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Thread: Chromatic diminished 7ths in Beethoven rondo, how does this harmony work?

  1. #16
    Senior Member millionrainbows's Avatar
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    I see caters struggling, but I see him as searching for some underlying principle of diminished chords rather than floundering, and the analysis, while I'm sure EB's is correct, doesn't explain the issues I think caters is struggling with, as evidenced by caters' zeroing-in on diminished 7th chords and the circle of fifths.

    EB, could you speak a bit more on the two diminished chords in measures 1 -2, the e:vii4/3, and viii˚V, and how they are related harmonically to each other and to B:I?
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  2. #17
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post
    I see caters struggling, but I see him as searching for some underlying principle of diminished chords rather than floundering, and the analysis, while I'm sure EB's is correct, doesn't explain the issues I think caters is struggling with, as evidenced by caters' zeroing-in on diminished 7th chords and the circle of fifths.

    EB, could you speak a bit more on the two diminished chords in measures 1 -2, the e:vii4/3, and viii˚V, and how they are related harmonically to each other and to B:I?
    Sure. And thanks for putting the focus back on Cater's inquiries. The way to approach this passage is not to wonder first about the dim 7th chord pairs. They are like an adverb and a verb hanging in the air, meaningless without the noun that follows. One needs to look at the (relatively) stable points first and then work backward to the dim 7th chords. In the 20mm example I posted above, those stable points are mm. 3, 7, 12, 16, and (not shown) 21.

    3 — B major
    7 — E major
    (11 — ? pivot chord; A major expected, but the pattern is broken) proves to be the vii 7/ii in Bb Minor)
    12 — C minor
    16 — Bb minor (cadence on — we've been in that key since m 11)
    21 — Ab Major

    So first (mm. 1-11) we have a cycle by 5ths, B-E-(A), with the final resiolution to A denied. Then (mm. 12-21) it descends by whole steps: Cm, Bbm, Ab.

    The first three of those stable-ish harmonies are preceded by their vii°7 chords, the last two by their V7 chords. Everything after measure 11 is straightforward.

    So given that the mysterious part of the passage falls into a pattern of tension-resolution in 4 measure units, the obvious question to ask is: Do the three chords in each of those units make grammatical sense within a key? The answer is yes. The chords in the first four measures are standard vocabulary for the key of E minor: vii4/3, vii°7/V, V, the next four measures just repeat the pattern in A minor. Now because we've just heard the same pattern twice, we assume that the dim 7 chords in mm. 9-10 are going to function the same way, as vii4/3 and vii°7/V in D minor. But that's where the pattern is broken. We don't get the A major we've been set up to expect. Instead the harmony repeats as a pivot chord to C minor — which is where the mystery ends. From there it's descent by whole steps. The Bb minor chord in m. 16 is the tonic in Bb minor becoming (another pivot chord) the ii chord in the key of Ab, our final (non)-destination.

    What's interesting about the pairs of dim 7th chords is that the leading tones of the vii4/3s resolve correctly to the tonic note in each case (D# to E, G# to A, C# to D) but the lower voices don't resolve down, instead sliding up to the root and third of the vii°7ths of V.

    In general, I think Caters is conceiving the analytical problem as a matter of taxonomy rather than understanding it as one of function. Her strategy seems to be to start with the key signature and try to compute the identities of the chords within that key. That is never going to work in unstable, continuously modulating passages like this because the signature has nothing to do with the key in these cases. That's why one must find the local points of stability and use them to anchor the 7th chords, both diminished and dominant. Also, Caters, you seem to expect unicorns and other crypto-zoological marvels, like Dorian mode. 'Fraid it's mostly just cows and horses.

    But her final observation about the circle of 5ths makes sense:

    B, E … Cm, F7, Bbm, Eb7, Ab.

    Progressions by 5ths are a standard way of spinning out sequential progressions in this style.
    Last edited by EdwardBast; May-26-2019 at 12:44.

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  4. #18
    Senior Member TalkingHead's Avatar
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    Quote Originally Posted by caters View Post
    Here is the passage I am talking about:

    Attachment 118884

    [...] But why does this work [...]? I think it has to do with not only the pattern and how it is deviated but also the circle of fifths.
    I think you're on the right track in that the "drive" in this passage (what makes it work, as you say) are the modulating sequences which are patterns built on the circle of fifths.

    Maybe it could be more useful to say that the satisfying sense of progression is more to do with the basic academic rule of "roots rising a fourth" in the sequential treatment of secondary sevenths.

    This is shown in the overall harmonic framework that EdwardBast has pointed out at the end of his latest post just above: B, E … Cm, F7, Bbm, Eb7, Ab.
    Last edited by TalkingHead; May-26-2019 at 15:10.

  5. #19
    Senior Member TalkingHead's Avatar
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    @ Caters:
    Thank you for raising these issues, they're very relevant and interesting!
    That said, we mustn't let the analysis get in front of the music too much!!
    If I'm not mistaken, this Rondo was subtitled "Rage Over a Lost Penny" (maybe by Schindler, maybe by Beethoven himself, I don't know).
    With that image in mind, I can see these fast sequences and scale passages as Beethoven himself running desperately after his lost penny as it rolls away from him !!
    Pure speculation, of course, but that image pleases me !

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