At the 4th measure, Bdim7 appears. It resolves to F/C. But I can't understand how this works.
Can someone explain what is going on ?
I think it's important to introduce another interpretation, one that I see has been proposed by piiperi Reinstate Monica and Alexander Woo in the comments:
This is not a common-tone diminished seventh, but rather an enharmonically spelled viio7/V that leads to the dominant that appears in m. 61.
True, this dominant is embellished by first a cadential six-four and then two further measures of counterpoint (including a possible common-tone dominant seventh with the D7/C), but this is still a very clear dominant chord here (made especially clear by its hypermetrical accent).
When I teach the common-tone diminished seventh, I especially caution them against this very misreading: what looks like a common-tone diminished seventh resolving to an F chord is actually a much more common tonicization of the dominant.
The Bdim7 is better viewed as an Fdim7. In this light, it's a "common-tone" diminished seventh chord. Whereas a "tonicizing" diminished seventh "resolves" to the following chord, a common-tone diminished seventh shares a note in common with the following chord and serves a prolongational function. In my interpretation, the primary purpose of the diminished chord is to prolong the pitch F from the previous chord into the next, rather than serving a tonicizing function in relation to the C.
By placing the Fdim7 in second inversion, a chromatic ascending bass line is achieved.
For more on common-tone diminished sevenths, see Steven G. Laitz, 1008, The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening, 2nd ed. (New York, Oxford: Oxford University Press), pages 820-21.
Look at the notes rather than the chord names. And look at the whole line of music.
Bass line. A, B♭, B♮ - where COULD it go next but C? (Well, lots of places. But you see that C is a good place to go, maintaining the strong rising line?)
F is common to the two chords.
G♯, being a sharpened chromatic note, rises nicely to A. (That's why it's written as G♯ even if A♭ would have been more 'correct' for naming the chord as Bdim. But the notes are important, the label someone slaps onto the chord isn't.) See the same thing happening in the first 3 bars - C rising to C♯ rising to D?
And that's why it works. Strong musical lines within the chords. When the notes go somewhere good, the chords will follow.
In other posts the idea has come up of secondary functions actually fulfilling their role in the secondary tonic without necessarily making a dominant to tonic progression, and I think this passage is a good example. The local tonic shifts around on nearly each chord change, yet the functions are perfectly clear, even if it is a tricky matter of writing out the analysis.
F/A A7 Bb Bo7 F/C F:I6 V7 vi viio7/V I6/4 (V 6/4 appoggiatura) \------/ deceptive progression in vi D7/C Gm/C C7 F V42/ii ii V7 I \----------------/ dominant pedal
So, in order...
A7 a dominant in the relative minor
Bo7 a dominant in the dominant
D7 a dominant in the supertonic
C7 a dominant in the tonic
Each dominant progresses to different types of chords and to the reading eye that obscures the function, but it should be clear to the ear there is a lot of dominant functioning. Everything should have a strong harmonic "pull" to the ear, that's the dominant function at work, and the step-wise bass helps hold it all together.
If it isn't clear, some theory regards the "cadential"
I6/4 as actually a root position
V chord where the sixth and fourth above the bass are non-chord tone appoggiaturas. This is a possible analysis of the
F/C. The fact that the
6/4 appoggiatura does not resolve doesn't matter. It's considering the chord to be a kind of
C chord that was approached by its dominant that matters. A
Bo7 moving to some kind of
C chord is one way to establish functions in