-sharps and it doesn't surprise me that AMEB might require one to be able to do so. But in practice, double-sharps and double-flats are avoided in diatonic scales, at least in 12-ET music, in favour of the enharmonic equivalent that avoids them.

The main points I am heading to in this series, though, are that (1) note naming, while systematic in its own way, has certain peculiarities caused largely by its bias towards C major; (2) constraints on note names are different depending on whether one is considering the note in isolation, in the context of a diatonic scale or in the context of an actual piece of chromatic music.

You make a good point that a choice of which enharmonic spelling you use might be based on what related keys you are going to use.

anonymous on Dec. 18, 2005:

When a note is already flatted once by the key signature, how do I write it so that it ends up being double flat?

For example, if I am in the key of Ab, and I want to write a B-double flat, how do I write it? (Do I just have to add one, extra flat-accidental to the B?)

rmac on Feb. 21, 2007:

why do you ask that
Created: Sept. 15, 2005
Last Modified: Sept. 15, 2005
Author: jtauber