While No. 3 was written more in the style of a funeral march, No. 4 is clearer in its inspirations and theme. The etudes of Chopin are considered some of the most well known piano pieces among musicians, and from these compositions one can draw many comparisons to this piece. It would not be unreasonable to say that No. 4 was at least in part inspired by Chopin's etudes, however No. 4 has many unique elements as well. The rapid and repetitive bass is quite similar to the style of some of Chopin's etudes, although throughout, Rachmaninoff's personal flair is apparent, with the wide intervals between notes and a nearly constant fortissimo or even fortississimo dynamic markings (Basically, the piece is to be played very to very very loudly). However, because of the main theme being a complex and crucially, repeating, left hand, I was able to learn No. 4 in a very similar manner to No. 3. In the case of No. 4, however, the melodies in the right hand are not as important to the piece, and rather the left hand took priority.
No. 4 is interesting in how the left hand is by far the most interesting section of the piece, though it doesn't create the melody. So, when I practiced, I did not focus on the right hand, but rather the left. The left hand would frequently repeat, so I centered my practicing on memorizing and improving the left hand, while the right hand, which had far fewer notes and was oftentimes much less complex, would be added later.
There were also sections where the main theme of a simple right-hand melody combined with a complex repeating bass changed. In the second and third pages, as well as the final page, both hands adopt a new melody with a descending core line of octaves in the right and left hand, embellished dramatically in both hands as well. These sections are the most technically demanding, as both the right and left hands have to be extremely active and synchronized perfectly, and while this could definitely fit under "Challenges", I believe these sections were more emblematic of how I learned the entire piece, which is that I memorized and practiced the main left-hand "runs" (Or long strings of notes played rapidly) as one idea, and then I filled in the gaps by practicing the intervening sections without the main left-hand themes, such as the one mentioned above, as well as a couple sections such as on the fourth and fifth pages.
The main challenge in No. 4 is the speed of the piece, which augments the challenge of the already-rapid bass line in the left hand. As I mentioned when talking about the challenges I had with No. 3, the faster the notes are played, the more likely one is to make a mistake, and when playing such a technically demanding section, speed can cause major issues which can derail the entire piece, rather than just resulting in a missed note or two.
The fast speed of the piece also compounded another difficulty in how the piece was written-namely, the sections where the left and right hand both simultaneously play a complex and identical part is made difficult not necessarily because on its own, the part would be hard. Rather, when combined, the real difficulty emerges; synchronizing the two hands perfectly. There are multiple sections with identical left/right hand parts, and each one is quite tough and requires much practice to attain proper speed and coordination.
 No.4.MOV
No.4.MOV