The presto should be very easy to do if you are doing it correctly.  Considering that it's been more than a couple of days since you started practicing it, you are practicing it incorrectly.

You have hit a speed wall because you are using an inappropriate technique which may be fine if you are playing slowly but not at presto.  You'll have to search for the most correct manner to play it.

When I first learned it, I learned it incorrectly but it did not prevent me from reaching the desired musical tempo.  The issue I had was that my hand would cramp up.  This should never happen.  It should be easy and if it is not, then you are doing it wrong.

I did manage 180 bpm this morning, but you are right, it is very difficult and uncomfortable. My whole shoulder and upper arm are tensing like crazy and I'm really sore afterwards.

I did search before starting this tread, but I couldn't find anything realy helpful. What I am doing now, is just starting the metronome at 100 bpm, and gradually increasing it until it falls apart at 180 bpm+. A few more specfic pointers on how to get this up to tempo would be very appreciated.

Do you run by gradually walking faster?  How fast do you think you'll be able to walk?  For how long do you think you'll be able to walk while your muscles build up lactic acid and burn?  How sore do you think they'll be if you continued?

Now pick up your knees and run.  Notice the ease?  The speeeed?

If you continue this kind of practice, it will take several months while you build up muscles and tolerance but the feeling of strain lessens.  But you still won't be able to play this piece.  So you have a choice: 1)continue with what you are doing and it will get better but you'll never be satisfied with it or have total control or 2)do something else.

If you decide on the second option, you've just chosen the more difficult of the two.  Why is it more difficult if it results in your ability to play this piece with ease?  Because it's easier to continue the same old instead of learning an entirely new set of coordinated movements that you currently do not possess.

I've listened to your practicing clips and you are using your fingers a lot without the coordination of the other parts of your body.  You are also pressing down to play chords and in order for to you to play loudly you probably push down even harder.  This is a waste of energy and creates tension, if only for a moment.  Also, from the closing arpeggios, you lack fine control (can be easily gained) and you are also holding an extreme amount of tension in the fingers (thus causing the lack of control.)

Here's some things you should consider in playing arpeggios:
1.   Lateral shift of the hand/forearm
2.   Rotation of the hand
3.   Slanting the hand in relation to the keyboard
4.   Backwards and forwards movement of the arm

All of these, in conjunction with the precise movements with your fingers will net the results you should want.  But you'll have to learn an entirely new way of playing beyond the utterly absurd "five-finger" position.

The easier part is just letting the keys that fall under the hands of the arpeggios.  The harder is connecting them with the lateral shifts.  This is tricky.

Generally, I do not believe that pieces can be out of someones abilities.  If you consider patience, intelligence and diligence, and perseverence in practice as abilites, then these are requirements for learning anything and these must be present for the quality of learning to be of the highest possible realm.

Technically, this sonata is actually quite easy if you are using the best practice techniques.
Musically, it is a bit of a challenge, but most music is challenging, even if it isn't technically challenging.

Any piece can be outlined.  It has numerous benefits including form, structure, motive...  all of which can greatly help the memorization process.

As for eveness of the touch, depending on how long you've been playing, the fine control may not be present if you've been learning the piano with an inferior and insecure technique which prevents your neuralogical system from developing properly.  If you have been practicing with excellent technique and excellent practice techniques, fine control can be gained quite quickly in a matter of a couple of months and it just develops from there.  This process shouldn't take more than a couple of months.

That's a simple summary.

Here is some more information about coordination: In order to gain coordination most effectively for something that should be really fast, and you can't immediately do it at that speed, you have to do it slowly.  This prevents any co-contraction that would occur because the muscles have not yet learned how to cooperate together for the task.  This really only takes a couple of days to get the coordination right.  The caveat of this kind of coordination practice is that it is very easy for someone without experience to practice the movement, which should be fast, incorrectly slowly.  As a example, walking is not the same as running and no matter how fast you walk you'll never be running.  Only running is running and you have to be sure that the movement you are practicing slowly is the same movement required for doing fast.  So per the example above, practicing running slowly is how you gain coordinatin to run fast.  (Running is actually a bad example.)

Fine control requires coordination of the muscles and muscular development.  Your muscles need to be conditioned for certain aspects of piano playing to be done effectively.  This is not an endorsement for exercising your fingers (actually your forearms).  This isn't an endorsement of finger exercises, either.  The most effective way to condition your muscles is by playing the piano in the most efficient and effective manner.  Playing the piano requires that these sets of muscles contract and relax in very specific patterns.

Fine control also requires a highly developed nervous system capable of sending electrical impulses at incredibly fast speeds.  As you learn how to play the piano properly and effectively, your nervous system will actual send electrical signals to your muscles faster because the nerves develop an insulating mechanism.  Just like insulated electrical wire sends electricity faster than non-insulated ones, so too does your nervous system.  But this insulation will only develop the minimum required for a certain activity - if the music you play never gets beyond a certain speed, don't expect to meraculously get it when you play a fast piece or the fourth movement of Op.2-1.  In order to get your muscles coordinated faster, you'd have to practice fast (but keep in mind how to gain coordination).

The one problem of developing your nervous system is that it is just as easy to develop it in a manner that prevents you from playing the piano well.  For beginners, any kind of development gets noticeable results but only the correct and proper development allows for ease in playing.  If you were to continue practicing the fourth movement with all of the tension, you'll actual condition your nervous system in the same manner.  You may be able to perform the piece to your satisfaction but you'll always have to practice it.  Do you really want to practice the same piece for years... decades just so you'll be able to play it well?  And imagine what you wouldn't be able to play because you developed this faulty system.

Yes, the arpeggios should be very easy to do.

From the recording, it sounds like every time there is a lateral shift, there is a break in the musical line.  At this point, I imagine this is the point where you are holding tension in the hand, probably the thumb is moving inward which causes the tension.  In other words, your thumb is reaching for the landing spot and seizes up under the hand.

The thumb can't reach any further inward because your hand just so happens to be in the way.  Experiment with just how much your thumb can move inward before it seizes up and becomes practically useless because it's stuck under your hand.  Then find out just how much it can move inward while maintaining the maximum amount of movement.  Make sure your thumb is relaxed.

Once you've figure this out, the other movement to combine is with the lateral shift and forearm rotation.  In this process, pay attention to how much forearm rotation you need to move the thumb just a bit closer to the landing key with the minimum amount of movement.  The rotation should be an inward rotation where your thumb rotates down.  If you notice, when you rotate this direction, your thumb actually moves closer to the desired location.  The shift should feel like your arm is floating to the desired spot and your thumb just lands correctly in place.

The other movement is the wrist.  This should fall naturally in place if you've figured out the issue with the thumb and lateral shift so you don't have to think about this one.

Specifically regarding the right hand as it plays the closing arpeggio patterns, it sounds like there is just a slight bit of tension in the fingers, probably the 3 or 4 finger, depending on which fingers you are using.  Maybe you are preparing this finger to play the note before it needs to play.  Some preparation is necessary to limit the amount of movement but the hand should still be relaxed.  Experiment to see if the chosen fingering is the easiest and most effective.  Make sure you are also adjusting the wrist to minimize the movement of the fingers.  As a quick example, you can place your five fingers on the white keys and play with the 3rd finger just be raising your wrist.


On using the metronome, it's important to be able to feel the pulse inside your mind and not on the metronome.  But that takes quite a bit of practice.  As soon as the metronome has done its job in providing an objectively consistent beat, and you are able to play with the beat, it should be done away with because you do not want to use it as a crutch.  Using the metronome also prevents developing an inner ear for musical phrases that can spand dozens of measures because music is never metronomic.

If you have the music memorized in your mind not just in your fingers, the next step is to play just the music in your mind.  This assumes that you have solved all technical problems and you are free to be able to shape the music as you like.  This also assumes you have specific opinions about how the piece should sound like.

In a piece like this movement, and you are still learning, this is the basic process you should go through.  As you gradually become more comfortable playing and more patterns are learned and ingrained, you will be able to listen to music in your mind before actually playing the music.  You should have listened to lots of music, performed by excellent musician-pianists, and also the same music performed by mediocre pianists.  And of course balance it all out by listening to bad performances so you'll develop an even greater appreciation for excellent performances.  This process helps to shape your musical preferences and helps you to make very precise musical decisions in performance and practice.

After reading most of this thread I think what you really have to do is get a teacher. You need a pro looking at your fingers - and the whole body. Tempo isn't magic, it is the appropriate use of the right movements and adaptation to the music. It is a bit like downhill skiing where the ground would represent the music. Actually it is better because you can study the "ground" perfectly before playing and decide how to play every single note or phrase.

The biggest breaks in the musical line, or at least the motion that feels most akward, is when I'm doing lateral shift above my thumb. (Ascending with my left and descending with my right). I am using the thumb over-method, but I guess it still needs some more work.

The reason this is more uncomfortable/awkward is because your torso is in the way.  You'll soon realize the reason playing the piano is so difficult is because something is always in the way; either the fingers are attached to the hand, the hand to the wrist, the wrist to the forearm, or the arm to your torso... it's just easier if nothing were attached to anything.  And ultimately, you'll learn that mastering the performance of piano is about mastering how you accomodate your body to yourself in relation to the piano.  Master yourself, not the piano.  Once you learn this, you can play any instrument because you mastered how your body works.

Moving outward is easy because nothing gets in the way so you don't have to be careful except for where you need to play.  Moving inward is complicated because you can only move in so far before your torso prevents any comfortable and easy movement.  This is just like the thumbs being seized up if passed under the palms of your hand.

So here's something to consider: holding your arms relaxed like you were playing the piano, jerk your elbow out and in.  Notice that your hands move quite a bit of distance very quickly.  (This is one major movement in playing the leaps in La Campanella and it's the difference between absolute, ridiculously insane speed and ease VS. laboured, muscle-building practice that you will never be satisfied with.)

Now to apply this to the arpeggio, you shouldn't be thinking about your elbow but thinking about how to move your finger over to the next note quickly enough to prevent the break.  In actuallity, you are really moving your shoulder out and in which makes the bent elbow leverage the forearm which moves the finger/hand.  But don't think about your shoulder, either.  Now experiment with just how the other movements interconnect with this movement.  You should notice an immediate increase in ease, if not accuracy.  Focus more on ease because this is a new concoction movements.  Accuracy will come soon.  And just like those large leaps in La Campanella can be rendered a brisk stroll through Central Park, so can large inward motions.

Notice one more thing: This is NOT thumb over.  Thumb over only effectively works moving outward.  But in both outward and inward movements, the shoulders' out/in movements, coupled with the bent elbow, provides the quick leverage needed to displace the fingers/hand to the desired location.

On my right hand it is my 4th finger causing the uneveness, and the fact that my hand is not big enough to do a F-minor chord with a double F. Well, not that fast anyway, so I have to really roll with my wrist.

  Is this a continuation of the same technical issue or is this referring to a different one? 

My own suggestion for a recording of all of Beethoven's piano sonatas would be by the musician John O'Conor.  He also happens to be pianist.   He recorded the complete cycle separately but you can now purchase the entire 9 disc set very cheaply.  The retail price is $80 but I paid $55 from a seller on Amazon.com.

These are excellent recordings both sonically and musically.  The recordings are very vibrant and the piano sounds good.  As a musician, you can hear how O'Conor put a lot on effort in making as much music as possible.  It seems like every articulation is clear and well-shaped and phrases connect to bring out musical ideas.  The only minor complaints to note are that on some sonatas, the tempo could be a bit faster like in the opening movement of Op.109.  But otherwise, I would recommend this set for O'Conors clear musical ideas, accurate obligation to the composer's intent, technical mastery, and excellent recorded sound.

A quick response:
You should use the 5th finger instead of the 4th where you have marked in the score.  You'll immediately notice that your hand returns to a more neutral (and comfortable) position if you make this change.

I'll respond more thoroughly when I have the time.

Chords:
I am not entirely sure how to play chords as easy as one should. I just move my fingers in position and push down, I guess. If you could elaborate on how to play these correctly, it would be great!

I'll let you figure this one out!   Just try a movement that allows you to follow through while achieving the necessary goal.  Notice that when you just push down, your entire arm stops (causing tension) when the key(s) can no longer be depressed any farther.  Now try another movement that prevents your arm from seizing up.  The result should be really easy when compared to just pushing down.  Try figuring out this motion playing loudly at first because this exagerates the necessary motion.  Once you've figured it out, you can use this motion to play softly and you'll gain quite a lot of control and huge dynamic range with just this one simple change.

Lateral shifting arpeggios inwards:
Your explanation, well, explains alot. Also, my thumb seems to automatically reach for that last note when I'm descending with my right hand. That is making the motion tense and forced, maybe I just need more wrist motion. I will isolate the problem and just do some more descending arpeggios, taking all your advice in consideration.

My techical issues causing unevenness:
I've uploaded an excerpt from the score. This is the part my right hand is looping on my recordings. My markings in red is were the unevenness occurs. There is my 4th finger, the big stretch of the four notes, and the descending lateral shift all at once in succession. Maybe the anticipation of the upcoming lateral shift is what is making my thumb tense and my playing weird.

You may be reaching because your other fingers are still over the keys they just depressed.  Do you stay on the toilet once you've finished unloading?  Once the fingers have released the keys, they no longer have to be anywhere near them.  Move them out of the way that allows your thumb as much freedom as necessary.  Once it's freed, you'll no longer have to hold your breath; it will be relaxed and you'll no longer have to reach for it.  This is also the technique to play Chopin's Etude Op. 10 No. 1 in C major with minimal practice, rediculous speed and ease.

The most critical part of the descending arpeggio pattern is the thumb because it has two functions: playing the note and pivoting the hand.  If your other fingers are still over the keys they just depressed, the thumb will only have one function like a urinal and you still need to do #2.  So get your fingers (hand) up into a better position that allows your thumb to be more like a toilet so it can play the note and pivot.  It may feel uncomfortable at first because your hand may momentarily not be touching any key and you'll have to learn to coordinate your entire hand and arm in the air.  Quite unsettling!

Sonata recordings:
I listened to some samples from the John O'Conor collection, and it did sound great. Different, but great! I have the impression that most people (maybe just the youtube-mob, I wouldn't know), tend to like the first version they hear the most. Was these the first recordings you heard, or did you hear a lot before "settling" on this one? Slightly off-topic perhaps, but interesting nonetheless.

As for myself, I first listened to all of Beethoven's piano sonatas from MIDI files.  It really spoiled my ear (in a good way).  I didn't (couldn't) hear any technical issues from these "recordings" and it was quite a shock to hear many of the sonatas later by real people and hearing all sorts of excruciatingly minor technical blunders.  These technical issues really interrupt the flow of the music and they distract it as well.  And surprisingly, MIDI files have quite a lot of musical expression when the correct tempo is selected!  Or maybe it was the person who encoded it...

The cycle by O'Conor was the first complete set I've ever purchased, and that was almost a year ago!  Beethoven was my favourite composer when I started playing the piano and I've never been satisfied with humans performing the sonatas.  As a result, I never could just give in and spontaneously buy a set because I knew the pianist was either not a good musician, pianist, or both for performing these sonatas.  I decided to purchase O'Conor's set because he offered what no other musician could with these sonatas.  There is a great deal of music in these sonatas and he brings it out.

Sorry for opening up this "old" thread!

Anyway, I meant to reply three months ago, but I lost my internet connection for a short period after your last post faulty_damper. I have read your posts like 200 times, and they have helped me alot.

So I've memorized the 3rd movement by now, and most of the 2nd. And almost until the repeat of the 4th movement! But progress has been slowing down lately. I just can't seem to "get" those =/&%#)/& polyrythmic passages in the 2nd and 4th movement. I can do 2 against 3, and 3 against 4 if I do it really slow. But this is crazy fast, and I'm stuck.  Any advice here would be extremely helpful!

I just recorded 20 seconds of the 4th movement on my phone, so quality isn't the greatest. Is this tempo ok, or should I aim to play it a little faster? This tempo is pretty comfortable, so it shouldn't be too hard.

This was probably way too hard for me when I started it, but now it's not that bad. My goal is to perform the entire sonata by the end of the summer! 

Thank you for another quick reply!

Kempff plays that part in 15 seconds, so I guess you're right. I'll aim for playing it about 25% faster. But I have a good start, I think. 

I'll try the metronome-thing asap. Counting just doesn't work at 200bpm.

Let's see... I'm really bad at writing these things but I'll give it a try. I think frustration might be the central feeling to this movement. I don't know, it certanly isn't funny. The loud parts is like someone banging on a locked door. Followed up with a part when you are trying to calm down. And the soft part is like realising it is useless to even try. But then you make another effort, etc. And the middle part is sort of looking back at something, or maybe picturing what could have been. It ends with one final effort.

This is sort of the picture I've got so far, but it might change as I get to know the piece more. I can only play 1/3 of it so far, so yeah. Feel free to share your interpretive ideas, if you have any!