# Function of augmented-fifth in figured bass

What is the harmonic function of the 5+ in the figured bass in the following snippet?

If I have interpreted the figuring correctly, a F♯ figured 5+ should realise the triad F♯ A C𝄪. I am confused for two reasons: firstly that the C double-sharp is completely out-of-place in this key; and; secondly, that the figure appears to be enharmonically equivalent to a D major first inversion triad (why then figure with a 5+, rather a 6?)

(Snippet was extracted from a work by Jacques Hotteterre, Deuxiéme Suitte from Premier livre de pieces pur la flûte-traversiere, et autres instruments. Op. 2 (Paris 1715), published at IMSLP.)

• An augmented chord on the note of F# consist of the notes F#-A#-Cx. An augmented chord consists of a root-note, a major third and a augmented fifth. Jan 7, 2021 at 12:13
• I think it is simply an error. Jan 7, 2021 at 12:34
• @NeilMeyer F#-A#-Cx is an augmented triad. Are you saying that is the chord when the score is giving a `A` natural? Jan 7, 2021 at 13:54
• it’s not an augmented triad, it’s figured bass not a chord symbol like C+
– user71850
Jan 7, 2021 at 17:33
• Please consider accepting one of the answers. I would accept Semiprime's answer as it is the best informed and best documented answer. Jan 10, 2021 at 18:04

It’s an error. In the early editions, it’s a 5 with a backslash through it. Confusingly, whilst the backslash (alternatively the forward slash) typically meant a raised interval, with a fifth it was just as often meant to signify a lowered interval, as here. This modern editor has mistakenly interpreted it as a raised interval and substituted the backslash figure for the alternative ‘ligature 5+‘ without noticing that the c# implied by that does not make sense.

The actual chord meant for the bar is V7. The extending line goes to the d in the bass: this is the root of the chord.

The original backslashed 5 is in a sense not correct either, as that would ‘strictly’ imply c-flat. Here it seems to have been added as a reminder that the c-natural continues through the bar. Other composers might have used 65, but there were no firm rules and practice varied widely.

EDIT:

ok this gets weirder. If you look in the first edition at the beginning of the first sonata, you’ll see the composer uses the strange ‘wiggly line crossed with a straight line’ even when there’s a 6 above the bass: i.e. as a shorthand for 65. There’s lots of examples through the sonatas. In the OP snippet if you replace the 5+ with 65 then the music sounds completely normal.

EDIT 2

so also checking Hotteterre’s book l’Art de Preluder, the backslashed 5 is used again as a substitution for 65 (plenty of examples of 6 in the melody around page 64ff). What we seem to have here is an example of a figured bass notation style that didn’t survive until the end of the Baroque. Short answer: a modern edition should use 65

• Comments are not for extended discussion; this conversation has been moved to chat. Jan 8, 2021 at 15:08

If you also look at the 5th bar...

...the `5+` figure is used again.

If the bass were unfigured, both of the chords could be `6` or `6/5` chords, some kind of dominant harmony.

I think the editor may be using `5+` to mean a tritone. From my understanding of figured bass that is incorrect. It's confusing.

As I understand figured bass, a plain numeric figure has the interval quality of whatever the key signature gives. So in a key signature of one sharp a `5` above a `F#` is `C` natural and above `C#` a `G` natural. Just to prove this basic point `6/5` above `F#` in `G` major would have us play `F# C D`. The point being a `5` doesn't always mean perfect fifth. It could be a diminished fifth depending on the key signature. The `+` means raise by a half step.

If that's all correct, then in `G` major `F#` bass with figure `5` is `#F C` and with figure `5+` it becomes `F# C#`. Likewise with bass `C#` a `5+` means `C# G#`. In either case that - diminished fifths above leading tones raised a half step to perfect fifths - simply doesn't make sense in this music.

If the intention is for `5+` to mean raise a perfect fifth by a half step to get the enharmonic equivalent of a minor sixth - to produce `F# Cx/D` and `C# Gx(A)` - it "fits" the obvious expectation for `6` or `6/5` chords, but it's really confusing, and given my understanding of figured bass, simply wrong.

Earlier I could not find the original edition, but here it is below.

Also, from a figured bass guide I have:

the following symbols indicate that the note referred to by that number should be lowered by a half step...a forward slash through a number (very rare)

That seems to make it all clear and confirms my suspicion: the interval is a diminished fifth.

I still don't understand why the editor chose `5+`. I haven't seen anything to say that figure would be a diminished fifth, and more importantly, it isn't the figure in the original score.

This diminished figure points out something I have seen before, but is confusing given most modern descriptions of figured bass I have seen. Modern guides would say the forward slash means "lower by a half step from the key signature." But, in the score the fifth is already diminished by the key signature. From the modern view the `5` doesn't need a slash. I think the convention is add the slash to make clear the fifth is diminished as a sort of "courtesy."

The score in this question has gotten a lot of attention, and maybe I sound overly critical about the question of the figured bass. I just want to say I think these editions at IMSLP from Andrea Bornstein very nicely done and he has made available a lot of great music. I downloaded several of his score about a year ago. Through his work I was able to access a lot of early music I wouldn't have known about otherwise. I just wanted make known my appreciation.

• "I think the editor may be using 5+ to mean a tritone": the practice clearly reflects the figures used in the source (discussed elsewhere on this page), but choosing that figure to do so in a modern edition is indeed confusing or simply wrong. This answer is correct to say that in general the plain figure normally means the diatonic interval, but as also noted elsewhere it's not uncommon to figure a diminished fifth with a flattened five (by whatever figure) even when the unaltered fifth would be diminished, as here. In other words, the error at least has a rational explanation. Jan 7, 2021 at 19:14
• it would be a strange choice, given that the 5+ symbol is unambiguously and uncontroversially used for ‘chromatically raise the fifth above the bass, but who knows? Something certainly a bit off with the edition
– user71850
Jan 7, 2021 at 19:40
• A modern edition would simply need to put square brackets around the 5
– user71850
Jan 7, 2021 at 19:46
• @Phoog, I made some answer edits after getting the original score. Jan 7, 2021 at 20:26
• @DamianleGassick but square brackets would imply that the figure is an editorial edition, which it is not. Michael Curtis: the second edition, however, uses 5 with a backslash, so practice in the early 18th century is clearly inconsistent. It seems possible that the editor was influenced by that edition (or perhaps worked only from that edition without giving too much thought to the meaning of the figure). Another fact (possibly not terribly significant) is that the second edition is engraved, unlike the first, which is set using movable type. Jan 7, 2021 at 21:15

I can‘t give a prove, but I bet in the old print posted by Michael Curtis the x is marked as key signature in both octaves and appears again in the bars where we have an F# like courtesy sharp: (red)

Now in the IMSLP version I think the + isn‘t just a failure or a bad transcription. It might design that this marks a V56 chord (dominant 7 - first inversion): play F#,A,C,D.

A wonderful piece, btw.

Well, the copy of the full score shows that + can mark an augmentation (yellow) or a first inversion of a dominant 7 (green), but as we can see the copyist in this case uses the notation 56 (blue).

Yellow: in bar 10 the 4+ defines the F# and in bar 14 we ha have 4+ and 5+ designing D#, the third of a B7 chord.

So finally I think the copyist is confusing by merging the same symbol (+) for different functions or this is simply an error, like Laurence Payne says.

• "appears again in the bars where we have an F# like courtesy sharp": I don't see that in the image posted by Michael Curtis. Can you point more specifically to an example? Jan 7, 2021 at 21:25
• @phoog: yes, done. (red) Jan 7, 2021 at 21:38
• the modern edition is based on the second edition 1715. Where the figures in E2 are normal sharp signs, the modern edition is correct to use the plus sign (your yellow). The slashed 5s in E2 have wrongly been transcribed as 5+ (green) because the editor seems not to have known that slashed 5 has meant both raised and lowered 5 at different times and has assumed raised. The modern editor also did not take the relatively short time needed to establish that the slashed 5 was an unconventional shorthand for 65 when the fifth above the bass is diminished.
– user71850
Jan 7, 2021 at 22:44
• That isn't a sharp, it's totally different. Furthermore, a sharp above the note applies to the third, not to the note itself. There are three examples in the second system of staves in the source, including the first note after the end of the example shown in the image. The sharp sign consists of two pairs of fine diagonal strokes, completely straight and parallel, as seen in the key signature here. The other sign is a single curved line (possibly s or 5) with a single diagonal stroke. Jan 8, 2021 at 1:28

Other responses have already indicated that the "5+" is a (less-than-ideal) attempt to transcribe the slashed-5 of the original publication. The question then becomes: what does the slashed-5 mean in the original?

When reading period sources, familiarity with instruction manuals from the same period and country is often useful. In this case, we can find the answer in Michel de Saint-Lambert's Nouveau traité de l'accompagnement du Clavecin, de l'Orgue et des autres instruments published in 1707. This is available on IMSLP: https://imslp.org/wiki/Nouveau_trait%C3%A9_de_l%27accompagnement_(Saint-Lambert%2C_Michel_de)

On page 11 of his manual, Saint-Lambert writes:

Le 5♭ ou ♭5 marque la fausse-Quinte.
Le [slashed-5] coupé marque aussi la fausse-Quinte.

That is:

The 5♭ or ♭5 marks the "fausse-Quinte" ["false fifth"].
The [slashed-5] cut also marks the "fausse-Quinte".

So according to Saint-Lambert's practice, slashed-5 means the same as flat-5 - what we would now call a diminished 5th.

Continuing, on page 14 he writes:

La fausse-Quinte s'accompagne de la Tierce, & de la Sixiéme.

The diminished fifth is accompanied by the third and the sixth.

Saint-Lambert then gives a caveat to this rule:

La fausse-Quinte s'accompagne de la Tierce & de l'Octave, comme la Quinte juste, lorsque la note suivante au lieu de monter d'un semi-ton selon la coûtume, fait un intervalle plus grand, soit en descendant, ou en montant.

The diminished fifth is accompanied by the third and the octave, like the perfect fifth, when the following note instead of rising by a semitone as is the custom, moves by a larger interval, either descending or ascending.

The case given here fits Saint-Lambert's rule perfectly, we have a slashed-5 figure in which the bass note rises a semitone, so we add the diminished fifth, a third and a sixth (C natural, A, D). In modern theory we have a very conventional first-inversion dominant seventh chord, with the bass note functioning as a leading tone moving to the tonic ("rising by a semitone as is the custom").

Another source for this rule in French music is Jean-François Dandrieu's Principes de l'Acompagnement du Clavecin (1718): https://imslp.org/wiki/Principes_de_l%27accompaignement_du_clavecin_(Dandrieu,_Jean-Fran%C3%A7ois)

Under his Table pour s'exercer sur l'Acord de la Fausse Quinte ("Table to practice the chord of the diminished fifth"), Dandrieu writes:

Cet acord est composé de la Fausse Quinte, de la Sixte et de la Tierce. On le fait comunément sur la sètième note du Ton, que l'on nom Soufinale, quand cete note remonte à la Finale. On marque l'acord de la Fausse Quinte de l'une de ces deux manieres [slashed-5]. ♭5.

This chord is composed of the diminished fifth, the sixth and the third. It is commonly found on the seventh note of the scale, which we call the "Soufinale", when this note rises to the "Finale" [Tonic]. The chord of the diminished fifth is marked in one of these two manners [slashed-5]. ♭5.

From my own practical (but most definitely amateur!) experience of playing continuo in French music, Saint-Lambert's caveat about larger intervals rarely occurs in practice, and my first instinct is to play a 6/5 chord whenever I see a slashed-5 symbol. We can see this in the Hotteterre. The next bar has another slashed-5 on an F-sharp, here the bass noodles around a bit before finally arriving at the G, so another 6/5 chord would be appropriate. In the following bar there is a slashed-5 on a C-sharp. Here the bass falls to an A before rising to a D, so strictly following Saint-Lambert we wouldn't add the sixth, but the C-sharp is clearly functioning as a leading tone to the D, so a 6/5 would work again. [Edit: But I note from Saint-Lambert's bottom-left example in the image above, which also has this pattern, that he doesn't add the sixth initially, but he makes the chord over the C into a dominant seventh. I'll try to remember this when I'm playing in the future - maybe it will sound more "French".]

• Thanks for giving some documentary context to what’s been discussed. I suppose the next step for the OP is to find a modern edition where the backslashed 5s have been correctly interpreted.
– user71850
Jan 8, 2021 at 23:54
• As the best informed and best documented answer to the question this deserves more upvotes. Jan 10, 2021 at 18:02

It's wrong. In bar 2, there's an A note against the F♯, whereas a major triad there would contain A♯. And the next bar has C♮ which would clash with the Cx from an F♯ augmented. So neither works musically.

If the 5 meant a V chord, thus D, then there's a bit of sense. But an augmented D chord would be D F♯ A♯ C. Thde A♯ then is dissonant against the Bs in both bars.

• there’s no a# indicated here - that would be a sharp under the 5. Also, 5+ in figured bass is nothing to do with chord V, it simply indicates that the note s fifth above the bass is raised - here c#. In any case, the whole thing is a transcription error detailed in my reply
– user71850
Jan 7, 2021 at 17:02