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The piece modulates from G minor to Bb major between the bars 12-14 but I don't know how to mark these chords as they have B natural in them, which doesnt't belong neither to G minor nor Bb major. So, what function does it actually have?

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Hmmm, this is a little off the cuff, but I think it's probably easiest to look at mm. 12-13 (primarily 13) as a viio/ii or V7/ii in the new Bb key. That is to say, the B-nat is part of a secondary leading-tone or secondary dominant chord. I suppose it could just as easily be a viio/iv or V7/iv in the old key, and then you could call the iv a pivot chord like you already have. Probably it's six of one, half a dozen the other.

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I like being able to call the iv a pivot chord, so probably I'd call m. 13 a V7/iv (your call as to whether you want to label the first beat as V6/5 becoming V7 on the third beat or not) and then call the arrival iv chord a pivot into ii in the new key. The B-nat in m. 12 is probably better thought of as a chromatic passing tone that prefigures the next measure. –  Pat Muchmore Feb 2 at 23:05
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Food for thought: consider that when this was written, theory students weren't trying to shoe-horn everything into roman numerals as the zeitgeist of the time focused on controlling dissonance linearly through counterpoint. No one has actually addressed the function of the chord, which is to increase harmonic intensity as the lines move into the predominant before reaching the dominant and cadencing in the "new key". –  jjmusicnotes Feb 3 at 5:31
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Definitely agreed that Roman numeral analysis doesn't say everything there is to say and wasn't part of how anyone thought in Bach's day. However, function is precisely what such an analysis does address--when I said it's a secondary dominant (V7/iv) that's just shorthand for precisely what you're saying about increasing harmonic intensity as the harmony moves to the pre-dominant. It's good to remind ourselves what the shorthand stands for every once in a while, but I don't think it's fair to say I didn't address function. –  Pat Muchmore Feb 3 at 14:20
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Well put; glad to see that we are in agreement. Also, welcome to the site, I'm sure many people here will benefit from your expertise. –  jjmusicnotes Feb 4 at 1:05
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Interestingly, there is a story that one of Bach's sons started showing him the new concept of "harmonies" in some detail. To which Bach responded "that's very interesting, but I just don't think that way." I personally would analyze it as a V/ii in the new key. –  BobRodes Feb 6 at 17:24
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Effectively it's a G dominant 7th leading to a C min. in the next bar. The Eb note works like an augmented 5th,(as in D#), pushing even more to the iim as in Cm. So I'd call it a dominant to the iim in bar 14.

Bar 13, now I've played it, could even be construed as an Fo, called Vo in this part going to Bb, or VIIo if you think it's still in Gm at that point. Putting in the 'missing' Ab sounds o.k. to me, and I think Bach used this sort of chord to modulate on occasions.

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But the Eb as augmented 5th thing would only make sense if it were moving to C MAJOR, right? Since Eb is part of the C minor chord, it isn't leading to anything during the G7, it's just a garden-variety passing tone. –  Pat Muchmore Feb 3 at 3:18
    
@PatMuchmore - yes, agreed, the Eb is a consonant non-chord tone. –  jjmusicnotes Feb 3 at 5:32
    
After your edit, I understand your analysis even less. I agree with your first paragraph that the harmony of m. 13 is leading to c min. Re-imagining the harmony as an F-dim-7 only makes sense (at least in common practice tonality) as an indication of a move to a Gb harmony. You're right that Bach would sometimes use enharmonic respellings of o7 chords to modulate, but one does this via a secondary leading tone. B-D-F already makes sense as viio leading to c min, the G on the third beat makes it more like V7 to c min. Am I misunderstanding your intention? –  Pat Muchmore Feb 3 at 21:35
    
I'm merely hypothesising, which, in the absence of 'key' notes, is all I can do. With a B-D-F playing, it's feasible to think 1, it could be the dominant G7 leading to the Cm. 2, it could be a stripped down diminished, 3, it could be a 7b9. Obviously, all this is supposition, as Bach left out the defining notes - probably on purpose, the teaser ! But it's fun to put in what may have been going through the composer's mind, to hear what would still work. –  Tim Feb 4 at 8:06
    
OK, I guess that's where you lose me, because in this case I don't think any defining notes are left out. Your option #1 requires no hypothesizing at all, G-B-D and F are all present and functioning precisely as one would expect for V7 of c to go to c. If there were only a D and an F or something, then maybe we'd need to resort to more exotic implications, but I think Occam's Razor applies in this case. –  Pat Muchmore Feb 4 at 16:27
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The B-natural in m. 12 is an anticipation of the B-natural in the next bar. The chord in m. 13 is the dominant 7th of the pivot chord that you correctly indicated on the score. V7/iv for the m. 13 chord.

Discussion of what the composer was thinking is impossible. Whether or not there were Roman numerals at the time, or something similar, is also conjecture. The point is the composer knew the same as we do, just in a different way.

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