Where do the double accidentals go in "theoretical" key signatures?
Recent questions led me to discussions of theoretical keys, which are defined by Wikipedia as keys with at least one double accidental in the key signature. (Unfortunately, the source of that definition is not given.)
The key signatures on Wikipedia (and most other sources I've seen) put the double accidental in the spot where the single accidental would go. In other words, for G? major, the F is in the spot where F? would normally go (i.e., at the beginning). This, I admit, seems intuitive to me:
Although the majority of online sources notate it that way, at least one other source puts the double sharp at the end. But this is hardly the greatest source, so I was skeptical that this notation would be correct. Imagine my surprise when I saw that LilyPond's default behavior (version 2.19.80) seems to notate it the same way:
While I can understand the logic of this latter key signature—the last added accidental appears last in the key signature—it's odd to see a key signature that begins with a C?. (With that said, I guess it's no more odd than seeing a key signature with an F!)
Is there an official rule for notating key signatures with double accidentals? Or is there no rule since these are just "theoretical" entities?
Note that, according to this discussion among the MuseScore community, the top key signature (with the F first) was custom made. The LilyPond key signature, however, exists by default.
(4)4 Comments
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I cannot give you any reference, but I'll try to give a typographer's insight into the problem and state my opinion. I hope it's fine.
Typography has some basic rules, and they are in general applied in this order:
Deliver the message.
Be consistent.
Be invisible (meaning smooth, not "shocking", eye-catching at the wrong places etc.)
Applying these rules, I would go with the double sharp in the end. The reason is that primarily you want to focus on the delivered message, and that is that the key is significantly odd. Basically, we want to break the "invisibility" rule, we want the signature to stand out. And this is what you do. First, it starts with C# rather than the usual F#, and second, I believe (I can't support this by any study though) that if you only count the sharps, the one at the end is more noticeable than the one at the beginning.
Actually, purely from my mathematical point of view, I would also consider the following option viable. It best delivers the message that the key is G# major / E# minor, but the first F# is or at least could be confusing.
Gould's engraving style guide Behind bars (Key signatures, p. 91) says only the following:
The order of accidentals follows the 'cycle of fifths'.
While there is no direct instruction on what to do in case of double sharps, it seems that the only two readings that are consistent with this principle are:
Add the double sharp last, cf. the second example of the OP.
Add a single sharp at the beginning and a double sharp at the end, cf. yo's answer.
Up to this question I would not have considered the double sharp as legal in the key signature. On the the other hand, I never read about a limit on the number of accidentals in the key signature and so I would have happily added an eighth (single) sharp, again at the f line.
This keeps the well-established order and appearance in place.
Update with all sparse references, which I could find:
This page lists under "extreme accidentals" 8 flats for Victor Ewald's brass quintet, (admittedly it also list John Foulds World Requiem with 6 sharps and a double sharp, so also no clear strategy here) and the German wikipedia offers under "double sharp":
Opposed to the simple sharp, the double sharp is typically not used in key signatures.
Personally, I can't see any logic in having both an F sharp AND an F double sharp. It can't be both.
I would put the F double sharp at the beginning for convenience. You are going to notice it there more than at the end of a group of sharps. We need to make life as uncomplicated as possible for the person reading the music.
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