Why isn't there a unique, compact, easy to write, double-flat symbol?
The current double-flat is not easy to write as the "x" symbol is for double sharp.
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I'll go ahead and answer this question in its current state. Many times, looking at musical practices, verbal languages, and many other topics, we ask questions like "Why do we do it this way? Wouldn't this other way be more efficient?" (Or "easier to understand," or "clearer," etc.) Why does the English language let you make a "k" sound with either "c" or "k"? And an "s" sound with either "c" or "s"? Why don't we just pick one letter for each phoneme? Why do we refer to musical pitches with the letters A-G and then modify them with flats and sharps, instead of just using 12 letters? Why does guitar have intervals of a 4th between all its strings, except for a 3rd between two of them?
Invariably, the short answer is "just because that's how it's done." And the longer answers often become insufferably long, dragging out the history of alphabets from Phoenicians to Greeks and of Germanic and Latinate linguistic influences, or brother Guido and his gamut, or the vihuela and re-entrant tunings.
Because all of these are living practices, evolved and amalgamated over centuries, not invented on the spot by one omniscient engineer who can see these glaring inefficiencies from the outset. We do things the way we do them because that's how they're done—and no, it's not just a matter of hidebound traditionalism, resistant to change. (I mean, it might also be that, but it's not only that.) We do things this way because there is an inertia to symbols and to tools. We use the QWERTY keyboard, even though it was invented specifically to slow us down, because so many people have learned on it that it's hard to create a big market for DVORAK. We write and talk about musical notes the way we do because everyone understands us; if we did otherwise we'd also have to disseminate our new systems along with our meanings or risk being ignored. George Bernard Shaw did his best to reform English phonetic spelling, but it didn't catch on, maybe because we're all too used to deriving the concept of a "circle" from the word "circle," and it's an extra cognitive step to decode the unfamiliar signifier sirkel.
And we use two flats for a double flat because it works perfectly well and everyone knows what it means. No one has felt so cramped by it that they bothered to "invent" another symbol; no winds of change have confused it with some other symbol used in some other way (like the troubled histories of time signatures, rests, and mensural notation). It is unaltered because no force with sufficient societal momentum has altered it.
There is. Unicode: 𝄫, Usually printed similar to this
It sure does look like two flats next to each other, but that's not really a problem (in fact it's probably a good thing. It makes the meaning easy to figure out).
A double flat is two flats together with varying degrees of spacing between the two depending on font...
It seems silly to have to post something so specific, but in response to @CarlWitthoft's comment, the spacing between the two flats signs of a double flat can vary. I've always understood the sign to be two flats "stuck together", slightly overlapped, but obviously whether that can be printed depends on the font available.
An old version of Grove's Dictionary...
I'm surprised the proposed double flat is reference, but I don't have access to Mus. Assoc. Proceedings 1890, p.101.
Apparently Ross' idea caught on, an example of use in Busoni edition of WTC II, prelude in A flat major...