TromboneChat

I am an adult played trombone for three years as hobby. I’m quite a keen learner and practice regularly though I do t do many gigs. I’m more into church/classical music. I don’t have perfect pitch, but I memorized a few notes such as the high c, high eflat, etc. my question is there a way to know if performed in a different key is there a way to tell to which position pitch the c moved to? I don’t have too much trouble identifying a key as I also regularly transcribe random songs (SATB) and try to keep it in that key, something I mostly do for reading rhythm. I can hear the keys f major b flat and eflat easily, cause the former are likely to land or rest on a natural and the latter on g, etc. Secondly I also want to learn basic improvisation, especially jazz. Got the Jamey Book and cd, will start with that in due course. However there is somebody offering better understanding of this book, but mostly for trumpet. Is there someone assisting trombonists in this way. I tried playing along few YouTube videos, but find that I slur too much (not clean) and don’t want to continue that way. I’m more comfortable with slow mellow tunes as I can clearly hear and see notes. Any advise?