Excuse me for reviving an old thread, butt this is probably the best place to continue the interesting discussion on another
now closed thread.
The law is actually quite clear on transcribed improvised solos, though it is not defined as such. I was concerned about this, so have contacted various royalty collection agencies and solicitors.
An improvised solo is an adaptation or development of the original theme (head), and/or part of the arrangement, and as such the copyright is owned by the composer of the theme. So for any tune that John Coltrane wrote himself, the copyright of the improvised solo is Coltrane's (and/or any assignee of the rights) . However the copyright of the improvised solo of My Favourite Things is not.
This is not just the law, but it's the way things have always been don, just look at the author/publishing credits of any jazz record. Nowhere are you likely to see a split.
For Example,I just picked up the forst Coltrane CD form my collection
Track 1: Little Old Lady - Hoagy Carmichael & Stanley Adams; Chappell
Track 2: Village Blues - John Coltrane; Jowcol
These are the composer/publisher details that radio stations etc. use for logging airplays so that royalties get paid appropriately. If Coltrane has any claim to the solo (or any other part of the arrangement) on Little Old lady it would be there.
What this means for transcribers is that any infringement of a copyright is an infringement of the author's copyright, not the improviser's. Generally nobody bothers about such infringements of copyright as either they don't know about them or there is little to gained financially from any such action (until the time that a book of transcriptions suddenly becomes very successful).
Another way to look at it:
If Transcriber A takes down a solo, and transcriber B was to publish it, it is sad but not an infringement of transcriber's A copyright, as he/she does not have a copyright to infringe in the first place.