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I'm wondering whether or not standalone accidentals always imply 3rds in figured bass notation.

Is (5)(♭)(8) the same as (5)(3♭)(8)? Is (9)(♮) the same as (9)(3)?

Can a figure 3 always be inserted beside a standalone accidental within a stack without changing its realization?

I may as well also ask: double flats and sharps (𝄫, 𝄪)- were they ever actually used in figured bass notation during the Baroque period? I don't recall ever spotting double accidentals in the figured bass sheets I've seen till now.

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Yes, an accidental by itself always refers to the third above the bass.

I also have not encountered a double-accidental in baroque music, though Wikipedia places them as early as 1615, which at least allows for the chronological possibility.

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  • Some manuscripts of Bach's WTC adopt the X for double sharp. Others just use a single sharp sign. I believe they all use single flats, though.
    – phoog
    Commented Mar 27 at 7:12
  • Wikipedia's source for the 1615 claim is geminimusicaltheatre.com, which is hardly an authoritative source and does not explain how it reached its conclusion. I rather suspect that it is a circular reference: they got it from Wikipedia and then someone addressed the "citation needed" tag that had been applied to the Wikipedia page by finding the geminimusicaltheatre.com/accidentals.html page through a web search and adding it as a reference.
    – phoog
    Commented Mar 27 at 7:58
  • I'd be surprised if any music written in 1615 or earlier even came close to a tonality that would call for double sharps or flats. When was the first piece written in A major? E major? B major? F minor? B-flat minor? After 1615, I suppose.
    – phoog
    Commented Mar 27 at 8:08
  • I've removed the 1615 claim from the Wikipedia article.
    – phoog
    Commented Mar 27 at 8:33
  • @phoog I had the same thought that keys requiring double accidentals weren’t in use that early — at least until Bach or closer to him. I also thought there was a detailed post here about the history and development of double accidentals, but haven’t found it. And thanks for letting me know you edited the Wikipedia article.
    – Aaron
    Commented Mar 27 at 15:11
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double flats and sharps (𝄫, 𝄪)- were they ever actually used in figured bass notation during the Baroque period? I don't recall ever spotting double accidentals in the figured bass sheets I've seen till now.

The most likely place to find a double-sharp figure would be in the third of a V/V chord in G♯ minor or perhaps as the Picardy third of a piece in A♯ minor. Have you ever seen a piece in G♯ minor with a continuo part? I seriously doubt that any exist. I rather doubt there are many pieces in G♯ minor (or D♯ minor or A♯ minor) at all, outside of the Well-Tempered Clavier.

The same line of reasoning may be applied to the double flat -- people simply weren't writing music for ensembles in keys that needed double-flat accidentals, especially not on the third of any chord. On top of that, the double flat sign had not yet come into use, as Aaron's answer implies, and the double sharp was only invented in the late baroque.

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