15: Enharmonic Equivalence

“Enharmonic equivalence” may sound daunting, but it really isn’t that hard. It merely puts a name to the fact that there are two reasonable ways (and many more ways that are so convoluted they border on absurd) to name many notes.


For example, would you not agree that G and A are a whole step apart, so there’s a note between them? And would you not agree that you can get there just as easily by sharpening G as by flattening A? This, of course, is true. (Just as one can sharpen F or flatten G to get to that note in the middle; or flatten D or sharpen C; and so on.)

When there exists a pair of notes like this, separated by a whole step, the note in between has two names: [upper note] flat and [lower note] sharp. These two notes—F sharp and G flat, for example—are said to be “enharmonically equivalent.”

Of course, one could say that, for example, E-triple-sharp and G natural are equivalent (because, yes, E and G are that far apart)—but if you actually see something asking you to play “E-triple-sharp,” then you’re either playing something ultra-modern in which rules don’t matter anymore, or you’re playing something written as gag to be deliberately funny or hard to play.

Double sharps or double flats can and do happen, but they are much rarer than their single cousins. Let me show you an example of a situation, rare as it may be, in which using a double-sharp (and not its much simpler enharmonic equivalent) is absolutely necessary.  

The key of G sharp major has 8 sharps (you’re much more likely to see it written as the 4-flats A-flat major, but just go with this for a moment), and we must use every letter name once, so we can start off with

G A B C D E F G

just as a baseline.

Then we need to spend 7 of our 8 sharps on our first pass, so we sharpen them in order (F C G D A E B)—but we end up sharpening everything, and we end up with

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

but this is a problem, for two reasons: 1) we haven’t spent all our sharps, and 2) F# to G# is a whole step, and the last interval in a major scale is a whole step—so we make another round of FCGDAEB, spending as many sharps as we still have, converting sharps to double-sharps.

So the final correct spelling of G-sharp major is indeed

G# A# B# C# D# E# Fx G#

(Where here “x” means “double-sharp”).

We do have to use the “Fx” and not the more intuitive “G” because although the note technically does sound as a G, recall that one of the rules of scale-building is that every letter name must be used.

“Fx” and “G” are equivalent, so even though “Fx” is more awkward most of the time, here, we must use it.

One last caveat about equivalence: Beware the pitfalls of B/C and E/F. B-sharp is C, and C-flat is B; and E-sharp is F, and F-flat is E. I’ve seen these two spots trip people up many times precisely because, unlike, say, C to D which has C-sharp/D-flat in the half-step between them, there is no gap-note between B and C, or between E and F.

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