I figure nearly every post in this thread is going to be one telling you that you should wait years before taking on the etudes, etc., so I'm not going to bother expressing that as my own view. Instead I'll just address the actual issue of speed.
In general, when your goal for a practice session is to increase the speed of a passage, you should do that work hands separate (unless the passage in question is very easy for you, in which case hands separate work would be a waste of time, but if you were working on something easy you would not have made this thread in the first place!). Most of the time, in any given passage, one hand's part will be more difficult than the other hand's. Regardless of which hand has the more difficult work, hands together work trying to increase the speed of a passage will be a generally terrible use of time. Say you are trying to increase the speed of Op. 25 No. 4 while practicing hands together. As you repeat a passage over and over again, your left hand will become fatigued by all the constant leaping, while your right hand will be having a (relatively!) comfortable time. However, although the right hand isn't getting nearly as punished, it isn't 100% trivial, and so you still have to put some focus into it. Simply put, you just can't have sufficient awareness of the movements you are making with both hands simultaneously. You won't be sure that you are using the correct movements, and you will probably end up ingraining in your memory movements that you really shouldn't be using without even being aware that you are doing something wrong (at a slower speed, it is too easy to get away with movements that just won't work at full tempo).
When you are working hands separate, you want to aim to be able to play each hand's part at a tempo faster than your hands together goal. This will make mastering HT much less time consuming, because the inevitable drop in speed you experience when coordinating the hands will actually land you right at goal tempo.
Are there some exercises you can recommend to help with my speed? One thing I did was print out the major scales and using a metronome trying to work my way up in speed.
Starting something from scratch simply by playing it at a slow speed and gradually working up the metronome is one of the worst things one can do. When you play something at a slow speed, you can get away with using movements that simply will not work when trying to play the same thing at a fast speed. Using the scales as an example: if you are playing a scale at a slow speed, chances are you will be using the thumb-under technique. Assuming a scale that uses normal 123-1234 fingering, after the first three, you bend the thumb underneath your third finger so as to continue the scale in a smooth legato. If you try to play it in any other way, at that slow speed the scale will sound choppy at that 3-1 transition, so you continue to use "thumb-under."
To put it simply, you will never be able to play that scale at high speeds while still completely using thumb-under. By practicing thumb-under at slow speeds, you are setting yourself up to hit a speed-wall. As you increase the metronome speed so gradually, you will continue to use those same motions that you were getting away with at the slow speed where you started, and you will eventually reach a speed that you can't comfortably handle with those motions. You will be stuck. Contrary to what I hear people say all the time, a speed wall is not a psychological problem.
It is a physical one that the pianist in question sets up himself by practicing incorrectly.A fast (and I mean
fast) scale requires a different way of making that 3-1 transition (or whatever specific finger it is for the given scale). Movements are hard to describe in words, but here is an attempt: You pivot the hand slightly around the third finger, and at the same time move the whole hand laterally, to make it so that you can play the next thumb note without actually bending the thumb under the hand at all. At a slow speed, this technique will probably sound somewhat choppy, which is why people go for thumb-under at slow speeds (and hence set up a speed wall if they try to make that passage faster), but this is the best movement to achieve high speeds at a scale.
As far as 'exercises to help you with your speed,' I cannot (or rather, will not) suggest any specific set of technical exercises. Different types of passages (fast stepwise motion, fast arpeggios, fast octaves, etc.) require different specific approaches, and even the same technical difficulty in two different musical settings will need to be approached differently, so I find pure technical exercises to be a fair waste of time. Instead of trying to practice a bunch of technical exercises to improve yourself in general (which really will not work as well as you may expect it to), just deal with each piece of music as you get to it, and you will find that the experience you gain by just working on actual repertoire will do a fine job of 'preparing you for anything,' not in the sense that you can pick up anything and already have the technique to play it well, but in the sense that you will know how to go about gaining that technique efficiently.
I will outline the type of approach to take to begin to master the left hand of Op. 25 No. 4, and you should be able to see how the same type of idea can be applied to many kinds of passages.
Let's take the first full measure of the etude. First of all, before you begin to actually put the practice into mastering something, you have to make absolutely certain that you know what fingering you want to use. Different people will prefer different fingerings in the same situation, so just find something that works for you. If necessary, experiment with numerous different fingerings for the same passage before deciding (you will get better at choosing a fingering with experience). For this bar, I would personally play the left hand with this fingering (keep in mind that hand size is a huge determining factor in what a comfortable fingering is for a passage like this): 5 - 31 - 5 - 21 - 5 - 31 - 21
Let's number each note / chord from 1 to 8 (just for purposes of explaining this here, there is no need to actually write down these numbers). Start practicing just 1 and 2, and practice this at full tempo since it is only one leap. Do not worry if you are not accurate right away, just keep focusing on where the hand needs to go, and I promise your accuracy and precision will improve. Once you have 1-2 perfected (which does not mean that you get it right once or twice, you must be able to do it perfectly several times in a row at least; in fact you should, relatively quickly, get to the point that you simply can't do it wrong), you can move on to practice 2-3. Do not include 1 at this step! You must master each individual leap by itself before moving onto larger groups. So continue this way: master 23, then 34, 45, 56, 67, and finally 78.
Once you have each group of 2 mastered, then start practicing groups of 3, while making sure you have large overlap (practice 123, then 234, then 345, etc.). Then do this for groups of 4, then 5, then 6, then 7, and finally the entire bar. With the increasingly large overlap between groups, as the groups become larger, they will also become increasingly quick for you to master.
With this approach, you will pretty quickly become able to play that entire bar's left hand part at full speed. It is important to note that if you are going to do this kind of note-group exercise, you must finish it one sitting for you to gain full benefit from it. Always make sure that you don't pick too long a passage to work on at one time, particularly if it is a passage that will require this kind of work.
It is useful to note that for this type of exercise, depending on the piece, you can use, say, 8 groups of 3 or 4 notes, rather than 8 individual notes/chords. But even still, this is a pretty time consuming practice device to use, so you should only use it when something is particularly difficult for you.
An important thing to remember as you move through the piece is that when you choose the next section to work on, it needs to have some overlap with the section you just worked on. If you were to work on one bar each sitting, with no overlap, then when you try to play the whole piece, you will have trouble at the links between each bar.
Sorry for the long-winded post
Likewise.
Topic: Building speed for self-taught beginner