Double sharps--What is the rule for using f double sharp when the key is C-sharp minor, where both f sharp?

Question

and g sharp are in the key signature. Beethoven uses f double sharp in measure 27 of Moonlight Sonata in a csharp- dim7 chord, and then uses it in measure 34 in a c sharp minor chord. In the second case in particular, why is it a double sharp, rather than g natural ? What are the rules?

Answer 1

I can see that this question was inspired by the Moonlight Sonata question posted some days ago.

This is music theory we're talking about here... For the first example, it is because we're making the F sharp sharper, and making it lead into the G# at bar 28. For this reason, it becomes like the leading note of the key of G#, and must be written Fx rather than plain G. Also, diminished 7th rules come into play here: since the bass note is Fx, the notes would be Fx-A#-C#-E. This is because the notes have to adhere rigidly to the triad with seventh, ie F-A-C-E. So if the bass note were plain G, the notes of G dim7 would be G-Bb-Dd-Fb, which is out of context.

For the second example, there are really no hard and fast rules. The chord in the right hand could easily be a C# dim7, in which case the notes would be C#-E-G-Bb. However, one could analyze it in such a way: the presence of the A# indicates that Beethoven meant it to be an Fx dim7 chord. This is to serve the purpose of leading into the B# dim7 chord with G# bass in bar 35, which is actually really a G#9 chord. Hence you have, again, the Fx-G# movement, which is important in classical music.

Answer 2

Actually, you have identified both of these chords incorrectly. They are both F## diminished seventh chords (in measure 34, the G# in the bass is a pedal and not counted as part of the chord).

F## is the root. The rest of the notes stack in thirds above it:
F## A# C# E.

(C# diminished 7th is spelled C# E G Bb. Even though the "notes" are enharmonically the same, the roots of the chords are different).

Beethoven is using the note a half step below (F##) to emphasize G# in both cases--in other words, be is using the leading tone, or 7th scale degree, in G#.

It might be easier to think in G for just a second. The 7th scale degree of G is F#. You would always use F#, not Gb, even though they are enharmonically equivalent. Tonally, F# goes to G, but Gb implies a motion to F natural.

Now apply the same logic back to G#--you can see why Beethoven would use F## and not G natural. F## resolves up to G#.

Answer 3

It has to follow the rules of the key. If F# is part of the key signature and you want to sharpen it, you must use F##. If you were to transpose it into another key, the double sharp indicates that the note will need to be sharpened, regardless of what key you are transposing into. Remember, the key is arbitrary - it needs to be able to be transposed into any key, while following the same format.

PS: This is one of my favourite pieces!

Answer 4

You generally use a double sharp to avoid writing the same note twice. If you can avoid two Fs for instance, it is easier to scan the part. You would use the F double sharp to avoid a G natural next to a G sharp.