Transcribing (either by writing or playing it by ear) is one of the most valuable things you can do in your practice. Jazz, folk, and most pop musicians at this point are saying, “Duh!,” so this is basically for classical musicians.
Case in point: Lizst’s transcriptions of all 9 Beethoven symphonies for piano. Classics (pun intended) in the piano rep. and some of the most challenging stuff you can find on piano. Here’s some history on how and why Lizst did it.
Transcribing means you strive to recreate every nuance of what you hear: not just the notes, but the timbre, dynamics, emotional content, the silence: everything. Written music shows only the notes, and the notes aren’t enough if you want to really make music that people with not only hear, but feel.
Here’s the 4th movement of Beethoven’s Symphony 9 (in 4 parts, with sheet music), as transcribed by Lizst, and played by Cyprien Katsaris.
When he started transcribing the ninth symphony Liszt ran into a problem in the 4th Movement, he did not know how to implement the choral parts into the music.
“After a great deal of experimentation in various directions, I was unable to deny the utter impossibility of even a partially satisfactory and effective arrangement of the 4th movement. I hope you will not take it amiss if I dispense with this and regard my arrangements of the Beethoven symphonies as complete at the end of the 3rd movement of the Ninth.” -Franz Liszt
But then only a few months later Liszt had figured out a way to implement the choral section, accomplishing what he thought would be impossible. The Symphony transcriptions that Liszt did are so revered that they are considered to be their own works rather than transcriptions.
“The range achieved by the pianoforte in recent years as a result of progress both in playing technique and in terms of mechanical improvements enables more and better things to be achieved than was previously possible. Through the immense development of its harmonic power the piano is trying increasingly to adopt all orchestral compositions. In the compass of its seven octaves it is able, with only a few exceptions, to reproduce all the characteristics, all the combination, all the forms of the deepest and most profound works of music. It was with this intention that I embark on the work which I now present to the world.”