What chord is this?

[Farnaby]

The leading tone of the key is E.

The phrase is in F. The key signature and cadence in bar two makes that unambiguous.

As to why the chord tone appears on what seems like a weak beat, that would be just standard harmonic acceleration as one approaches the end of the phrase.

Some things become subjective when analyzing very complex tonal harmony. This not so much. This would be a textbook use of the half diminished chord. What you don’t ever see is a ii in its root position as a neighbour chord to the tonic.

If this were an example that was using modern idioms, then open season but I can just look at the passage and see how it is some Bach passage appropriated to teach simple tonal harmony.

There are two interpretations,

1. The D is chord tone.
2. E is the chord tone.

Now try each gbd , then gbe.

Notice that gbd doesn’t sound right ? Notice the parallel 5ths occurring gd to fc. This is why it is clear that the D cannot work without the E which is why the E is the chord tone and the reason why you would label it a half diminished first inversion among other things. The reason the D is there is because without some sort of movement approaching the end of the phrase, it would be uttterly stale. This is why the D is there. The D is not necessary, the E is.

Hope that sort of takes the subjectivity out of it,

Clearly the 1st phrase is in Bb definitely not F. The perfect cadence in bar 1-2 proves that. A brief study of Bach chorales will show that the chromatic passing note (E natural in this case) is quite common in approaching a perfect cadence. Modulation is not uncommon either, so just because the key signature says F and the final cadence is in F, the phrase in question can still be in B flat. We only know that the music will finish in F major if we continue onwards - but at the start of bar 2 we are firmly in Bb.

Substitute an E flat for the E natural and all will still sound well. It doesn't function as a leading note here so no interpretation of a C7 (without the C) is needed.

I think you have bent a simple solution into a complex one. I'm not saying your version is impossible, but if it looks like a duck and sounds like a duck then.....

Your solution involves crowbarring a C7 chord into the final quaver of the bar. Not impossible I grant, though I suspect Bach would have raised an eyebrow in this particular example- but there is a simpler solution quite in accordance with Bach's practice. It's G minor - but with a chromatic passing note (as you point out) to avoid the potential parallel 5ths.

Plenty of scope for subjectivity and differing interpretations.

[BertKoor]

Look, to the op, [...]

Let's see whether he's still involved...

Thank you in advance!

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[Farnaby]

He probably lost interest once Master Bach raised his head

[jancivil]

If we play through this and allow the ear to be the judge*, the entire passage is pretty clearly in F.

1) Does it sound like Bb to F is I to V after the seeming (not quite) cadence to Bb? It's IV - I.
2) Is there any harmony containing Eb? Absent that, there is no effect of chromaticism present.
3) "Since the 'dominant' harmony explanation is only supported by a weak passing note (E)" - *La Si Do is not weak. It's a semi-strong (actual V is actually stronger because rising fourth root movement) dominant move to the F harmony.

"I would interpret this more as a passing chord using the dominant 7 second inversion that is lacking a root. I would notate it if V 4/3 . Technically is would be VII half diminished 6 but those all tend to fall under the dominant group so it’s usually just easier to think of it as a V 4/3."
No, and no.
The E may be said to create a momentary vii6/5, which besides the fact of the (non-emphasized) dominant function is a real scale degree and a real harmony.

The question in the OP was asked and answered. G minor triad, ie., ii5/3 on a strong beat. The E {on the 'and' after 3} is a diatonic passing tone, & not every Si-Do spells V-I per se.

If a teacher indicated a V4/3 the student writes a C dominant 7th, bass = G. Pertaining to 'It's easier just to say V4/3 because it's a dominant harmony anyway': Occam's Razor applies. You've decided there is a vii owing to a simple stepwise passing tone and assumed a note not written, C; but there's no avoiding the simple fact.