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Second-guessing Beethoven...

At the beginning of the 3rd movement (Adagio, ma non troppo), the bass in the first measure is all Bb. Beethoven really wanted you to know this was in Bb minor. Yet in the second measure he added a Cb and Fb. This changes the key to Ab minor. Why didn't he make that section Ab minor in the first place?

The Arioso dolente is set in Eb minor. Again, he quickly added an Fb, making the key Ab minor. As before, why didn't he make that section Ab minor in the first place?

In the L'istesso tempo di Arioso (measures 11-12) there are tied 16th notes instead of 8th notes. Why did Beethoven write them this way? This is similar to the question of the tied 8th notes in the Grosse Fuge.
 

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Second-guessing Beethoven...

At the beginning of the 3rd movement (Adagio, ma non troppo), the bass in the first measure is all Bb. Beethoven really wanted you to know this was in Bb minor. Yet in the second measure he added a Cb and Fb. This changes the key to Ab minor. Why didn't he make that section Ab minor in the first place?
Trying some answers ... He does not change the key to Ab minor. He is modulating. This is what composers do if they find out that it can be very boring to restrict themselves for a whole movement to the tones contained in a given scale.

At the end of the first bar, Beethoven already arrived more or less in E-flat minor. Already the d does not belong to Bb minor. Then he switches to Cb major, which is a mediant key to E-flat minor. - Schubert does this very often. - And Beethoven stays for the whole second bar in Cb major, using a deceptive cadenza at the beginning of the third bar to get to Ab minor.

Everything is fine. What do you feel is wrong with that?
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Since you asked "Why didn't he make that section Ab minor in the first place?" - well, we should ask this to Beethoven. My most honest answer is: Very likely, he did so, because he wanted. I do not think that he felt bound to rules that one can learn in school. He did what he thought to be what he wanted.
The Arioso dolente is set in Eb minor. Again, he quickly added an Fb, making the key Ab minor. As before, why didn't he make that section Ab minor in the first place?
I agree that nobody would feel that it was false if Beethoven had set Ab minor. The Arioso dolente is starting in Ab minor and it ends in Ab minor. Why he did not? We should ask Beethoven ... maybe he wanted to indicate that the music is not what it seems to be? It is in the wrong environment, some Ab-minor-music in a Eb-minor set? And why is the "repetition" in G minor set in the "right" key?
In the L'istesso tempo di Arioso (measures 11-12) there are tied 16th notes instead of 8th notes. Why did Beethoven write them this way? This is similar to the question of the tied 8th notes in the Grosse Fuge.
That's a good question. How to play this on a grand piano? The notes are looking as if stammered ... in the "Große Fuge" there is at least the possibility to play two notes (some ensembles do).
 

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At the beginning of the 3rd movement (Adagio, ma non troppo), the bass in the first measure is all Bb. Beethoven really wanted you to know this was in Bb minor. Yet in the second measure he added a Cb and Fb. This changes the key to Ab minor. Why didn't he make that section Ab minor in the first place?
Beethoven choses Bb minor as his opening key because the previous movement ends on an F major chord. But the introduction is of an extremely improvisational nature, immediately modulating to far away keys.
The key element here is Neapolitan harmony: it enables him to use Cb major as a means to reach Ab minor and back to B major (=Cb major enharmonically). And then back to Ab minor again for the Arioso. So apart from the opening Bb minor measure it's a clever interplay of those two keys, Cb and Ab.
Why did he write it this way, with that seemingly random key change in the middle of a long measure (and again, the next measure)? Who knows, maybe for aesthetic reasons? It surely looks nice and exotic on paper.

The Arioso dolente is set in Eb minor. Again, he quickly added an Fb, making the key Ab minor. As before, why didn't he make that section Ab minor in the first place?
Again, maybe he was thinking about having the same upwards fouth relationship between the 3rd and 4th movement (Eb-Ab) as between the 2nd and 3rd movement (F-Bb). Or maybe he considered an Fb in the key a too exotic element that would be confusing for the player? The Arioso is clearly in Ab minor, not Eb minor.

In the L'istesso tempo di Arioso (measures 11-12) there are tied 16th notes instead of 8th notes. Why did Beethoven write them this way? This is similar to the question of the tied 8th notes in the Grosse Fuge.
There's been a lot of discussion about this, I personally think it was his way of notating an extreme legato, the notes almost becoming one note, an effect that was more easily achieved on a fortepiano than on a modern instrument.
 
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