How do the alternating C and Db function in this modulation?

Question

So I am writing a rondo in Eb major and there are 3 different key areas used. Those key areas are Eb major obviously, C minor, and Eb minor. For the modulation to C minor, I simply did this:

Passage in Eb major | Eb, C, G, Eb | Passage in C minor

A simple arpeggiation of a first inversion C minor chord smoothly brings me to C minor. Then, of course, I had to modulate out of C minor. I did this by first emphasizing the ambiguity of the diminished seventh by resolving it to C minor and then resolving it to Eb major. Then I took the bass note of the diminished seventh, B and alternated it with Bb, eventually reaching a Bb pedal in the bass. This Bb pedal over the chromatic alternation(which slowly gets faster and faster until a trill is reached) then led to a perfect authentic cadence in Eb. This is easy to explain functionally. Functionally, it is as though you have an alternation between vii°7 of C minor and V7 of Eb major, even though the full chords aren't used.

Now, I'm doing something similar to the modulation out of C minor to modulate from Eb major to Eb minor, using the slowly accelerating chromatic alternation and reaching a pedal point and then releasing that tension with the new tonic chord. Here is the chromatic modulating passage:

I think I can more easily explain the C than the Db. Given that we were just a measure or two back, in Eb major, this appearance of C in the bass is functioning like a C minor chord, it is the vi. The Db is harder to explain, because with there being no Bb, it is hard to say that it is functioning as v6 of Eb minor(The minor dominant is rare, but it is used for more than just the lament bass(which is its most common usage)). It couldn't possibly be functioning as a diminished seventh, because the diminished seventh of Eb minor and of the minor dominant of Eb minor, Bb minor both don't include a Db. One has a D natural and the other has an Ebb, two enharmonic spellings of the same key on the piano. The diminished seventh of Bb major also doesn't have a Db or any rare accidentals like double flats or double sharps. Also, how often do you see vii°7/iv? Pretty rarely, right, especially compared to vii°7 and vii°7/V?

And unlike the B and Bb alternation in the C minor section, the notes C and Db are only chromatic in the sense that Db is not in Eb major and in the sense that C and Db are a half step away. One is not the chromatic alteration of the other.

So, if C is functioning as a C minor chord, then how is Db functioning? Just as a pivot note between Eb major and Eb minor? Or does it have a harmonic basis behind it like how the C has the harmonic basis behind it of C minor. If the Db bass it has a harmonic basis behind it, what is it?

Answer 1

Sorry, but for me this doesn't sound anything at all like a modulation from C minor to (presumably) Eb minor - not major, since the G flats in the final chord makes no sense at all in Eb major.

The bare C - Db octaves sound to me like a C is the dominant chord of something - i.e. The C Db is a very incomplete C7(b9) that is heading in the direction of F minor (or maybe F major).

But then when the D flats appear on the beat in the bass, the whole thing just falls apart. It would make some kind of sense in the bass line ascended from E flat to E natural (continuing the C-dominant-something harmony) but my ears say the Eb followed by the Eb minor chord is just a lurch in a random direction.

It's your music, and you can write whatever you like, but if you can't "explain" what is supposed to be going on, its a reasonable bet that your listeners won't be able to explain it either.

And to play a broken record yet again, understanding it by listening to it is the only thing that matters. Solving sudoku puzzles with the notes in the score to invent an explanation is beside the point.

Answer 2

The Db in the bass helps shift the tonality to Eb minor at least because it's part of the Eb minor key signature. But, it doesn't seem to imply a chord. It's just part of the bass stepping up to Eb at m. 166.

At that point - m. 166 - the C and Db in the treble do seem to take on harmonic significance. C moving down to Bb over Eb in the bass sounds like IV6/4 i to me. That's a major IV to a minor tonic. With that and the Db in the trill the tonality seems to be Dorian.

FWIF, C minor to Eb minor would be a chromatic mediant relationship with the Eb being the tone linking the two keys. If the movement around C in mm. 159-165 were around the Eb that might be a more straight forward way to make a chromatic mediant change. You could then play around with the G/Gb above that Eb and whether it's the fifth of the one key or the lowered third of the other key.