Good grief...I did a Google search for "The Chime Child" and discovered that *I* had posted, and then forgotten, in 1999, "The Broomsquire's Bird Song"...with midi/ABC transcription. It has some places that 'feel' like bird song.

(Note...there are other mentions of it in Mudcat threads reminding us that the history of the book is in doubt, and that the author may have written, instead of collected, most of the songs. Nevertheless, 'Broomsquires' is a lovely little song.)