This is an excerpt of the Sinfonia Nr. 1 in C major by J.S. Bach. I thought this were a "clean" modulation to G major, but to my surprise, Bach uses an f natural in the lower voice of m. 8. Is there a harmonic meaning/justification behind this? I experimented a little and found that the passage does not sound much differently if the f is sharpened.
The beginning of m. 8 is briefly back in (i.e., tonicizing) C major. Note the C major chord (C G E from lowest to highest) at the beginning of beat two. The three sixteenth notes leading into beat two constitute a G7 chord.
In my opinion, the compositional reason is rather complex but explainable, and this doesn't affect Bach's genius; quite the opposite.
From a melodic point of view, what he is writing here is an upper neighboring tone or an upper auxiliary note but changing register E-(F-E).
Also pay attention to the choice of F natural to match the mirroring lines interval-wise: F-E-D-C (bass) vs B-C-D-E (soprano), in both cases we have 1/2-1-1 tone sequence.
Please also note that F-E(bass) vs B-C (soprano) makes a harmonic progression well established in the practice: augmented 4th (F-B) resolving by contrary movement on to (E-C) by half-tones.
This is congruent with other more harmonically-oriented answers given so far: from a harmonic point of view, F natural belongs to C Major, which here is the subdominant of G Major, the tone in which the main theme of the piece is going to (re)appear, namely at the beginning of the second half of the second bar. Bear in mind that this D-C scale, the beginning of the main theme, belongs to the dominant function, here the D Major chord, so we have a IV(C Maj)-V (D Maj) progression leading to I (G Maj), not shown in the excerpt.
Even more, from an structural point of view, we could note the harmonic repetition (here creating tension) of the pattern IV(C Maj)-V(D Maj). The second time (2nd bar here), we have the first inversion in both chords, which melodically produces, in rhythmically accented places (half-note wise), the tetrachord C-D-E-F#-(G). In fact, regarding tension, in this harmonic sequence, the 2nd-3rd chords ---that is, V-IV from IV-[V-IV]-V--- are a (variation of the) deceptive cadence (usually V-VI, but note how the first beat of the second bar can be seen as a mixture of VI/IV from a melodic-harmonic point of view). Choosing F natural is coherent with/reinforces the violence of the contrast (delaying resolution, stepping back from the expected musical progression), which finally ends as expected ---this is typical from Bach's style; he is able to tease the listener as long as he wishes, but he never "disappoints" you in the end.
Nothing weird or mysterious, but truly the work of a master. The Master.
Nice melodic handover from C, B, A, G in the alto to the continuation F, E, D, C etc. in the bass. Yes, he chose to re-establish C major at that point. I think we just accept it as an artistic decision.
Well, we don't know why Bach wrote it that way. It make sense to believe that he simply wanted it to sound that way.
When the F natural is introduced in the first beat of that bar, the resulting harmony on that beat becomes a G7 chord which turns it into a dominant to C Major. but since we stay in the key of G Major at this point the C major is actually the subdominant in which case the G7 chord is a secondary dominant to the subdominant C Major.
It is impossible to answer why Bach wrote it that way, since we can't ask him.
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An elaboration. @AGuyCalledGerald wrote:
Is there a harmonic meaning/justification behind this? I experimented a little and found that the passage does not sound much differently if the f is sharpened.
Hmm the harmonic meaning is the choise Bach made. When adding a natural sign he emphasized a dominant type of feeling making the chord into a G7.
You could also say that by adding the natural sign he created an expressive feeling that is different from having an F sharp.
But since your experience is that the passage does not sound much differently it is just a little detail. But then you can say that Bach often has small details that kind of works like tasty spice on a great meal.
