5/7b in figured bass
What does 5/7b mean in figured bass?
If it is just a 7th chord in root position, then why is it not just 7b?
In other places in the same score, 7 or 7b are used to denote a 7th chord.
Here is the example, from Vivaldi's "Filiae maestae Jerusalem" (source):
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I wish the IMSLP had another source beside the Martin Straeten version. It could help confirm the meaning. I notice the key is C minor and this notation uses the modern three flats rather than two flats which was common in the Baroque era. Straeten may have modernized some things in the score. Perhaps too he changed bass figures?
Usually a modification of the numeric figure with b, #, + means an alteration from the key signature. In this case both the 6b and 7b refer to the A and that is already a flat from the key signature. So I think this may mean two things:
It simply confirms the flat of the key signature.
If the original score was for a key signature of two flats, it would have been Eb and Bb, in which case these figure would require the flat to mean Ab, because the flat wasn't in the key signature. (I suspect this is the actual case, but we would need to see the original score to confirm.)
EDIT
About the 5 figure.
As far as I can tell the 5 is redundant. Plain 7 means a root position seventh chord and 7/5 also means a root position seventh chord. The 5 doesn't seem necessary to clear up some possible confusion from the previous chord. Either way a Bb dominant seventh chord should be played.
The 5 is not redundant, and it doesn't mean you have "a four note chord."
The point of the notation is that the 7b 5 intervals from the new bass note are the same notes as the 6b 4 intervals from the previous bass note.
In other words, since the continuo is for organ (which can sustain notes indefinitely), you simply hold those two notes down, and only the bass note moves.
That is exactly the same as what the violins are playing, of course.
What is more interesting about this example is that the second chord played by the strings is actually a 6b 4 2 chord, which then becomes a complete 7 5 3 dominant 7th. But Vivaldi wanted the D played only the viola, not by the organ continuo. Otherwise the figuring would have been 6b 4 2 followed by just 7b.
A typical organ continuo registration might have made the complete 6b 4 2 chord sound muddy, especially if a cloth-eared organist voiced it with the D in the tenor, a second above the bass C!
Re the edition, you can view an alternative professionally published edition here - though I don't agree with the continuo realization: www.prestomusic.com/sheet-music/works/52700--vivaldi-introduzione-al-miserere-rv-638-filiae-maestae-jerusalem/browse
In traditional figured bass pedagogy, a single figure indicates a non-chord tone or its resolution (e.g. 7-6 for a suspension). Thus to indicate a chord, at least two figures are required, and 7/5 is traditional for root-position 7th chords (6/5, 4/3, and 4/2 for the other inversions).
It means you have a four-note chord in root position.
It means you have what looks like Eb:V7 in root position, the notation is derived from the distance the root the third, fifth and seventh are from the root note. It also looks like the sevenths wants to be flatten for some reason.
In this case, 7/5/3, 7/5 and 7 all mean the same thing a four-note chord in root position.
You can find a thorough explanation of all the names for inversions and how the names where derived in my answer here.
How to memorize seventh chords and inversions on piano?
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