I edited the question extensively. The comments helped me to phrase it to reflect more what I really wanted to ask.
I don't have perfect pitch and badly trained and imprecise relative pitch. I only started two years ago to learn musical notation as a hobby and writing little stuff for myself and friends (For example). I said this just to give a context that I am not a musician and that I certainly ignore many basic things about notation, terminology, and the capabilities of the different musical instruments. .....................
I imagine there are ways to get a recorded natural occurring sound and somehow make the sound into a MIDI file, for example, and then open the MIDI, let's say in Sibelius and that should give an approximation for how its transcription into the score should look like.
Some composers manage to write down parts for an instrument that makes it resemble a particular natural occurring sound (horse whinnying, bird songs, rain, ...). My aim is to have a technical procedure to help myself in the process of doing that. Something that gives me a first approximation of notes that I can afterwards, by hand, tweak to make it more like the natural sound I wanted, or make it more playable, and then be able to elaborate them into a larger composition.
Does anyone know ways in which this can be done? Suggestions?
Edit: Also if someone knows of a collection, or a place to find transcriptions into musical notation of a few naturally occurring sounds that helps a little bit too?