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In Beethoven last sonata's arietta, the variations starting at bar 33 seems to be clearly a reference to the contrapunctus 2 from die Kunst der fuge. Since as well Beethoven seems to attempt to do both a conclusion of what a sonata can be, a synthesis of the state of the art, involving fugue-like, as well as an attempt to use the sonata form as well as not do a sonata: the Op. 111 is not starting nor ending, as well as trying to reconcile extremes, opposites.

Is there any actual strong element from analysis and history of writing that supports such idea aside of the obvious use of the rythm and the accents ?

111v2

111v3

contrapunctus2

For instance, I see a use of a signature in the beginning of the variation (blue point), which is like the beginning of the rythmed section of contrapunctus 2, with double mirror of notes (vertical and horizontal or reverse in time, reverse in pitch, the rythm is conserved), also referenced with a blue point. Both are coming back many times all along each variation.

I'm looking for any other possible references, from analysis, logic, perception, esthetics, history.

111-c2

c2-double reverse

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  • For clarification: are you asking if Beethoven was specifically referencing the Bach fugue; about Beethoven's compositional intentions in incorporating a fugue; something else?
    – Aaron
    Sep 14, 2020 at 23:49
  • @Aaron Yes, and what are the formal (analysis, logic/perceptual/esthetical) elements supporting this.
    – Soleil
    Sep 15, 2020 at 10:27
  • @Soleil-MathieuPrévot I worry that your question is still a little unclear. Aaron asked three separate questions, to which you answered "yes" (and also added another one). Are there four questions here?
    – Richard
    Sep 15, 2020 at 13:43
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    Imho, this question is not really answerable, unless we find a note by Beethoven specifically making the connection. I personally, like Richard, don't hear enough resemblance to make the reference likely- such patterns occur often enough to be part of the common stock of tropes.
    – Scott Wallace
    Sep 15, 2020 at 14:53
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    @Soleil-MathieuPrévot - Tovey wrote "A Companion to the Beethoven piano sonatas" (or something like that), which is a "bar-by-bar" analysis of all the Beethoven sonatas intended for pianists. Schenker included with his editions of the last 3 Beethoven sonatas a detailed analysis of each of them; these are the analyses that started "Schenkerian music theory". I don't know if they have been translated from the German, but there is a significant amount of secondary literature among music theorists on Schenker's work.
    – Alexander Woo
    Sep 16, 2020 at 15:47

2 Answers 2

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If it's terminology you're looking for, we could say that Beethoven fragments the Bach fugue to focus on only a small portion of it. Then he both retrogrades it (plays it backwards) as well as inverts it (plays it upside down). He then develops this fragmented motive in various ways, largely through sequence (moving it up and down in tonal space).

But if I can be honest, although I understand the connection you're making, I think it's a little bit tenuous. The alleged fragment is ultimately just outlining a third and throwing in a lower neighbor tone, which is a very common pattern in this style. And furthermore, the fragmentation isn't exact: in the Bach, it all moves by step, but it looks like Beethoven never moves it completely by step.

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  • I'm not looking for terminology nor a comment on the signature, but a more thorough analysis.
    – Soleil
    Sep 15, 2020 at 13:38
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    @Soleil this answer is giving an initial analysis that concludes that further analysis would not be fruitful. A more thorough analysis to support that conclusion would need to analyze several other pieces to show that the elements you have identified as common to these two pieces are actually common in general, so they don't establish that the Beethoven was derived from the Bach. That's asking a lot of a stack exchange answer.
    – phoog
    Jun 12, 2021 at 16:26
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I'm not a music theory person; all i can say is that when I listen to the two pieces, Op. 111 is so clearly a reference, almost to the point of copyright infringement :) I can't imagine Beethoven denying this. In a scathing review of the piece in 1824 a critic said: "I cast only one more glance at the next three variations. True enough, they are worked out (though I will not mention those by Bach), but where is there here a pleasing, tasteful, brilliant figuration? The voices are forced into and through each other as if frightened, and so things are drawn out endlessly until one is ready to lose one’s breath." I'm not sure what he meant here exactly, but perhaps he too thought it was a reference?

“As a Review of the Sonata Op. 111. Letter from a Critic to the Editor.” Berliner allgemeine musikalische Zeitung 1 (17 March 1824): 95–99. https://www.bu.edu/beethovencenter/files/2020/07/crit_recep_beethoven_op101_to_111_jul27c.pdf p.68

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