You may know this Italian expression: "Traduttore, traditore" ("Translator, traitor") which is sometimes summed up by saying "To translate is to betray". This is probably true for literature, it is certainly true for musical transcription.
When musicians improvise, some of their choices are unconscious. They can sometimes take liberties with the tempo, with the structure, with the harmony. My goal is to try to understand what they are thinking while playing, to guess their intentions, to be faithful to their thinking (as much as possible).
But, at the same time, I have to make a score that is readable and understandable for a performer
These questions came up while working on the solo piano version of Ruby My Dear by Thelonious Monk. Most of the song is rubato, and I had to make a choice: should I follow the leadsheet and have a proposer 8-bars structure ; or should I write down what my ears tell me, and what I imagine Monk is thinking? (I did kind of both).
Transcribing Martial Solal is also a challenge. Most of his recent piano solo works are played "free" (for lack of a better word), and there is no structure to rely on. I guess I tried my best to translate his thoughts on such works as Round Midnight or his Happy Birthday! (He told me that I did a good job, which I'm very proud of).
These are the main requirements that I have in mind. I don't always manage to achieve them as much as I would like! I also have my more or less conscious biases, my flaws. I do hope nevertheless that my choices seems judicious to you!