Bach Die kunst der fuge reference in Beethoven Op. 111
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 ?
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.
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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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